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Family curves, torsion subgroup Z/2: record curves

The curves of the family collection with torsion subgroup Z/2, by rank: for each rank the ten smallest conductors, with generators of the Mordell-Weil group and of the torsion subgroup. Every curve has proven rank, is given by its global minimal model, and has rank larger than the generic rank of the family it comes from. Conductors are exact integers; heights are natural logarithms; the naive height is log max(abs(c4)^3, c6^2).

rank curves smallest log N smallest naive height smallest log abs(disc)
10 707,851 56.172623 121.073681 110.410655
11 614,832 65.938322 134.275546 122.394856
12 320,923 74.054696 141.410349 128.305541
13 96,853 85.035191 157.790960 149.299036
14 14,118 95.518922 187.269944 175.739804
15 1,219 101.025835 188.974204 178.606341
16 74 131.965650 231.597131 219.663625
17 1 146.353183 272.250904 256.582739

Rank 10

# a-invariants conductor N log N naive h log abs(disc) torsion generators
1 [1,0,1,-7014056479127717,221483537524540059698900] 2485766715136584389804778 56.172623381 121.073681000 110.41065524 [[170383463/4,-170383467/8]]
2 [1,0,1,-29499173172906148,8316765760147324691627078] 10817942205250900617851910 57.643248303 128.283777000 120.77250614 [[-1001681673/4,1001681669/8]]
3 [1,0,0,-306245784794605070,64040074904742348830845956] 58287634249314930726735678 59.327432197 132.403096000 121.62905738 [[354129852,-177064926]]
4 [0,-1,0,-3908966416437847720,2875119211480731452257216432] 188622615993334511234840880 60.501790510 140.043017000 129.86749488 [[-2274437831,0]]
5 [1,1,0,-79670263216654392,8794677070351063157969340] 368839630407777086661212802 61.172404175 128.395523000 117.47980481 [[-1306023045/4,1306023045/8]]
6 [0,-1,0,-408478237571450680,99125510937918042227099056] 417410406183293374812352656 61.296112157 133.267248000 122.19603204 [[-736884023,0]]
7 [1,0,1,-11139873239497155088,14277824795848257713407032938] 462431203432201179694386570 61.398540028 143.184791000 130.35359657 [[8008801591/4,-8008801595/8]]
8 [1,1,0,-339541249831039300,76131684036776550440582500] 680955709929518222129434350 61.785539499 132.712719000 117.76922534 [[1327273915/4,-1327273915/8]]
9 [1,0,0,-2047211693548203705,1124005177063808706565310841] 851978969154242345159363202 62.009604074 138.102634000 125.54489800 [[863015322,-431507661]]
10 [1,0,0,-4133580926822654595,3063148522585045345660745025] 1118069939084988074572750110 62.281401441 140.210630000 130.48552500 [[-2333699410,1166849705]]
generators for these ten

1. [1,0,1,-7014056479127717,221483537524540059698900] N = 2485766715136584389804778

E = ellinit([1,0,1,-7014056479127717,221483537524540059698900]);
generators:
  [-75590370,565513296979]
  [-1901412,484576305403]
  [-802688489661/9409,407149773618562492/912673]
  [-13342028085/169,1169204415379060/2197]
  [-7882795431/289,3078078791533862/4913]
  [-1610480772/49,221369589080653/343]
  [386510805/16,16458857793535/64]
  [61657592553/1681,8024607878461088/68921]
  [514381463955/47089,3906605042607795772/10218313]
  [127140579684279/2992900,69846704323751412473/5177717000]
torsion generators:
  [170383463/4,-170383467/8]

2. [1,0,1,-29499173172906148,8316765760147324691627078] N = 10817942205250900617851910

E = ellinit([1,0,1,-29499173172906148,8316765760147324691627078]);
generators:
  [29130763,2735337832913]
  [112851499,2534693206115]
  [172231504,2888702716130]
  [459906724,9592824727985]
  [25147710946/25,3945808286721691/125]
  [26821198513/49,4286317835939411/343]
  [30421158913/529,31751877436170379/12167]
  [103423438693951/124609,1036793371170365156275/43986977]
  [2788252446514099/1371241,146775891974810817532385/1605723211]
  [311790935011846561/49729,174098544242564675071780715/11089567]
torsion generators:
  [-1001681673/4,1001681669/8]

3. [1,0,0,-306245784794605070,64040074904742348830845956] N = 58287634249314930726735678

E = ellinit([1,0,0,-306245784794605070,64040074904742348830845956]);
generators:
  [-398130470,11084378779744]
  [282934750,204830623366]
  [383433340,1728400859746]
  [447621052,4079657364514]
  [1236546652,39699401800354]
  [-13851337964/25,997185912343394/125]
  [-7981736/9,216525318370006/27]
  [10924815979/100,5646818916905563/1000]
  [260337695122/529,69378772748445848/12167]
  [59691365402140/157609,96504804645491159242/62570773]
torsion generators:
  [354129852,-177064926]

4. [0,-1,0,-3908966416437847720,2875119211480731452257216432] N = 188622615993334511234840880

E = ellinit([0,-1,0,-3908966416437847720,2875119211480731452257216432]);
generators:
  [878558717,10908335505054]
  [3586143324,187019594796320]
  [68851525844,18058976726161800]
  [-64104617145014/380689,13952609328653665865910/234885113]
  [13881180418921/10609,798152710794543000/1092727]
  [16491463944946/2209,64819609160516174250/103823]
  [47833739116153/49729,25037118280730392848/11089567]
  [227028873825121/235225,136165707416169560844/114084125]
  [2974141203828796/1006009,132170788764257239900800/1009027027]
  [39089448856378308436/40798748169,25302117525815482726837177000/8240816746411803]
torsion generators:
  [-2274437831,0]

5. [1,1,0,-79670263216654392,8794677070351063157969340] N = 368839630407777086661212802

E = ellinit([1,1,0,-79670263216654392,8794677070351063157969340]);
generators:
  [133542924,732629145414]
  [151273098,452002998690]
  [163291434,373044958914]
  [3591693158,214605795358582]
  [8806374839,825986676840964]
  [-1217692388083/6889,2382042771612811050/571787]
  [-1150772978834/6889,2388035041786164668/571787]
  [-29445706380/121,4939436292474150/1331]
  [55797957286/289,3835765425557732/4913]
  [91450124226902/450241,300877330951492466172/302111711]
torsion generators:
  [-1306023045/4,1306023045/8]

6. [0,-1,0,-408478237571450680,99125510937918042227099056] N = 417410406183293374812352656

E = ellinit([0,-1,0,-408478237571450680,99125510937918042227099056]);
generators:
  [7244802,9806454366610]
  [329835785,527397702216]
  [-6519849995/36,2792701233048419/216]
  [8572146181/4,761718622168251/8]
  [12562864834/9,1280366989254298/27]
  [20291033569/25,2173224457960728/125]
  [384222017909/1156,10856648084390163/39304]
  [19540857966865/175561,545727844375071697944/73560059]
  [389302297572508/844561,2299595710411669905048/776151559]
  [1034757783040801/3222025,5968930243967875430124/5783534875]
torsion generators:
  [-736884023,0]

7. [1,0,1,-11139873239497155088,14277824795848257713407032938] N = 462431203432201179694386570

E = ellinit([1,0,1,-11139873239497155088,14277824795848257713407032938]);
generators:
  [1504961749,30352902907805]
  [1849882429,886174908785]
  [4261042804,210178532632910]
  [5315576479,324429874583435]
  [-52882197259799/12166144,5079203807156159808724795/42435510272]
  [747817139494/361,65295290636197190/6859]
  [84174367343236/61009,590287413903769796930/15069223]
  [281238637499341/139129,227748396189348005345/51895117]
  [565974495389011/124609,10536693633737097067945/43986977]
  [22442506363079176/8779369,1302022623582553359182770/26013270347]
torsion generators:
  [8008801591/4,-8008801595/8]

8. [1,1,0,-339541249831039300,76131684036776550440582500] N = 680955709929518222129434350

E = ellinit([1,1,0,-339541249831039300,76131684036776550440582500]);
generators:
  [-658850115,3720884395745]
  [-463964490,11567096589620]
  [84691695,6926921402665]
  [179919344,4567820820530]
  [327582535,238345257520]
  [1370687775/4,1082484888875/8]
  [411451920,2466083861890]
  [7979744894/25,65329696506118/125]
  [44530601665/64,6806369382479315/512]
  [12775074468255/37249,1069049430513881080/7189057]
torsion generators:
  [1327273915/4,-1327273915/8]

9. [1,0,0,-2047211693548203705,1124005177063808706565310841] N = 851978969154242345159363202

E = ellinit([1,0,0,-2047211693548203705,1124005177063808706565310841]);
generators:
  [-1066389862,45765650091059]
  [204085071642/289,27118769385305859/4913]
  [468817507614/529,29180387020301601/12167]
  [598787360438/361,328353153224175221/6859]
  [2647115649066/841,3922283381917361919/24389]
  [11987705269362/25921,69348678056320872579/4173281]
  [40816179708474/52441,17440705419748863015/12008989]
  [78842396618742/113569,233922034025135976747/38272753]
  [485779206992214/931225,12645292277675391907407/898632125]
  [137007560051585994/174108025,1277761429739902497292713/2297355389875]
torsion generators:
  [863015322,-431507661]

10. [1,0,0,-4133580926822654595,3063148522585045345660745025] N = 1118069939084988074572750110

E = ellinit([1,0,0,-4133580926822654595,3063148522585045345660745025]);
generators:
  [-1760720850,69877580250345]
  [918538590,6424336899705]
  [1972187340,50810630499705]
  [10811275950,1105451814661545]
  [-227853185683170/100489,888668876803392237165/31855013]
  [68235495510/289,225159343218250665/4913]
  [3522605299320/961,5742968301139544175/29791]
  [15105447989840/10201,14169059474220066205/1030301]
  [66284265565290/34969,295231842664409620515/6539203]
  [172839733152510/332929,6245781194457035205465/192100033]
torsion generators:
  [-2333699410,1166849705]

Rank 11

# a-invariants conductor N log N naive h log abs(disc) torsion generators
1 [0,-1,0,-11946911268550493608,15893653014210611705201601712] 43316108595835552276361984400 65.938322100 143.394616000 125.71123381 [[1988642617,0]]
2 [1,0,1,-8935444839098988438628,325066122267677796797923301076998] 498653576436666580377542225670 68.381709130 163.246542000 147.42871288 [[220224282871/4,-220224282875/8]]
3 [1,1,0,-1576373756450214922,759926798530798069794077800] 672519215577201888821790774558 68.680828195 137.318579000 124.54394536 [[3015936475/4,-3015936475/8]]
4 [1,1,0,-628194012441407122,175424217648985174555974640] 686044836958354728450143389446 68.700740496 134.558479000 125.28410686 [[-3625940645/4,3625940645/8]]
5 [1,1,0,-10890191097078268972,13664254157182253537901636340] 1758821889262453385218180898874 69.642196994 143.116786000 131.93989013 [[8297469755/4,-8297469755/8]]
6 [1,0,0,-5572586182117973719,443264061932761831373441736809] 2355694911715481929719037783146 69.934388553 150.051072000 142.59622146 [[-7868207018,3934103509]]
7 [1,0,0,-13799859692500506680,19254614592101304671643180096] 2681265063185100898944986344566 70.063841511 143.827173000 133.33074884 [[2411520112,-1205760056]]
8 [1,0,0,-24194951415416541970,47127484848391869821967941636] 4306646989411129903500146530806 70.537712430 145.568453000 135.21764698 [[-5697893308,2848946654]]
9 [1,0,1,-64954321782232905188,199567246029562063472807719982] 4666956724488780574610050527762 70.618059984 148.474251000 137.05750531 [[17106259703/4,-17106259707/8]]
10 [1,-1,1,-923688794862317894717,10764868390432162818440919471109] 5886315249990041930455188423990 70.850182997 156.438324000 144.08657409 [[16663184623,-8331592312]]
generators for these ten

1. [0,-1,0,-11946911268550493608,15893653014210611705201601712] N = 43316108595835552276361984400

E = ellinit([0,-1,0,-11946911268550493608,15893653014210611705201601712]);
generators:
  [1615407172,28460446799400]
  [1939993962,4246541094950]
  [2002794953,160455647484]
  [4177832092,197237214939600]
  [8428679196,716932725701392]
  [277975518892,146546823407014800]
  [7359598258/9,2205269635129550/27]
  [48131888314/25,672549719058162/125]
  [422519133212/961,3085345472821894800/29791]
  [1147353037924/529,165399112248905304/12167]
  [23799337064332/11881,308083882692366000/1295029]
torsion generators:
  [1988642617,0]

2. [1,0,1,-8935444839098988438628,325066122267677796797923301076998] N = 498653576436666580377542225670

E = ellinit([1,0,1,-8935444839098988438628,325066122267677796797923301076998]);
generators:
  [90849893599,16221235778859725]
  [-13297486649964311/175561,1752102709239385668748375/73560059]
  [1384678995481/25,33180825114705781/125]
  [5636785329979/121,4189010028203017225/1331]
  [26050808170561/289,77999130572462486725/4913]
  [272681396989564/5041,3823877038545377455/357911]
  [630646071597559/7225,8902764273781351788953/614125]
  [25057580156841469/712336,4429196406502496956099295/601211584]
  [21212032149651664/72361,2945345560626496493355850/19465109]
  [69398666062871364/185761,17746017088081257746357375/80062991]
  [251739970325161208194/439279681,3942967583352781096634701345625/9206862834079]
torsion generators:
  [220224282871/4,-220224282875/8]

3. [1,1,0,-1576373756450214922,759926798530798069794077800] N = 672519215577201888821790774558

E = ellinit([1,1,0,-1576373756450214922,759926798530798069794077800]);
generators:
  [-1421837642,11263734044692]
  [-1036404363,35783898016732]
  [408741102754,261318455289453262]
  [-96556513372113/73441,470921814710516251681/19902511]
  [-46070557043/144,60640894748153695/1728]
  [145837229314/169,14273443950074278/2197]
  [941823615477/1369,51833408920992100/50653]
  [3191540073454/3721,1414559400681173902/226981]
  [9855074830156/11881,6219678376863383776/1295029]
  [12672084477346/3481,42718516724929271936/205379]
  [54838010696629/70225,42145142761670670103/18609625]
torsion generators:
  [3015936475/4,-3015936475/8]

4. [1,1,0,-628194012441407122,175424217648985174555974640] N = 686044836958354728450143389446

E = ellinit([1,1,0,-628194012441407122,175424217648985174555974640]);
generators:
  [-1482167189/4,151224869583521/8]
  [321243547,2602232340742]
  [342655102,634125949546]
  [621800606,5021969024810]
  [634992070,5706194944000]
  [-1552757380843097/15342889,927079705887704426814251/60098096213]
  [-322025129766/1369,892098157001095042/50653]
  [8213282257/9,513810198946984/27]
  [8620679761/49,2876881576926601/343]
  [26937795382/81,1322221417754768/729]
  [21081992078679/62500,21569076167632305967/15625000]
torsion generators:
  [-3625940645/4,3625940645/8]

5. [1,1,0,-10890191097078268972,13664254157182253537901636340] N = 1758821889262453385218180898874

E = ellinit([1,1,0,-10890191097078268972,13664254157182253537901636340]);
generators:
  [-3464888264,98996703655114]
  [-2136223080,164863394160730]
  [1454569048,30020172774010]
  [194958535704,86069853692658254]
  [-4415185658936/2809,24416960399789032298/148877]
  [19035807246/25,9530801636606804/125]
  [805350423047/484,130643297899744265/10648]
  [1981108094520/1681,3423009335010014030/68921]
  [5605289921443/3249,618664844481406841/185193]
  [104148391583314/36481,532570967508362362292/6967871]
  [755063997469576/2809,20746395243403910625614/148877]
torsion generators:
  [8297469755/4,-8297469755/8]

6. [1,0,0,-5572586182117973719,443264061932761831373441736809] N = 2355694911715481929719037783146

E = ellinit([1,0,0,-5572586182117973719,443264061932761831373441736809]);
generators:
  [-7844380666,65418087507317]
  [61147647887/4,15860269155571273/8]
  [30679895894,5399052557203157]
  [60656141270,14942170130125013]
  [-98733789549706/14161,637662179867025215923/1685159]
  [-882108559786/2401,78504775673157189413/117649]
  [-385088931610/361,4590897181431263783/6859]
  [-180115082194/25,41354102929278889/125]
  [22601649254/25,82817985896384257/125]
  [67634849354/49,227054884423953851/343]
  [39273366634952/17161,1495437380966100961999/2248091]
torsion generators:
  [-7868207018,3934103509]

7. [1,0,0,-13799859692500506680,19254614592101304671643180096] N = 2681265063185100898944986344566

E = ellinit([1,0,0,-13799859692500506680,19254614592101304671643180096]);
generators:
  [-3961591856,108399267259240]
  [1649520112,31298937887944]
  [1696426840,26948140515616]
  [2422224880,6312616273096]
  [6244160848,420167152299208]
  [11010085480,1096343603006224]
  [-472162943034/7921,99889423559536089942/704969]
  [-17928090704/25,21206628235490216/125]
  [7150920046992/2209,9574875102792550104/103823]
  [404099797175176/14161,8057552424115565494544/1685159]
  [1412127997173832/2209,53064430390721141243384/103823]
torsion generators:
  [2411520112,-1205760056]

8. [1,0,0,-24194951415416541970,47127484848391869821967941636] N = 4306646989411129903500146530806

E = ellinit([1,0,0,-24194951415416541970,47127484848391869821967941636]);
generators:
  [-3715015612,292815637613534]
  [3540769444,76480499207710]
  [3906269348,110546761117214]
  [4209639980,140975799852566]
  [-2588450969860/529,2675746790296463338/12167]
  [305043854036/289,741279586310470510/4913]
  [3529674681284/1369,2199280906752582854/50653]
  [4285055044004/3025,20844384138890027282/166375]
  [12275913839000/3721,12866547580007625686/226981]
  [82081035320900/32041,253758785167343439466/5735339]
  [419415274575092/113569,3453462180110638954574/38272753]
torsion generators:
  [-5697893308,2848946654]

9. [1,0,1,-64954321782232905188,199567246029562063472807719982] N = 4666956724488780574610050527762

E = ellinit([1,0,1,-64954321782232905188,199567246029562063472807719982]);
generators:
  [3528496734,119609851203307]
  [3765847551,91458192192535]
  [3961540851,66478844139535]
  [5062747380,22026600925273]
  [8166393654,462317620470598]
  [64753622751,16355625049680535]
  [130785113526/25,6772625762357159/125]
  [693716970171/169,100808867392169851/2197]
  [1426294478634/625,3928715678542954798/15625]
  [1696974680523/289,705473325259183733/4913]
  [1913202219615/2809,58734329981811151787/148877]
torsion generators:
  [17106259703/4,-17106259707/8]

10. [1,-1,1,-923688794862317894717,10764868390432162818440919471109] N = 5886315249990041930455188423990

E = ellinit([1,-1,1,-923688794862317894717,10764868390432162818440919471109]);
generators:
  [16244391523,216047782525268]
  [4090842570317,8273839481484232316]
  [1286969737951/49,737464755847846424/343]
  [4523630624713/289,1849142687313192058/4913]
  [24061254722023/1444,269009754102367777/54872]
  [26136466023487/361,123346606030661657144/6859]
  [44338184421143/1849,123271252270969799512/79507]
  [62189962163617/2401,241598935616828256284/117649]
  [113151160856183/2809,928763151675324621032/148877]
  [890818534926913/54289,2050864523708319788092/12649337]
  [2171121413645483/1849,101130437888598927709912/79507]
torsion generators:
  [16663184623,-8331592312]

Rank 12

# a-invariants conductor N log N naive h log abs(disc) torsion generators
1 [1,0,1,-6166000806909576551,5882858220756238497524991998] 145059433532653065217081920420450 74.054696335 141.410349000 128.30554070 [[5536995783/4,-5536995787/8]]
2 [1,-1,0,-106891136267469572664,422858173212173751446470249404] 2521187658201578085610417610020422 76.910038152 149.968631000 138.06975170 [[22364143491/4,-22364143491/8]]
3 [1,1,1,-6893400811406274474520,293410482046238687449751456975321] 3070143408623089579456273867631802 77.107032342 163.041396000 154.75725848 [[-99246124155,49623062077]]
4 [1,-1,1,-233636783676286373627,894153434637738073293054084075] 3744534523427843486091406117969518 77.305605385 152.314501000 144.30959153 [[-16925310901,8462655450]]
5 [1,1,1,-1621798311910830552290,24644776741169831070627868749551] 5823102912675542002999614449352786 77.747141335 158.127071000 147.42590598 [[25863435385,-12931717693]]
6 [0,1,0,-22546842745086570220760,143033305149276646344856595782381908] 11537416688626259646150573805118160 78.430903448 175.419917000 167.96511373 [[-537340177773,0]]
7 [1,-1,1,-12090879806196036593705,511520847322406944394817377336297] 56919847097224919772703369225430550 80.026952156 164.153818000 149.55571984 [[62451432519,-31225716260]]
8 [0,1,0,-480041640930470559338200,131913819933085547066311488422279348] 69124330894680935061847174333300560 80.221214849 175.258059000 164.95970483 [[-802728719309,0]]
9 [1,1,0,-3675056362010790890172,85383903655263236884036244026884] 119800842028802930650603533023243310 80.771138783 160.581169000 148.36650421 [[147424828987/4,-147424828987/8]]
10 [1,0,0,-143579084753628471275,547663613975314117128331400241] 137218907269704557279238053943454386 80.906885583 150.853856000 142.24711353 [[4412887102,-2206443551]]
generators for these ten

1. [1,0,1,-6166000806909576551,5882858220756238497524991998] N = 145059433532653065217081920420450

E = ellinit([1,0,1,-6166000806909576551,5882858220756238497524991998]);
generators:
  [-11463097657/4,33560084995653/8]
  [-5284941717/4,866193811757963/8]
  [1047798917,23926227272766]
  [1234834062,12318639748156]
  [1383255792,646457287141]
  [4732653327,287579480754286]
  [23948824317/16,169704240868009/64]
  [13077417273/49,22377249845745598/343]
  [3023258161407/2209,285063488160582662/103823]
  [58763925544302/22801,290312431099631267236/3442951]
  [61438850069104508/40921609,813878614377003895676838/261775532773]
  [599507739526216983/64850809,448915061488365584221885462/522243564877]
torsion generators:
  [5536995783/4,-5536995787/8]

2. [1,-1,0,-106891136267469572664,422858173212173751446470249404] N = 2521187658201578085610417610020422

E = ellinit([1,-1,0,-106891136267469572664,422858173212173751446470249404]);
generators:
  [-547226705029308/49729,5725869786720358335030/11089567]
  [8681998641555/1369,294914630133175899/50653]
  [61034424381507/6241,275760471270464934762/493039]
  [442964639418780/57121,3352100279963233675722/13651919]
  [4085055012798975/139129,246690479062815476918466/51895117]
  [5274024958408350/822649,24490487888777065759014/746142643]
  [31421875589512131/8994001,8183945225246681004875025/26973008999]
  [513064421771629197/125193721,324392402642237420477201592/1400792544269]
  [863782513743488985/8404201,798882495966038615435506188/24363778699]
  [1286312806628622219/293471161,987086543871613227459052098/5027454459091]
  [9981033972422058990/1514999929,3996344551337697480805294326/58968342236467]
  [150154328453348563542/9781803409,1498480740977184729440699777424/967449702560327]
torsion generators:
  [22364143491/4,-22364143491/8]

3. [1,1,1,-6893400811406274474520,293410482046238687449751456975321] N = 3070143408623089579456273867631802

E = ellinit([1,1,1,-6893400811406274474520,293410482046238687449751456975321]);
generators:
  [-84867688443,16345557587117629]
  [-5827045413,18258721035400489]
  [16029634949,13675904580124221]
  [51262821509,8645648983727421]
  [65732989595,11149291936135227]
  [105591943477,27254983549905469]
  [225843029509,101270437519963069]
  [26276840364421,134696871007753207357]
  [-1013894745434067/11881,20890072987733879312641/1295029]
  [552627568117/9,272210522708937559/27]
  [2614227240509/25,3344776913107437513/125]
  [2636136431659/25,3397956436869362117/125]
torsion generators:
  [-99246124155,49623062077]

4. [1,-1,1,-233636783676286373627,894153434637738073293054084075] N = 3744534523427843486091406117969518

E = ellinit([1,-1,1,-233636783676286373627,894153434637738073293054084075]);
generators:
  [-8894264653,1506183000190362]
  [-4166105965,1339852921415634]
  [37038417131,6561350226610266]
  [63889280027,15708344574285450]
  [503428604555,357032521890142554]
  [-107391107628757/9409,1314358402215245342106/912673]
  [-1483401773317/121,1842313037670777942/1331]
  [-1245788111905/169,3270402467580976038/2197]
  [-148758444221/9,13234350457065854/27]
  [-12921500693/9,29903436912618814/27]
  [14005285583675/529,44314556597849383350/12167]
  [25606842889349/1225,97244474520121145412/42875]
torsion generators:
  [-16925310901,8462655450]

5. [1,1,1,-1621798311910830552290,24644776741169831070627868749551] N = 5823102912675542002999614449352786

E = ellinit([1,1,1,-1621798311910830552290,24644776741169831070627868749551]);
generators:
  [-45953609519,1459630107017771]
  [-43086734727,3812328161487427]
  [11190585661,2810206492805987]
  [11243676297,2798427858983203]
  [15128525969,1889928775149059]
  [26571554049,558425733441979]
  [26970535049,722924255973971]
  [130623884789,45183805517420039]
  [365819895657,219970069911133219]
  [259430756265/289,23658853853056453091/4913]
  [30581525469447/1849,121764821153031601813/79507]
  [454463771709241/29929,9713449321425190752607/5177717]
torsion generators:
  [25863435385,-12931717693]

6. [0,1,0,-22546842745086570220760,143033305149276646344856595782381908] N = 11537416688626259646150573805118160

E = ellinit([0,1,0,-22546842745086570220760,143033305149276646344856595782381908]);
generators:
  [104903799646,376593284277452880]
  [-270698040591600463634/672313041,5137014128691421509481810751120/17432404840089]
  [-30943077278197049684/129709321,542449701074924114594899355370/1477259456869]
  [-26667086420967130658/57592921,101757046409328853507865226480/437072677469]
  [-4527259607401088189/18190225,28317511515842396816420154384/77581309625]
  [-49786524092343641/97969,4675711847224476841663650/30664297]
  [-13920530530152074/25921,66747725285940548067240/4173281]
  [2878265104830937/1024,154694088218828092949091/32768]
  [20054677157801854/49,2840033637034625535870960/343]
  [28208602212434254/12769,4758191317875770685670320/1442897]
  [1272178773606290854/17530969,27638550757058300754571838280/73402167203]
  [10362707801212530784324/352425529,1054885779006612965798891473557270/6616084455917]
torsion generators:
  [-537340177773,0]

7. [1,-1,1,-12090879806196036593705,511520847322406944394817377336297] N = 56919847097224919772703369225430550

E = ellinit([1,-1,1,-12090879806196036593705,511520847322406944394817377336297]);
generators:
  [-118345679961,16879340957446780]
  [-79343733081,31166586323049340]
  [64600061199,190162520199100]
  [314646184975/4,54939819428980503/8]
  [109603596919,22427145005413740]
  [3922436621775,7765419467183950708]
  [19134343882119,83697629356294720540]
  [897797094045/16,199821355888084417/64]
  [81562686136431/1369,82367876743141552300/50653]
  [2618903507450119/40401,3051615675794746887740/8120601]
  [6019899295879239/961,467000435812568684457700/29791]
  [14148520112773131/139129,947886785645085394528960/51895117]
torsion generators:
  [62451432519,-31225716260]

8. [0,1,0,-480041640930470559338200,131913819933085547066311488422279348] N = 69124330894680935061847174333300560

E = ellinit([0,1,0,-480041640930470559338200,131913819933085547066311488422279348]);
generators:
  [-159551100958874581/243049,48546879157435478896128360/119823157]
  [-162125895488086/289,2328698176827552527340/4913]
  [3181226250521/256,1453649695986269887875/4096]
  [32843652813554/289,1379379811777235078580/4913]
  [84804353375324/289,627586481562494973750/4913]
  [138003489823826/361,448155124852551847500/6859]
  [392589430692041/26896,1558942478161206668321715/4410944]
  [703863333332314/729,14840867934024079528700/19683]
  [4025429905131811/12321,136433005229483592206500/1367631]
  [38339550675499964/5329,7473514676530334595644250/389017]
  [85082490381318551/961,24816871526112046513959750/29791]
  [96871602423855866/358801,31870067063198363381302500/214921799]
torsion generators:
  [-802728719309,0]

9. [1,1,0,-3675056362010790890172,85383903655263236884036244026884] N = 119800842028802930650603533023243310

E = ellinit([1,1,0,-3675056362010790890172,85383903655263236884036244026884]);
generators:
  [-41730826501,12887006528882833]
  [-36833652195,13068177238320153]
  [-19664019472,12249365941788486]
  [147632078271/4,1159886194638879/8]
  [39775463078,1461177051080236]
  [320373812923,178300040635238836]
  [16642561851728,67893365766166612986]
  [242171862286843/4356,2091067425875587584181/287496]
  [68217567030722/1849,9865792208741808652/79507]
  [169257508981392/2809,1353976154484666291102/148877]
  [2658666323810493/80656,5575974238401810544869/22906304]
  [12554593129310275623/1093691041,241849207692491970063314420271/36169456416911]
torsion generators:
  [147424828987/4,-147424828987/8]

10. [1,0,0,-143579084753628471275,547663613975314117128331400241] N = 137218907269704557279238053943454386

E = ellinit([1,0,0,-143579084753628471275,547663613975314117128331400241]);
generators:
  [-12966910010,478728368841001]
  [-1932171596,904362449160001]
  [4109006008,164535064252159]
  [1145148392539/100,636529719114170743/1000]
  [3082293699844/49,5318381829154805293/343]
  [3317595261238/361,451047956566054531/6859]
  [88553883201262/1681,813075264701119444649/68921]
  [446623456275988/22201,7967107123762367800301/3307949]
  [615517713312622/146689,7759431529462483455551/56181887]
  [1476724990371934/431649,88097537883259377427249/283593393]
  [41228200751714686/3845521,3699247882279755030810521/7541066681]
  [49703021091613150/4464769,5410331904462770759188513/9434056897]
torsion generators:
  [4412887102,-2206443551]

Rank 13

# a-invariants conductor N log N naive h log abs(disc) torsion generators
1 [1,0,0,-1449906033237470410635,17073586021555823773300048810225] 8517544174435024143004460515381044430 85.035191405 157.790960000 149.29903623 [[-42978640130,21489320065]]
2 [1,1,1,-817732582601069158567499815,9294691321682809931409995675785428600797] 142345695678637990158711155259549347070 87.851321923 197.583670000 187.35328486 [[-33139203043509,16569601521754]]
3 [1,1,1,-78799314921090126336635,8509215482293751203148041509575561] 455514655953569565656462935595492873046 89.014491239 169.777177000 155.52355747 [[158934200115,-79467100058]]
4 [1,0,1,-26584447235992210259588,1883021637908148057017778972149102] 551664926630833203374698683114972985506 89.206004193 166.759517000 157.76768960 [[-763651246857/4,763651246853/8]]
5 [1,1,1,-419672873567864790074815,104614921796713109015272026649125797] 1284522297763555835148164816047706661990 90.051205523 174.794890000 159.84591892 [[368914963707,-184457481854]]
6 [1,-1,0,-17803752379518557867553819,28715279586360864633133293861598588569] 3876086637366268034930325790341578339682 91.155644673 186.037957000 174.29516270 [[9076333397331/4,-9076333397331/8]]
7 [1,1,1,-2233443137462509978628350,1284661641797067684243151033873099067] 4727844089153187242364522073324833073890 91.354287930 179.810363000 163.14488220 [[857847762737,-428923881369]]
8 [1,0,0,-3774568349934480475073365,2809826711276838077079501611286373601] 6459246194228230642493258817227938296774 91.666331250 181.384588000 169.22254942 [[1059507223442,-529753611721]]
9 [1,1,0,-20511201738925605387733302,35145307775672090738931920931846257040] 7883356805482701562636987661831032795698 91.865572430 186.462643000 175.62075233 [[9323361020955/4,-9323361020955/8]]
10 [1,0,1,-1783056570632975776524426,911992231539582131905632900888890248] 8439784420249846645897414985383540399350 91.933775392 179.134717000 167.03873200 [[2907003855383/4,-2907003855387/8]]
generators for these ten

1. [1,0,0,-1449906033237470410635,17073586021555823773300048810225] N = 8517544174435024143004460515381044430

E = ellinit([1,0,0,-1449906033237470410635,17073586021555823773300048810225]);
generators:
  [642998256463902,16304770252901039521441]
  [-1082604861778690/26569,12626439696697732579755/4330747]
  [-1028345520020370/24649,8609367015441893855045/3869893]
  [-36302761587770/8649,3864715856739211216405/804357]
  [774552365845/16,497106550180425535/64]
  [19379923473630/2809,404954673922084296605/148877]
  [52091107629310/9,375955046155281021115/27]
  [2402155348381470/196249,93641309059065339504355/86938307]
  [71270177161463070/1739761,11796061363856241089249335/2294744759]
  [158193677749124270/5248681,10432987622587004418638315/12024728171]
  [2237332065773628670/69239041,1146781850352455313960446465/576138060161]
  [3783959112265361330/344213809,10022791775877118878197219505/6386198798377]
  [1061577159127196192270/29580216121,17072488116289920360218086341485/5087471790434669]
torsion generators:
  [-42978640130,21489320065]

2. [1,1,1,-817732582601069158567499815,9294691321682809931409995675785428600797] N = 142345695678637990158711155259549347070

E = ellinit([1,1,1,-817732582601069158567499815,9294691321682809931409995675785428600797]);
generators:
  [-32125316545493,49093064295994145946]
  [-30680015895133,74194116435422433906]
  [-20131942379573,132656931772193654106]
  [16993362554837,17490350397031078386]
  [18259099096907,21239527677838304346]
  [107582018835707,1080029531343693169146]
  [333358188622243/9,4662694715294001126782/27]
  [20322673562771603/1369,1046592310395283200252978/50653]
  [21833417777310437/841,1819045154717885721773994/24389]
  [1200179143607378467/84681,578941653401145215323435966/24642171]
  [3389457379306819627/40401,5918480260584382539640401466/8120601]
  [3903463771915938323/458329,16847399168896210707668929458/310288733]
  [4884479909441928667/269361,2895810411952166941768109974/139798359]
torsion generators:
  [-33139203043509,16569601521754]

3. [1,1,1,-78799314921090126336635,8509215482293751203148041509575561] N = 455514655953569565656462935595492873046

E = ellinit([1,1,1,-78799314921090126336635,8509215482293751203148041509575561]);
generators:
  [136975485403,16900049119712534]
  [-21342102184229/121,173135843458133284306/1331]
  [-15783081350461/49,7453908939379158698/343]
  [12809124036063/169,119774482860609802438/2197]
  [160221606163411/225,1889657427228542709946/3375]
  [5860864089980091/37249,17620391238430943288302/7189057]
  [5875730590422265/136161,3619324592691474753612928/50243409]
  [10835622926510413/69169,55622798740791208173538/18191447]
  [11776358776075347/52441,555310088664689933554822/12008989]
  [108022578708368691/410881,20339919858737708931107942/263374721]
  [304675932725825699/5329,168171334476281740427089654/389017]
  [2908388942949335179/19193161,582928367452960545245988734/84085238341]
  [4015906108044053039/23863225,440791490872502887069780642/116571854125]
torsion generators:
  [158934200115,-79467100058]

4. [1,0,1,-26584447235992210259588,1883021637908148057017778972149102] N = 551664926630833203374698683114972985506

E = ellinit([1,0,1,-26584447235992210259588,1883021637908148057017778972149102]);
generators:
  [-183830241354,23617228343695558]
  [-164268709683,42630508966552441]
  [-27740385429,50981750012106133]
  [601674726,43209103667138278]
  [23241539760,35745093131163493]
  [25080144429,35100637236226177]
  [62530420215,21568053176674081]
  [-124140812528490/5041,17976836370414805133573/357911]
  [838667783619/49,12984370708861759339/343]
  [214961515825449/256,3096789656852165404867/4096]
  [1486146486122229/784,57087395558460140154721/21952]
  [519209165870076/961,11353025978269864997758/29791]
  [3043703389005759/44521,184343767087289987445037/9393931]
torsion generators:
  [-763651246857/4,763651246853/8]

5. [1,1,1,-419672873567864790074815,104614921796713109015272026649125797] N = 1284522297763555835148164816047706661990

E = ellinit([1,1,1,-419672873567864790074815,104614921796713109015272026649125797]);
generators:
  [-739980079813,99866341560850626]
  [-695453973793,245188933397930646]
  [-418062552343,454969449064279746]
  [1447210593203/4,93482152657207293/8]
  [363278237755,9955746927195138]
  [379103896907,150947988673746]
  [510021524027,152448159655536066]
  [3224138878843/9,423856368128490862/27]
  [391552054771267/81,7681631728225505255434/729]
  [2488609601429275/6241,12784130083356131744862/493039]
  [3394068702935107/10201,43886305603604409781946/1030301]
  [7481805254580955/22201,126295256399581434059762/3307949]
  [15899482391642627/44521,158979692904498319859766/9393931]
torsion generators:
  [368914963707,-184457481854]

6. [1,-1,0,-17803752379518557867553819,28715279586360864633133293861598588569] N = 3876086637366268034930325790341578339682

E = ellinit([1,-1,0,-17803752379518557867553819,28715279586360864633133293861598588569]);
generators:
  [-1076651077572,6829032608831654487]
  [11318545558755/4,7974290393657163009/8]
  [-4301248407006018384/1739761,17418933533156642678060777565/2294744759]
  [3128674627403902/1089,40643228340651059923219/35937]
  [83589561806361091/32041,888521435043077419306150/5735339]
  [259305413708325828/96721,15149985945061465510861947/30080231]
  [1872160404339860316/844561,292425113131314370032803265/776151559]
  [3342884970018917952/1481089,308874941987764916783675781/1802485313]
  [26227556237596681593/9935104,10515977561076493790327039109/31315447808]
  [42756686683042951704/305809,279454090497309163640210388843/169112377]
  [24821885936483765859054/9470987761,219101533778879022524480184533757/921707057912759]
  [4252829305029252571822833/828449476864,6424945327427893609138349556472579935/754048086245797888]
  [66716939374470277815027870/13467630209929,389446461078915200895079087270129979661/49423872970413112283]
torsion generators:
  [9076333397331/4,-9076333397331/8]

7. [1,1,1,-2233443137462509978628350,1284661641797067684243151033873099067] N = 4727844089153187242364522073324833073890

E = ellinit([1,1,1,-2233443137462509978628350,1284661641797067684243151033873099067]);
generators:
  [687338878081,272492043388008439]
  [21229970350429/25,2544684142448317707/125]
  [386927342527553/169,6280676492043502907307/2197]
  [5633363932579399/2500,346713310624922814953543/125000]
  [2803249447065677/3721,39081404832335237746911/226981]
  [47971476783289313/1849,10489841187564900282121317/79507]
  [249116594818249537/295936,5272091639071999653163089/160989184]
  [100015629166146257/185761,39077798457395830604032521/80062991]
  [219989228467453713/253009,907442994906831242546657/127263527]
  [5267458373834531653/5702544,1344779496492646914221576357/13617675072]
  [46836268035080939297/20620681,263677764288235396834038730851/93638512421]
  [944835068501362582769/721298449,15088653590067345731771820827487/19371912444793]
  [61054029734173106113972927/69575800946521,12939851165238985627825574087329833911/580346436188931376931]
torsion generators:
  [857847762737,-428923881369]

8. [1,0,0,-3774568349934480475073365,2809826711276838077079501611286373601] N = 6459246194228230642493258817227938296774

E = ellinit([1,0,0,-3774568349934480475073365,2809826711276838077079501611286373601]);
generators:
  [1014752925854,156483898644902495]
  [34523758544642,202536440689679320919]
  [-867213616038493913230/6721212289,1000182407461642646503497265445257/551025147089087]
  [-355246331052526/169,2651023809373015309091/2197]
  [4661272303085/16,84298207400291671691/64]
  [148237214252690/169,916035382545104689187/2197]
  [1922971750978946/1849,7599538929241698743957/79507]
  [3690221771181602/4489,154077770362658339361677/300763]
  [5640026032448750/4489,67753537754697155332913/300763]
  [121790282802349127/1865956,4081211315374761298504859999/2548895896]
  [564727107314358722/80089,409721446316434276101123653/22665187]
  [6082855170462966530/5755201,451410087400814316790526089/13806727199]
  [8214730547653753394/6661561,2998833810720690936578856395/17193488941]
torsion generators:
  [1059507223442,-529753611721]

9. [1,1,0,-20511201738925605387733302,35145307775672090738931920931846257040] N = 7883356805482701562636987661831032795698

E = ellinit([1,1,0,-20511201738925605387733302,35145307775672090738931920931846257040]);
generators:
  [-4834471923877,4616742029859463747]
  [-3103847488392,8301018896815947600]
  [-2743594495017,8412363680229257475]
  [2287476579542,442432694984022886]
  [4724529731194,6610338738036106294]
  [-204385211141695860480/40081561,678321126361532455911950625660/253756362691]
  [671484838665558/289,870559406535213326598/4913]
  [1931357096810395/841,9535700990015601529295/24389]
  [27765330170692206/8281,1519587194001567434452164/753571]
  [52959941001179679/6889,10415248690604952228268065/571787]
  [976203655678525454/80089,905492886824333673738232740/22665187]
  [5955969820397661529/2839225,5557036615930643112387830588/4784094125]
  [3760252251513634551387/3829849,230579583668937048385982000661186/7495014493]
torsion generators:
  [9323361020955/4,-9323361020955/8]

10. [1,0,1,-1783056570632975776524426,911992231539582131905632900888890248] N = 8439784420249846645897414985383540399350

E = ellinit([1,0,1,-1783056570632975776524426,911992231539582131905632900888890248]);
generators:
  [8119353563854472/8281,245710470036250225473501/753571]
  [22345560188201842/5041,3203437138841735805141916/357911]
  [119770019502032761/168921,4498130932111221956361221/69426531]
  [492916406665745837/45212176,287210552011371306190603674219/304006671424]
  [221271228011815193/1682209,1798823941637074726316605203/2181825073]
  [364339753024353118/514089,24131398865190640331576153/368601813]
  [709716263806064177/2374681,2331084502687810331513128911/3659383421]
  [1147378501967407823/1408969,4432298705691490707950373/1672446203]
  [1164587899828895507/1615441,72122590594829151075683421/2053225511]
  [1738234249758477647/410881,2189067335701513868463549801/263374721]
  [2636347268330583932/94249,4275801588297779569827693777/28934443]
  [4540153361068885817/6255001,210997718655854066048130891/15643757501]
  [58893257167722009851/28462225,374467279919124199582227992871/151845970375]
torsion generators:
  [2907003855383/4,-2907003855387/8]

Rank 14

# a-invariants conductor N log N naive h log abs(disc) torsion generators
1 [1,0,0,-39211499476584808467394120940,1333820595356270317012457647091674096534416] 304327139592757069203804262254572708025894 95.518921867 209.129906000 201.45305954 [[-213229518501288,106614759250644]]
2 [1,0,1,-9401745906324336774583921258,348880727126591652241550711849023093044968] 4858903795077400145101018027817292162914370 98.289386762 204.845682000 192.91450186 [[237594575940631/4,-237594575940635/8]]
3 [1,0,0,-26844785415316950775425605,53078430978883527280513999906842557121] 52730095526316529723237209878616107447931486 100.673760271 187.269944000 175.73980379 [[2762872651762,-1381436325881]]
4 [1,1,1,-86374399929534275305324462913,9855469784322937076113338981697664456740031] 84518160226589403767572961475020918466832050 101.145540331 211.516347000 199.99462128 [[-339687689313665,169843844656832]]
5 [0,0,0,-78907404335076126358349007,244810445251631987769046702357699521106] 85468703986756648905003803597594316557982840 101.156724179 190.504555000 181.31597209 [[3795351025526,0]]
6 [1,0,1,-47150895435824082237969612348,3920522858450780250277322153420722026062878] 105313271826844476571278144767156849073593310 101.365513355 209.683055000 197.64865520 [[530551022837111/4,-530551022837115/8]]
7 [1,1,1,-8681332614227516477562299230,321488738143298625656711550300073291382171] 197360698876438380985679121710016580862432238 101.993606919 204.670708000 194.43811329 [[-107975693093455,53987846546727]]
8 [1,-1,1,-29987048533957114353134099931767,60838154561872193400955653963549381347129690959] 600960580937885755418479715464629443672290830 103.107103249 229.048558000 218.98309992 [[-6296737413667133,3148368706833566]]
9 [1,0,1,-20295837335427080962077761258,1107062187939803015835794294312352453954968] 789775713498323533692179524392094706920655310 103.380322904 207.154243000 195.14073389 [[348284247742487/4,-348284247742491/8]]
10 [1,1,1,-5089841477845778701914393659,139742554070973196205444450874019523701961] 1346259072323476202308604032530420986710202358 103.913658873 203.004736000 187.58989596 [[40744813067955,-20372406533978]]
generators for these ten

1. [1,0,0,-39211499476584808467394120940,1333820595356270317012457647091674096534416] N = 304327139592757069203804262254572708025894

E = ellinit([1,0,0,-39211499476584808467394120940,1333820595356270317012457647091674096534416]);
generators:
  [-140148145316424,2019039286251875890548]
  [-88388380975496,2027098167770009382580]
  [-45657438921416,1740384940487610288340]
  [193670307863788,1001967849743938185808]
  [343197786067584,5319772008421981751340]
  [468438060110314,9260507332124504125600]
  [-59165253291925920440/310249,236703185193410889964315457012/172808693]
  [-3416617957242374696/16129,751779883704445153311203884/2048383]
  [-60909623840426774/2209,160642428552230359217487200/103823]
  [7323866022345208/9,608732888150654179554908/27]
  [49874703145357720/9,11131270753803727089307612/27]
  [627856720037590456/2209,376493476293568849383245420/103823]
  [2188654843421713240/97969,20999435586510301866132657652/30664297]
  [1434431601418880101912/48288601,148269382800394110235857704372356/335557488349]
torsion generators:
  [-213229518501288,106614759250644]

2. [1,0,1,-9401745906324336774583921258,348880727126591652241550711849023093044968] N = 4858903795077400145101018027817292162914370

E = ellinit([1,0,1,-9401745906324336774583921258,348880727126591652241550711849023093044968]);
generators:
  [-6676247798144744711/63001,6229025367045041504342558005/15813251]
  [-72214492395752789/6724,369299250156721340786162915/551368]
  [-1167627466509864/49,256536795112284919436665/343]
  [25544700705016921/289,2243001664415180277007315/4913]
  [10808796856962554776/305809,41675766241034160853367466935/169112377]
  [26421245072990246569/1918225,1251762649011620470492654132627/2656741625]
  [77334535112489949289/3236401,2161845307037460567778027721845/5822285399]
  [312851945351432706699/6105841,616680903014484491197103214455/15087533111]
  [1246214398715912318662/19562929,7964356572081712584179289201611/86526834967]
  [43818955091918019033094/736525321,213986702670965002895520971372420/19988560686619]
  [510784333803417111889039/118243876,364962174369734534205151606297221745/1285783907624]
  [2900435326518811421392564/64262757001,2091547048069415367054766669647757280/16290673162510501]
  [7748059194553642502332054/20759334561,20901273315800323948733455483662913805/2991025682883441]
  [14556310661252676628478931679/38294673216361,1703871622227946118508152135682376852586045/236977739129937069109]
torsion generators:
  [237594575940631/4,-237594575940635/8]

3. [1,0,0,-26844785415316950775425605,53078430978883527280513999906842557121] N = 52730095526316529723237209878616107447931486

E = ellinit([1,0,0,-26844785415316950775425605,53078430978883527280513999906842557121]);
generators:
  [2744993348530,270492323384302471]
  [3588059963734,1717857507293552395]
  [-6892997802664256690/1164241,2658434546377179804569101001/1256216039]
  [-20170153738118276/6241,5078073203933881759673545/493039]
  [-130923827481359/64,5105479194265758846155/512]
  [10957461718429/16,378711332743068346099/64]
  [43942428668157586/5041,7853225112404850818324321/357911]
  [52105349524128538/19321,1462089790391458907311597/2685619]
  [274976860125142750/127449,103784034551569266067708723/45499293]
  [954201995338712866/290521,91233583613669663732249909/156590819]
  [1080022111679406876/326041,131932424921627117587421973/186169411]
  [113167514087470352530/52171729,847216983197427929671718419793/376836398567]
  [163452520385516912530/707281,2089195959565796959709499352879/594823321]
  [3016743851994613779682/927994369,11482631822057360799205984302361/28269492462847]
torsion generators:
  [2762872651762,-1381436325881]

4. [1,1,1,-86374399929534275305324462913,9855469784322937076113338981697664456740031] N = 84518160226589403767572961475020918466832050

E = ellinit([1,1,1,-86374399929534275305324462913,9855469784322937076113338981697664456740031]);
generators:
  [-238644710244435,4108179458614153564042]
  [-188579236247435,4408810495291602930392]
  [173687088201055,304968260589798877472]
  [383895309535815,5768322588638028403792]
  [2930434854135415/9,108845376563237961664064/27]
  [8307885531825231/49,99870495682830193816384/343]
  [13216661435690378215/729,48042537208162462928295096256/19683]
  [49779750086093919551/297025,47740671665086070458331478464/161878625]
  [116441217397012396295/273529,1013893524637339840183922511424/143055667]
  [575473705287041346335/3996001,5072480924666665759194444175168/7988005999]
  [590497480367429852135/2968729,3774508988974582188978953920064/5115120067]
  [174805508556681069035595/1068439969,11225569723415773685968794742963316/34924097266703]
  [258876945727843615189215/2778238681,236855560385929576557970115798304368/146438182636829]
  [82798079153146389433990215/62374563001,736336637403837876527580108926383702208/15577984734936749]
torsion generators:
  [-339687689313665,169843844656832]

5. [0,0,0,-78907404335076126358349007,244810445251631987769046702357699521106] N = 85468703986756648905003803597594316557982840

E = ellinit([0,0,0,-78907404335076126358349007,244810445251631987769046702357699521106]);
generators:
  [-679675943687593800853941238/119661917902081,29553881562765542263884969061170708489990/1308982796888125177729]
  [-135775740826118032437091/13491519409,6948362274532410760054298569674630/1567080453913577]
  [-1599417649145057683/18826921,1295535860834753298897047944890/81690010219]
  [-1856179014986249/225,61709955644330587195624/3375]
  [295607188568239005/24649,123796264379260096010671178/3869893]
  [1038421764728299475/312481,767144888123031739639862136/174676879]
  [1474502765858785523/61009,1681764377313739648509090720/15069223]
  [45261172645900978313/12020089,43248969389478416283583793910/41673648563]
  [65594323425857585847/9728161,133343636363483050264209423160/30342134159]
  [8876841522447891822422/653364721,684652769769518007350901032335320/16700655633481]
  [359019745624300468239981/53111350681,55145114201350709078818066465444870/12239988766592579]
  [501062001074119247745227/161518681,354678958127999803303180592833529520/2052740916829]
  [826668655699504704280778/36215231809,700717744950292015405151027839078410/6891867258948127]
  [1503303702102022779812417/230568990976,303215820856520007076556583841153695/110713695810891776]
torsion generators:
  [3795351025526,0]

6. [1,0,1,-47150895435824082237969612348,3920522858450780250277322153420722026062878] N = 105313271826844476571278144767156849073593310

E = ellinit([1,0,1,-47150895435824082237969612348,3920522858450780250277322153420722026062878]);
generators:
  [114586558757102,148978559541183802230]
  [955079761470959,28811278277254132905045]
  [-18075756530303401/196,7507014992228520149365095/2744]
  [16667714273236654/81,1248100392921852331970630/729]
  [1036272148365088847/27556,6785621094028664624061264135/4574296]
  [2604455432694565396/26569,2123606091763232914707258515/4330747]
  [10440040412802535544/5041,33554426074307907711561857670/357911]
  [44656601688924514139/219961,170010029026889115065770517085/103161709]
  [62356060845876129311/452929,59849810760426788176308221115/304821217]
  [81185897700851738216/537289,195286723563615792068745377985/393832837]
  [1196441819913809042891/10355524,4099395649644912501748974021315/33324076232]
  [707932146453713002739/96721,18827749799374863073379902035645/30080231]
  [777511647119652964874/1515361,19987077256983040504762396094745/1865409391]
  [101075344314645028929696209/65986820641,1006470770467013744287212411670011837315/16950628499439439]
torsion generators:
  [530551022837111/4,-530551022837115/8]

7. [1,1,1,-8681332614227516477562299230,321488738143298625656711550300073291382171] N = 197360698876438380985679121710016580862432238

E = ellinit([1,1,1,-8681332614227516477562299230,321488738143298625656711550300073291382171]);
generators:
  [-23769852816155,717225659418073406547]
  [-3877737483094776103/44521,6065233677920746320851160429/9393931]
  [-1217922001304729479/51529,8381789351470843692772974717/11697083]
  [-747569068912681543/80089,14365313170334461315022488773/22665187]
  [-30246937733795695/289,1420907391209900723532471/4913]
  [20120516999439329/289,1147429518498430629802023/4913]
  [244668129179396329/5184,48508322589031431725960671/373248]
  [1932304413654682705/2209,2671413016711182063576749001/103823]
  [60981247871804554305/1183744,134953011443613482868494475329/1287913472]
  [201337421022442074497/2768896,1259246204011697758176273420927/4607442944]
  [912833908631631913553/18809569,9816116769195138000403013219607/81577100753]
  [11317882173139251040793/29929,1204058918698619666553899817804243/5177717]
  [129147270594571955271359/2597533156,14957626791929766801176489605578189/132385874828696]
  [23020093257291454945331337/332039860441,43986542876740948524768924171882202987/191330996742056989]
torsion generators:
  [-107975693093455,53987846546727]

8. [1,-1,1,-29987048533957114353134099931767,60838154561872193400955653963549381347129690959] N = 600960580937885755418479715464629443672290830

E = ellinit([1,-1,1,-29987048533957114353134099931767,60838154561872193400955653963549381347129690959]);
generators:
  [-3957582932823953,342824871403589706401486]
  [-29902988615933,248464947631095499454366]
  [8201230295182843/4,714399774794434808654653/8]
  [3654834292826947,7813886870225099469086]
  [3711097408818367,25757237685843395582066]
  [8005293641718787,577754336094288360911966]
  [18841980431716867,2486987512690354778025566]
  [99735273881371423,31450743876479430544363538]
  [-4490089174280417218157/786769,149834922583798147785726513184498/697864103]
  [37800435186218891/25,17209183635458527595083174/125]
  [4628467630874067163/169,9771585727339430530036019702/2197]
  [13274361921807832483/1849,36915492768036583406491482962/79507]
  [492007797297975746167/10201,10845756684009358716012080445466/1030301]
  [13581656563222883169337/1577536,1315517158634436864102350581106881/1981385216]
torsion generators:
  [-6296737413667133,3148368706833566]

9. [1,0,1,-20295837335427080962077761258,1107062187939803015835794294312352453954968] N = 789775713498323533692179524392094706920655310

E = ellinit([1,0,1,-20295837335427080962077761258,1107062187939803015835794294312352453954968]);
generators:
  [-129327273641376,1252516942369213419160]
  [33166559802324,685859289095115469915]
  [56043712629864,381622406131776419080]
  [-6156620203313814/49,443732351370462700118215/343]
  [12222253927635789/16,1329223020244867748038075/64]
  [3683191724051151/49,26972509101394443375895/343]
  [9175694853242094/121,84798360341986671006980/1331]
  [11304607032383527/9,1194522996694898839827541/27]
  [122597668952819433741/1607824,108357965433332442074857889225/2038720832]
  [59721518576473660131/597529,128143950577979279580653122085/461889917]
  [63912661682566221039/1104601,412815707854746838246048232005/1160935651]
  [86785895011672089951/124609,792745484204559409305600078335/43986977]
  [516803351763748071639/201601,11730880321900804680865501466945/90518849]
  [22717582850648719174593/439028209,4066332015037727815868825914599115/9198958063177]
torsion generators:
  [348284247742487/4,-348284247742491/8]

10. [1,1,1,-5089841477845778701914393659,139742554070973196205444450874019523701961] N = 1346259072323476202308604032530420986710202358

E = ellinit([1,1,1,-5089841477845778701914393659,139742554070973196205444450874019523701961]);
generators:
  [-4511804127911,403255600949410221440]
  [1151008655674707,38976423623686705213030]
  [21671681948035209/1369,12727505076349737763476472/50653]
  [210360591027234603/5041,1228721626143877825103810/357911]
  [573800666116570587/10609,164533276140954320428339090/1092727]
  [2271801784911685055/39601,1506579936214353500474310398/7880599]
  [4836976285424664523/100489,2522312513129216257906161406/31855013]
  [10118857627540756123/257049,2543359851126503986686621266/130323843]
  [38667302423474612931/954529,5319504065862515269570479350/932574833]
  [182835300759212672405/4490161,16187969200254311518520761508/9514651159]
  [21411353062297818128210787/585373419409,22423225600351710195323450644414411510/447867447069567673]
  [147015812624844514767098283/6937571441329,3717962262540694611943815737418416581946/18273056733745368983]
  [2468633235771130580917521891/123450336025,122654107272623024152656409411110500793346/43374892814063875]
  [11827850055987275132036441347/2419322043889,1286212498197944265319462525530706386942038/3763054635539696713]
torsion generators:
  [40744813067955,-20372406533978]

Rank 15

# a-invariants conductor N log N naive h log abs(disc) torsion generators
1 [1,-1,0,-47377997631934616131259094,122064326885475393485584567015835076600] 74982942042145889714439140878353729492075810 101.025834554 188.974204000 178.60634078 [[13690851677475/4,-13690851677475/8]]
2 [1,-1,1,-460855466999674963016476998152,114346210304297863156871290426720957935291979] 12334433622321215895724716304610404854359954238330 113.036479296 216.522249000 206.74798737 [[317693260060237,-158846630030119]]
3 [1,0,0,-24341212570918907364975008993335,46017718934663050280692506168501437161981737641] 44025871847742350339136611296547024333859559593162 114.308861921 228.422774000 216.24382281 [[2691897204184342,-1345948602092171]]
4 [1,1,0,-12537268201897972664569190300,537407455719654951639069821483479971892500] 46743260634842018618863285423770046153816518554850 114.368754552 205.709113000 193.72231854 [[273938270585915/4,-273938270585915/8]]
5 [0,1,0,-1248869357683141748660243160,-4876649751055622525002422594205126924716] 66489049159927911945099447956450941788165109722672 114.721121724 198.789711000 191.24898359 [[-33195841876077,0]]
6 [1,0,0,-409400407501145672374429749475,91075658316227433599720258143475077076650625] 177599378108948787912335962451915637757725844372530 115.703614793 216.167077000 207.01980827 [[-730773266756050,365386633378025]]
7 [1,0,0,-3635332259215271286970001417235900,84311290079639932822856655654964969491572101846032] 216095858582728308893742177217643607485136038653170 115.899806563 243.441629000 229.32751403 [[35527834228813304,-17763917114406652]]
8 [1,-1,1,-44700175175144584563197015384837,112606878837296599453184780505115482103256620285] 373194485014698697229027713931389442079902239969278 116.446184155 230.246194000 219.61398397 [[3393090920476159,-1696545460238080]]
9 [1,1,0,-34444685391230787101989206997,1860441465752852048025411799379070728824585] 640259658391727630453646333422455570202860388634738 116.985958274 208.741060000 200.43840550 [[-833089813048405/4,833089813048405/8]]
10 [1,0,0,-436520984169712563844803206505720,3494719553345674650555909435913973121316373774400] 685257784586218399524469100121851164597964542700910 117.053879559 237.082771000 224.90747963 [[11398379614036976,-5699189807018488]]
generators for these ten

1. [1,-1,0,-47377997631934616131259094,122064326885475393485584567015835076600] N = 74982942042145889714439140878353729492075810

E = ellinit([1,-1,0,-47377997631934616131259094,122064326885475393485584567015835076600]);
generators:
  [-2574560108244,15065747833641861912]
  [-94069685004360059481/147306769,22046550279081198180770463040581/1787862255353]
  [-29400782454365344106/12467961,653986561156470526669218304834/44024370291]
  [-6429586375302678804/1560001,30642097436790849570461288028/1948441249]
  [-267875344172183691/44944,132271746629062852402826511/9528128]
  [-648123971361861/625,203773060928143158582237/15625]
  [-100226937110961/100,12982412418852997051467/1000]
  [1805286024723046/361,21901827130163221386108/6859]
  [110920556414671594/33489,7447326842190232890963184/6128487]
  [131891759640452076/9025,43302155097118740511809864/857375]
  [140941780987533294/24649,23889322060939209688082526/3869893]
  [1163926349438778426/383161,589373961081265617021622128/237176659]
  [8145805666385274621/151321,23067158419801824363152038938/58863869]
  [209898531902728084161/46526041,119929673402671214137210782702/317354125661]
  [1678672756511499518719/520843684,20049038077497156426248387390541/11886694556248]
torsion generators:
  [13690851677475/4,-13690851677475/8]

2. [1,-1,1,-460855466999674963016476998152,114346210304297863156871290426720957935291979] N = 12334433622321215895724716304610404854359954238330

E = ellinit([1,-1,1,-460855466999674963016476998152,114346210304297863156871290426720957935291979]);
generators:
  [500377196720737,3004621962976095962381]
  [510232259383039,3469178130626886039287]
  [771611998707149,14769930934745969270873]
  [972614224161487,24211230454173535299881]
  [-16997923422676499677715147/23001665569,24998400109735179669722872576776781607/3488501605191247]
  [-1965470045313711707/11449,16814923987923146188227278683/1225043]
  [-82575272110633243/121,14024423438722708344713531/1331]
  [118962591094178053/169,25877659521017541478914557/2197]
  [415992646427510557/361,228872960220413725272363779/6859]
  [505804140331391767/841,180417793995221963535548659/24389]
  [167051245226477568613/66049,2087785399375569396967997508433/16974593]
  [362706393811116758893/1520289,7947634909249770703200697117897/1874516337]
  [865769947136977192201/5329,25474165930487603658452034170969/389017]
  [2259143602660144643509/7209225,16210790235559601053595801092253/19356769125]
  [3066581192810895907237/6446521,27205264631705234617670722523099/16367716819]
torsion generators:
  [317693260060237,-158846630030119]

3. [1,0,0,-24341212570918907364975008993335,46017718934663050280692506168501437161981737641] N = 44025871847742350339136611296547024333859559593162

E = ellinit([1,0,0,-24341212570918907364975008993335,46017718934663050280692506168501437161981737641]);
generators:
  [2679684176319766,5743208724939292751221]
  [3830205657410930,94746009226532528783681]
  [248692530822412292,123996459263874675185619989]
  [-24357366219621893729194/12369289,12780800324711069089205146322709305/43502789413]
  [-5689713812753183550106/1026169,106637181529781606685706325392561/1039509197]
  [-3474886522146359304061/770884,171425807990884197857194899480901/676836152]
  [-10893684461757643546/4489,90627209338751588956935955319/300763]
  [1450448593689441038/961,3359585621085550111111077683/29791]
  [3617391324999309902/9409,174881828890788008423472793997/912673]
  [14661523308436763374/173889,15204303785954660322126305820773/72511713]
  [71365277967895836518/19321,216566162988367157446427039951/2685619]
  [1024993157877255420854/323761,4829985843888039178710611304829/184220009]
  [1524114951491195305814/289,59501291886636930990369390776293/4913]
  [261345408258091968329750/189310081,319493036894756548050563346446048459/2604717404479]
  [62290281358323173311179254/3667392481,472830044484806929867950462519865063259/222093621256879]
torsion generators:
  [2691897204184342,-1345948602092171]

4. [1,1,0,-12537268201897972664569190300,537407455719654951639069821483479971892500] N = 46743260634842018618863285423770046153816518554850

E = ellinit([1,1,0,-12537268201897972664569190300,537407455719654951639069821483479971892500]);
generators:
  [440897999982527050,292756926324632028831015050]
  [-1156305732313161536518030/55649281801,11660354191656270884754823054507079290/13127721226137701]
  [-190697020545093296473935/5365123009,380627299501487686711611384039193335/392979165040223]
  [-20787558961327550/289,5075048129879403743065650/4913]
  [17987491699959896/25,2384806260747161132239066/125]
  [505879232188055960/121,359679812070870427081298470/1331]
  [70793355310323558425/678976,337402427062849740267540526825/559476224]
  [1980728604421653934719/32615521,18738227195017137089402547135/186267240431]
  [24718566890043784790105/421398784,534911727353849571300588745926955/8650474237952]
  [20183125691306015348859/11015761,2862128832376019620526025058878759/36561310759]
  [931206326097028480084840/9692993209,447227295702151041082823516575511490/954304260405677]
  [4459398429426190656287870/62145005521,1319563507756819821037782482840520260/15492066281324569]
  [6981827892134623952260028945/29027192760721,528891226933414061103493419472493896097510/156389487137816163769]
  [10422144319273227829929328990/108975915357409,525180122351283237983989168141151712477790/1137616253731042234577]
  [915890509382186397291307323705/5589073598651449,709528011558488185711408398294880123702139595/417839740266057382945043]
torsion generators:
  [273938270585915/4,-273938270585915/8]

5. [0,1,0,-1248869357683141748660243160,-4876649751055622525002422594205126924716] N = 66489049159927911945099447956450941788165109722672

E = ellinit([0,1,0,-1248869357683141748660243160,-4876649751055622525002422594205126924716]);
generators:
  [-16003029846420,104931961248755966622]
  [-11138017107933,87473122005189162396]
  [-7808317302402,66323802436362562080]
  [1887399160320750,81982156390805741994528]
  [121743491764184454,42478445202717796605052632]
  [-25879752251231239428/2301289,307245001477945283510248993590/3491055413]
  [-4811400031279389/625,1022360636501127748203984/15625]
  [-3553826403626106/289,456173382553645720202712/4913]
  [-181898675677194/25,7730694939400586495496/125]
  [336437066233732/9,701967728028195414170/27]
  [1933578120393684/49,29282765019897822775518/343]
  [93335319290666406/2401,8580428512188730511408424/117649]
  [598011854981587356/361,462344408670181128858396234/6859]
  [9407382976931797398/121801,25484006268034431464358162360/42508549]
  [21659978818433618046/494209,54464269435368534247761774816/347428927]
torsion generators:
  [-33195841876077,0]

6. [1,0,0,-409400407501145672374429749475,91075658316227433599720258143475077076650625] N = 177599378108948787912335962451915637757725844372530

E = ellinit([1,0,0,-409400407501145672374429749475,91075658316227433599720258143475077076650625]);
generators:
  [-2335864005896935129745586309284290/4577138393556897961,126582341530562225240314450610136186980650676336125/9792443305242158231251771541]
  [-3715373275101014957436788050/7988983537441,303697636377659203148802537494153593087975/22580694199922700239]
  [-362050639803131808612994/9238093225,9187296566565440473676110067365837859/887919330320875]
  [-11793695147606852029090/152448409,20814707151874450193847993771795355/1882280505923]
  [-4283243745082981816450/15031129,791774944740445679217558893884325/58275687133]
  [-9701360227697093895119/89113600,9750853930743964047723760556198759/841232384000]
  [2798858178321520750/2209,4161187146005479234094289575/103823]
  [25004065108141168942/159201,351666882944680178622652662919/63521199]
  [43419043896221025902/160801,30055346315835942653521815577/64481201]
  [785852881184857361684/1481089,8687004856134712864262184010531/1802485313]
  [3837122899092591007550/16008001,165963834110824936130665071978025/64048012001]
  [143335895999980615957310/559369801,22892321981730785223509142387907315/13229655163451]
  [430057826317780571974400/362635849,246432198431566791348182068112357125/6905674472507]
  [119465119438878449676903550/28778747449,1290991664718071927770975679373182033675/4882113053490707]
  [568388326843547054465577609950/2344208697186841,279512331533406381398373490330897139737214725/113499620473747499115389]
torsion generators:
  [-730773266756050,365386633378025]

7. [1,0,0,-3635332259215271286970001417235900,84311290079639932822856655654964969491572101846032] N = 216095858582728308893742177217643607485136038653170

E = ellinit([1,0,0,-3635332259215271286970001417235900,84311290079639932822856655654964969491572101846032]);
generators:
  [-65190603024930516,6652278419230975966040928]
  [23998194782033304,3300115022899654561593348]
  [29391200688944304,1689344115135726282966348]
  [29420146807628304,1680399762414432386073348]
  [31584462345719304,999624046964685922239348]
  [144357933635405091/4,2757434274236009285496159/8]
  [466441332170465904,316023929611923409666002948]
  [515111910532102904,367275981952250591129542148]
  [2600084813769317091/4,4175150443397367506982967659/8]
  [-168978512601106805481864/8720209,312720578507529989260084017473367396/25750777177]
  [-485147613487664876/81,7500916281543350892163020692/729]
  [148044979510031128/9,145306817181490729468338796/27]
  [19068116877419614392/529,3981274245413000608702763292/12167]
  [3899823088292135073111/77284,116411993534498724577730306654871/21484952]
  [77445206462484645004584/19321,21549785865935750076883820403644412/2685619]
torsion generators:
  [35527834228813304,-17763917114406652]

8. [1,-1,1,-44700175175144584563197015384837,112606878837296599453184780505115482103256620285] N = 373194485014698697229027713931389442079902239969278

E = ellinit([1,-1,1,-44700175175144584563197015384837,112606878837296599453184780505115482103256620285]);
generators:
  [-6674497450763009,337070405992539082633472]
  [3370317424408375,15384030974988478275560]
  [4712529176184991,81311270159101668469472]
  [5547697914584959,188055955665835775594240]
  [195317847999145459,86270356969368338446219340]
  [-509986188707079721/625,6021971894336665627147381408/15625]
  [-50640995165925689/25,55176095225381211889288576/125]
  [-15645192302294681/9,11614976509186423313374144/27]
  [517116188387614039/169,147039860879691871186214144/2197]
  [963524197526109079/289,123884510840525079307022056/4913]
  [21086036830735608823/3721,46113459407310498803541749504/226981]
  [34596284014333506535/10201,4197544081312655329120248640/1030301]
  [48266542259758564903/10201,86408116035293547872379104512/1030301]
  [54954793261166911517839/31798321,36092964203786370015008508171573760/179310732119]
  [2922556219235105732704285/44209201,4971612774155090849503519241497919726/293946977449]
torsion generators:
  [3393090920476159,-1696545460238080]

9. [1,1,0,-34444685391230787101989206997,1860441465752852048025411799379070728824585] N = 640259658391727630453646333422455570202860388634738

E = ellinit([1,1,0,-34444685391230787101989206997,1860441465752852048025411799379070728824585]);
generators:
  [-76781306939349455370328421814791/659840790694999104,1110543775663006431774936022406845081478430618425/535992533030491756533960192]
  [-1174218216835538341643620996106/21998242472622025,6144816327328464528471630757209817296093753613/3262736316975264771941125]
  [-141045541341465820945863790968/6742298596473001,887840570532414249138210864507479486797892761/553620257946591418084501]
  [-2245977562098000940123373/19214949924,5516547045703547265479672681155472989/2663537928565032]
  [-476517116657577293025932/2291632641,19608724668173730760275265345040047/109702746157311]
  [182480823600648126/841,52321100539808121056555705/24389]
  [1465938174524165456245/9840769,5778104002262919700926037543745/30870492353]
  [4699889619028607022606/27363361,143945466870643181129436318529675/143137741391]
  [130366775420850308239119/503778025,36247412233520798160998183910539182/11307297771125]
  [162807514315863148801820/652444849,49446516440289948701601896215426445/16665398778007]
  [189883103846819741314013105/1230699578161,638721991239420374690963225660297415490/1365299960324890409]
  [296847449011458386133856620/48490986821209,433719145574976840006896122315148237049355/337669265805869468323]
  [329224857035772081857992736720/2553805351969,188902835179087726689881316884730963764478115/4081141842183636047]
  [1030588967292859335471214284192/30461957711727151009,229249640634256358703146752280058122707497076147315/168126710695187957095764414223]
  [28691445333350186047401279422467/182200791030223716,45432110367023165141513838792085529573561557531/77772379592329174520147736]
torsion generators:
  [-833089813048405/4,833089813048405/8]

10. [1,0,0,-436520984169712563844803206505720,3494719553345674650555909435913973121316373774400] N = 685257784586218399524469100121851164597964542700910

E = ellinit([1,0,0,-436520984169712563844803206505720,3494719553345674650555909435913973121316373774400]);
generators:
  [11220302256204240,96975107231981048983080]
  [25707896710982640,3043505874168882776899080]
  [-687556742725164658978720780560/29275468883761,141006899476748568142184283634844143742462280/158400223255456851241]
  [-450735045255537000650771268684/39002335684225,644258422979242717366589385434920990752802356/243576801780086706625]
  [-1471919635118171727/64,599093990665871664315291597/512]
  [31776970521520036890/3481,106831776140423175379354163820/205379]
  [1840942275972193808040/185761,30170056412904059283593239943280/80062991]
  [2120011057652493336100/1610361,3493409012729241552849142111956920/2043548109]
  [86077557159846629612400/2550409,21244903406938887558351651438897960/4073003173]
  [1354333939109462221141968/272019049,5392617037865686792170618623263905192/4486410175157]
  [3577107378160919470285440/315879529,339261494877412175465999949781569960/5614126868917]
  [36747289440719828915501040/2791114561,25416548317881634851450352541200671480/147457373372191]
  [94423367976419520595713420/130942249,917146874960442124142403985426596420360/1498372155307]
  [109153647134375511014590320/8488121161,69137461287170585874834798504252835800/782019090684091]
  [51621118818862559479900037514600/5747345171695009,238082501921921223154324969864636330698534304560/435713404405627735966223]
torsion generators:
  [11398379614036976,-5699189807018488]

Rank 16

# a-invariants conductor N log N naive h log abs(disc) torsion generators
1 [1,0,0,-70125739284257541584773900448595,224743012466763550759810773071275962457173164961] 2050943799731838770795008718676624626173063235165279006502 131.965650378 231.597131000 219.66362497 [[5129584179510542,-2564792089755271]]
2 [1,1,1,-357585268017125482099980994221405145,78511122853996073065207742221224270468256045274555495] 2774700096374548868697941163846920764265826133256711902170 132.267892969 257.207649000 247.34531136 [[404106371493727023,-202053185746863512]]
3 [1,0,0,-74478614497001051213037130703918863,7813308578453199795281011676368530519633974132260217] 4037723001611237548976485813408801349432131894744731730350 132.643031220 252.501063000 239.08558777 [[162161356727836102,-81080678363918051]]
4 [1,0,0,-2706381903778836656039400049062720,53529269933708805299470502391666979470354686054400] 4657372890037610572108520563138067741151339367609178987970 132.785801832 242.556365000 231.38410134 [[27281908556595840,-13640954278297920]]
5 [0,1,0,-13827205010356214233064186665515960,25588766749629734994801221790706597827765337655589108] 20694146997734910275982913658882094552149846425111944376080 134.277201207 254.871132000 247.41581367 [[-310306452720468589,0]]
6 [1,0,0,-5835343777752052984977406988936611537865,170517842323488583002289008130018056310590148361407089651225] 24873521719121352454158663977256178321790788520720666774670 134.461154154 286.307858000 274.45145645 [[41249130521081666746,-20624565260540833373]]
7 [1,0,1,-350118034100627899199059381753771143,79718109217596160364013393657928989116028766152608806] 44669319913005297558669849962700626503968806944547821921770 135.046637211 257.144338000 242.12705220 [[1348466899527896519/4,-1348466899527896523/8]]
8 [1,0,0,-2653537278084187322695250426187488,52377999300372020618268203510163981734577882350592] 53400310113364992979902636017282809299958520515445675366550 135.225166854 242.497208000 230.31859483 [[28105779981180352,-14052889990590176]]
9 [1,1,1,-13289838994665810001275530484957555,473548064728498241109179227952712848094866812097841] 63934647124365089579328637948067895428628586695757133189454 135.405211724 247.330527000 238.84053281 [[-130112861446692445,65056430723346222]]
10 [1,0,0,-10324797226271342424445978043326788,390142228304621475813271888061311995159824186034192] 68662277096507810514384315090839189136158273578762149529950 135.476550253 246.573173000 236.40819751 [[49619113514201352,-24809556757100676]]
generators for these ten

1. [1,0,0,-70125739284257541584773900448595,224743012466763550759810773071275962457173164961] N = 2050943799731838770795008718676624626173063235165279006502

E = ellinit([1,0,0,-70125739284257541584773900448595,224743012466763550759810773071275962457173164961]);
generators:
  [4011125375232078,89416913858436189809529]
  [6576372845569758,219064937612195671731273]
  [20693955204040404,2763247892048250754871955]
  [101814396335978814,32380710357493942041363225]
  [1768348194780203985/64,2254042173260881531239849213/512]
  [6661029569181270834/25,17183040655816079582336464713/125]
  [7140827896366670526/1369,1500999993494766220087386165/50653]
  [14304799441228871058/1681,34060039425423379190003026329/68921]
  [14678575361306770758/3481,13018372123599098657811079971/205379]
  [18076771028524845598/81,76803271743698979341113018817/729]
  [322330764564225228540/9409,5628086295050009828955380074473/912673]
  [164548871336383594449456/28058209,18315428816338941065096354853878223/148624333073]
  [516542169431021749047642/114340249,14541921904075744266251065549375761/1222640282557]
  [3416375559827424969684606/759829225,384845062875762659866079899322823501/20944692587125]
  [20377855121971249896247182/2999424289,40871033643489795133236697377701434839/164269470035663]
  [598946995332182445750772854/112766341249,1742280565256025560591922699365082985623/37867726755802943]
torsion generators:
  [5129584179510542,-2564792089755271]

2. [1,1,1,-357585268017125482099980994221405145,78511122853996073065207742221224270468256045274555495] N = 2774700096374548868697941163846920764265826133256711902170

E = ellinit([1,1,1,-357585268017125482099980994221405145,78511122853996073065207742221224270468256045274555495]);
generators:
  [436367904425598959,74593788848706085046383080]
  [-138559834988342037237487777/226472401,890520691993236561938976947107962716712/3408183162649]
  [-32334673496301996584137337/182007081,906962413065040224076410674757764803448/2455457529771]
  [-71981611334895918470177/3243601,1717464128053591113598017046874331688/5841725401]
  [-71742921369976977754513/113569,8753577523888195469611813308727464/38272753]
  [3000422110363073411257/10609,1088947129672333688465647139026/1092727]
  [9493418701686607673623/22201,203731275184211567680442776639112/3307949]
  [89450547725477665096623/201601,7681756970030738599315102117291112/90518849]
  [621918845310719667960887/1530169,33601003606374885225370427383185864/1892819053]
  [1616691537061762363015367/5929,2055605182067286803658142200839524104/456533]
  [471405565182214779354164047/2229445089,11700799584440316886671469513538966528744/105267708767313]
  [896492895387936362606983167/58874929,26821926418671806397901752778116669705896/451747330217]
  [2666692768900812844258389103/4839845761,74348675494265537742377243891715430372392/336703229747009]
  [6005247140560563430771247055/33497418529,870635001210684441752615177489759996031128/6130798031433167]
  [39889718302054752323142029167/97764404929,707915935470821487790561470024285790945896/30568289782365217]
  [462166352624941524318849543783/27656022601,313995135278429243675591648771758741244244488/4599224214568901]
torsion generators:
  [404106371493727023,-202053185746863512]

3. [1,0,0,-74478614497001051213037130703918863,7813308578453199795281011676368530519633974132260217] N = 4037723001611237548976485813408801349432131894744731730350

E = ellinit([1,0,0,-74478614497001051213037130703918863,7813308578453199795281011676368530519633974132260217]);
generators:
  [-310720537090836082,30921345983613377367432077]
  [-237906260208257158,109849389448240194789714629]
  [-154270142490639358,125026466140984196544965429]
  [177288480792769598,13472149756402112242668845]
  [1159975142075985683/4,823743855739228492917291667/8]
  [586329223354907438,407079511491991301643000965]
  [-4268142720661780865443/913936,78930722991572916201191293642622029/873722816]
  [-363974277303453525292/5329,43635200499636613673578116110933/389017]
  [-7055503944221450914/361,660086647903860703699062894095/6859]
  [14264963340788166713/64,24479482998833027941910176273/512]
  [2764409561766147910958/11449,76572041912665819822750773512047/1225043]
  [22230144638597768803238/214369,3445401120213003698384902728765203/99252847]
  [27732438078959310770542/201601,1183778864131379436468527939435021/90518849]
  [151529577575708468807468/923521,2841093182264491090118066520788327/887503681]
  [336763059968161217203582/447561,184033774648337232701656011140699521/299418309]
  [275188664581017270069721448/1903315129,681477300669137981971591410261652163327/83035929132883]
torsion generators:
  [162161356727836102,-81080678363918051]

4. [1,0,0,-2706381903778836656039400049062720,53529269933708805299470502391666979470354686054400] N = 4657372890037610572108520563138067741151339367609178987970

E = ellinit([1,0,0,-2706381903778836656039400049062720,53529269933708805299470502391666979470354686054400]);
generators:
  [-2444046140789992946886720/143017681,16651828122563729682860030248908178560/1710348447079]
  [-2076774779730084522360/657721,4201553727509615618081412340404480/533411731]
  [-25977384715861011210/3721,1927108165601262954032226304230/226981]
  [2135076990478270689/64,311745418559039860277318979/512]
  [271925412154445852301/10000,207282615316348628231529371499/1000000]
  [108225208733951064524520/2301289,19204781562837876115380502355953920/3491055413]
  [176834239890189215404800/5340721,5774056458550050561959509574393280/12342406231]
  [1775644256142638001637955/1811716,2362836415839724165861226030852895415/2438569736]
  [1575854446583075401302528/45738169,336445051947159598333610044353507264/309327236947]
  [1691720375353861939340160/35129329,1229655154972523797314657691180319040/208211532983]
  [18096175034864370351464880/133148521,72000571228563946467976336663992531120/1536400783819]
  [1731776776819240223845947648/29387216329,50046035415357575609060600250020858121408/5037762333631483]
  [1928799843893888043256928220/142815212281,237972255189638450521361226188291950906320/53971154057900429]
  [1976208709812282482164086240/47777653561,36703551513464631230946551312248850297280/10443287293016941]
  [3272723992107066014754499200/86789749201,57711903370207855967938473354638658889920/25568346904363801]
  [12840002751040210974917164800/392450878681,17659385451964071789582345819721118819520/245854385007620579]
torsion generators:
  [27281908556595840,-13640954278297920]

5. [0,1,0,-13827205010356214233064186665515960,25588766749629734994801221790706597827765337655589108] N = 20694146997734910275982913658882094552149846425111944376080

E = ellinit([0,1,0,-13827205010356214233064186665515960,25588766749629734994801221790706597827765337655589108]);
generators:
  [-375604811545369835485467569767054446/3152180152208892289,894469484496439577003880438106216667645329507717484100/5596500478664513895348750913]
  [-1606882326080455192253021826650361/5411889116884849,23614640019139738433726667168642412643087188714950/398128561539424385158007]
  [-89890587751894789325786009766846/345544117459489,691237976033132869494311767082205326678983584300/6423256364880945934513]
  [-617066391706946227245368169/2679201121,17843723561497612605104203527904231648950/138678129224081]
  [-79073116275369166720769406/255136729,41744492708606026891349289527064390900/4075298972317]
  [-2195162079539698076511564/14055001,8152575974162741549288619477372001950/52692198749]
  [103416112919650115277/4,1051666753144846722148996005429/8]
  [237094391218094951298786/32761,115435462765020751954379371715056620/5929741]
  [5727466990889137227529719/22118209,20640365165423190892319231923405991430/104021936927]
  [434409319838980465567602476/5524800241,64913910671465562546628894578889297416150/410652877113289]
  [5813053400029724784515877066/7890481,443206849192585766864529751791935305402500/22164361129]
  [63538336564965659314400612514/726682936849,98040591886849053930058484688454401514092300/619465956297487993]
  [5511600157961476560446649428706/15009278420761,15387784387868076249066471782197929767817836820/58148661281422271741]
  [2057860603385337380601768876438135084/6545185100383147969,3830211892447333739931830791240126510482335843298375450/16744913160329167581240641953]
  [2422012484868160700455074836037759114/2086036356883609,3769333497515052959444707818877036681864018457899329660/95275845175289535747523]
  [321006037538460624181201420523016743826/307029065319285806641,5779292347622757431475752466213224076138069122916134962500/5379838465038779702798359988311]
torsion generators:
  [-310306452720468589,0]

6. [1,0,0,-5835343777752052984977406988936611537865,170517842323488583002289008130018056310590148361407089651225] N = 24873521719121352454158663977256178321790788520720666774670

E = ellinit([1,0,0,-5835343777752052984977406988936611537865,170517842323488583002289008130018056310590148361407089651225]);
generators:
  [74014334626401055930,379576461508251232138903894435]
  [-58500990487130642905415318182418150/1181549258016241,23614332897020651297261353551929433114427976411845765/40614185465344380790711]
  [-27973657365211750712877861793670/425248756321,144020198859784213675287717331272877313010999085/277309391733243631]
  [-120450411339871705043144983646/1648766025,30453908876092698954486643540943089855705823/66948144445125]
  [-461032749275875539048449030/8567329,14377029291891311487705335574649119856205/25076571983]
  [8669452629792710061322/121,461515637174418413139284110253657/1331]
  [79300442469157195198288/289,21544199608097274494997372657565061/4913]
  [288895707442296252423850/1369,146251418034788256536749904075548855/50653]
  [1476987538586619167761516810/51529,56762786378202284627604559749999016535825/11697083]
  [88879445889965500197905205730/1885904329,1109632396909627996663881210036344818915385/81899167295483]
  [1231725399818760863270269707610/33558942481,467612586362736697011588227242447241645024885/6147696232036871]
  [11876945965524024362173113006010/7744176001,40881617746997151269285399792213279907275507555/681495232264001]
  [56211369220555959317886883035745/1377130414144,29721310907042485276315108603402693249941961205/1616079066562953728]
  [54692541757082092184809784706718/1122165218329,51641839426314582127339154819227684470289105649/1188735425575931267]
  [136547557928668367552050387531930/10161412163809,9958999547842947057887640698726238817197473285555/32391503070337457873]
  [177494852139723587667154031201376869050/4337653289920696321,144058652241091615782398954937442997823843928600308604835/9034045085770541651207034881]
torsion generators:
  [41249130521081666746,-20624565260540833373]

7. [1,0,1,-350118034100627899199059381753771143,79718109217596160364013393657928989116028766152608806] N = 44669319913005297558669849962700626503968806944547821921770

E = ellinit([1,0,1,-350118034100627899199059381753771143,79718109217596160364013393657928989116028766152608806]);
generators:
  [336723639306484325,1939783285706651332429632]
  [100304027013478586123/4,1004286701102481817409869147839/8]
  [-190796507246457898091087859949136755/1087765889089464649,417970992072996486299306753849344584406146977250077376/1134496482463992637366989893]
  [-253219474021160411940304675/1022784361,12720000982820226661114418266563776737362/32709666649141]
  [16739931735380598108644/49729,24232619716782336362131771853778/11089567]
  [2101245384445273844417531/122899396,369970822943236918935776359647890353869/1362462704056]
  [2514610358438468694305720/7219969,97149647057384817261055857514143171/19400056703]
  [3407488916351076119572730/619369,6255043086629375944835529993033211071/487443403]
  [7954951877440925879234888/21187609,3365669916052609678348374467220437358/97526564227]
  [32485240982384442001628165/144024001,191087418367187361090986365418119567482/1728432036001]
  [177312097848877669212260005/587383696,557967831424152034813695806109342142147/14235831256256]
  [2193963036111735666495800789/6326611600,1304063546948965494669122698229757490533/503218686664000]
  [26077237932572393807597078005/77502662449,54445719968455985141417012868476328344074/21576198707164457]
  [144174552310166095669917472675/180704908836,42648911383786447365265859463928269676258753/76816572516730584]
  [1752306117849194400534791843555/5326674745681,146174601811236960044569850471651230606927998/12293746919367175079]
  [152658079389260696386403812537064/430575572599225,110355956242832188115528607056606599925667954183/8934578762739287505875]
torsion generators:
  [1348466899527896519/4,-1348466899527896523/8]

8. [1,0,0,-2653537278084187322695250426187488,52377999300372020618268203510163981734577882350592] N = 53400310113364992979902636017282809299958520515445675366550

E = ellinit([1,0,0,-2653537278084187322695250426187488,52377999300372020618268203510163981734577882350592]);
generators:
  [112218440801456419/4,971239976528185947279215/8]
  [-1481731459068902970853232/30283009,1344303228551963143739090926351273648/166647398527]
  [-237495860332869901054478/95199049,7133618470768715061768367034895253516/928857121093]
  [15824662583703134015488/310249,1218652920596981622735385313112992/172808693]
  [256982201004641863503808/1814409,122633687073103410718965927879420512/2444008923]
  [769905107009859655615008/28015849,67940821897342342501075062812737728/148287888757]
  [9494313233032827441547912/126990361,23596980591930688822421873989795714936/1431054378109]
  [10414720650916475257239808/332223529,155436285395729047545000858015634592/6055438263083]
  [56388458021304880319440432/3348821161,684368328974845746224061965309525690096/193792931765909]
  [210482485171580879011823872/6695985241,89314302788478751769009086476486914656/547925776285789]
  [196086490592611908219909070912/6049430474481,9672399594861375706457598418884264202812896/14878931168384013879]
  [309000117219521927362787610688/9852272601889,2195509381446608871632579240394792956802848/30924638367805055537]
  [539635754564083630100319416386/15011897481361,107905907814189819652670788149323231453904196/58163882017585340359]
  [606777413127470774157204679648/29176342689169,392017413119854012348299619937786086856416288/157596394328001312697]
  [139840260922877615799398949014940667/635723733510705316,50971646319298486405843313372819287545932522406156641/506877061558291002106091864]
  [43334586209616100125137682447450784/1592322804383871169,1134985981039241716381685216515822971204005062590752/2009308735355391110681419553]
torsion generators:
  [28105779981180352,-14052889990590176]

9. [1,1,1,-13289838994665810001275530484957555,473548064728498241109179227952712848094866812097841] N = 63934647124365089579328637948067895428628586695757133189454

E = ellinit([1,1,1,-13289838994665810001275530484957555,473548064728498241109179227952712848094866812097841]);
generators:
  [-215317405760846432053780042100098821/1744931678394221641,35302090198760028432014871042754217264906363469247334/2304982543630846513263717061]
  [-34787331426017813315140377172357277/483338677999348161,10926018785760998621903432956292957443940536238236562/336029437398802642819914591]
  [-18354209760856239243652766468822297/141832629834506361,273697043306133100833201964637426344478402362844494/53415123071106511614915891]
  [-1557126029648746607208087536293157/42433131292483369,263943837339108249819871655099905071176659454760454/8740929584358384452301653]
  [-1609313669262904885099153743705/12843457585729,602719773119818509929992093237953260934916866/46028087896211118433]
  [-17684732225297607681301445429/8211909803449,527335013082957880334857891737736850092143338/23532401844885002707]
  [-1690319845352891551005798809/170157075001,1725856063761715668885063866907788747568302/70189963594987501]
  [-1587848945602921802322716301/20500226041,94577179764571289224057101656751445597986/2935201864324339]
  [-45997833712810128769/24649,86389839220022476236990752332398/3869893]
  [34077565928515757270171/310249,3181646874822068842727410341566598/172808693]
  [121975569442302771554763/85849,42463040960933334046923637945901398/25153757]
  [109803516912717538271732069/2864818576,693887859751480558429314257668374072981/153336549461824]
  [8461744623999466006916827147/141443449,778375334464241633445470890478186160909014/1682186938957]
  [434333681430099694640342720899/29563219960849,2696763663479699854120761801669874617603419426/160741346513667908743]
  [2971065901020411025487781218887/90303416901721,7277196535106359601668410115494812928137128558/858136303471260237731]
  [897079116953510273136554074487955/10025528471808721,900434664752313971533267840542844577077218376062/1003831713618264492259481]
torsion generators:
  [-130112861446692445,65056430723346222]

10. [1,0,0,-10324797226271342424445978043326788,390142228304621475813271888061311995159824186034192] N = 68662277096507810514384315090839189136158273578762149529950

E = ellinit([1,0,0,-10324797226271342424445978043326788,390142228304621475813271888061311995159824186034192]);
generators:
  [-4302284271334368,20844251181794696155174884]
  [31808559245937672,9690650600837588595645564]
  [44987369554785702,4087181339733125379422424]
  [47342411937297752,2729498205143313473276924]
  [128810488475041032,34604074297919522615509884]
  [161529732731328852,54194010517975152608629824]
  [292426231085538132,149590020956346498854539884]
  [316248421183346696,169569793622624672769062780]
  [-37011091318218949383672/954529,25234436077995270822418632421706172/932574833]
  [-8511845248282400070728/114921,1065878478335573710988580257693396/38958219]
  [9198521954044940616/25,26926765117984801479361869324/125]
  [11913695328458761608/529,158189053672573946406961438308/12167]
  [24333272542434910692/361,4601464519683300026315588976/6859]
  [26108474509484820552/361,31961668756364159266990870356/6859]
  [55413590111582358216/25,412074189237796306744215897996/125]
  [6293552205013999379322/160801,437317895892237053301286910066814/64481201]
torsion generators:
  [49619113514201352,-24809556757100676]

Rank 17

# a-invariants conductor N log N naive h log abs(disc) torsion generators
1 [1,0,0,-53841083898236582744512394752567955238,152040732478837697112301241289765721129521047217147781092] 3633958535429087440559985546561230089154484056735382962822667450 146.353183418 272.250904000 256.58273925 [[4196064619378355052,-2098032309689177526]]
generators for these ten

1. [1,0,0,-53841083898236582744512394752567955238,152040732478837697112301241289765721129521047217147781092] N = 3633958535429087440559985546561230089154484056735382962822667450

E = ellinit([1,0,0,-53841083898236582744512394752567955238,152040732478837697112301241289765721129521047217147781092]);
generators:
  [-4802607414307397416462368/1164241,21900930456404710104591694598978918586/1256216039]
  [-6412672703849423502384/13225,20292926270812982671743346722817794/1520875]
  [79778036415196702270113/10816,14058328124430909411630699345809253/1124864]
  [9247500360920298363596343/2244004,1289443545413676144223126458705211893/3361517992]
  [17055575604334797626963028/3988009,88487536331349967758400616905749642/7964053973]
  [1077734389391706310395463842/285238321,7692101853399726461616000057838556666256/4817390003369]
  [1614994576485744722333183148/377175241,553506387622937569242082474352040264882/7325120355461]
  [5507240000019512659764152772/16738925641,25103248429448149799270650307504461845407406/2165665460506939]
  [47000638699673378861884541772/10866603049,321222750377731705699611002100014538538734/1132767301636907]
  [75924507648322840132605774252/10576271281,12660218325367796210788316090549813465305434/1087674314809321]
  [186806501067797048081492313852/44669245201,1225312108918336100862440618166341123722374/9440889642476551]
  [477548328864233486977033084104/38803090225,281203507561078797192609597434904825646550238/7643626727971625]
  [8641053249013966174255122398706/1953870000481,1782972684410882486102975668815027064626964320/2731137071502346129]
  [72849655150974142636675968983622/17666360640769,27738320813515876751709568165330506619250921070/74254134064559892353]
  [4497791835397316855343558730552596/627663381410521,182161395677868565848488729058482704431049376320230/15724983131451260232931]
  [5240980104291669418608357119239068/484157664837889,308331551486467429448202420231897351071842696612278/10653203363346672156287]
  [15165488900656768857840906840162732/7326413123391961,4410280808249198865392758173263011419775820781782946/627100440971366380663709]
torsion generators:
  [4196064619378355052,-2098032309689177526]