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Elliptic curves by rank › curves from Mestre’s ten-point construction

Curves from Mestre's ten-point construction: record curves

Snapshot of 2026-10-31; the list is still being extended. For each rank, the ten curves of this collection with the smallest conductor, with generators of the Mordell-Weil group. Every curve has proven rank, trivial torsion, and is given by its global minimal model. 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)
13 122,726 67.155222 84.406821 73.845529
14 113,111 75.515870 91.057097 79.770709
15 58,427 83.958062 98.836190 87.589944
16 10,072 90.067823 108.812563 99.031223
17 608 103.439446 123.030334 115.516854
18 11 113.074489 134.945190 126.760832
19 2 124.678458 163.859885 149.550411

Rank 13

# a-invariants conductor N log N naive h log abs(disc)
1 [1,-1,1,-2971687864242,1881785334032062641] 146265588369231452805642705490 67.155221578 97.774057000 87.90220394
2 [1,-1,1,-1079779952922,432109467195771225] 343444999462279087088765280122 68.008824492 94.738055000 80.48547374
3 [1,-1,1,-822040310517,288067415917133325] 369848615542101461913873714338 68.082891286 93.927086000 81.67877211
4 [1,-1,1,-1997181598887,1111190865312138975] 393047963291423116150164292118 68.143729159 96.627073000 86.05307642
5 [0,0,0,-2954299893412,1958242043083352260] 416331338827329267393795115976 68.201278942 97.760303000 84.74442060
6 [1,1,0,-259000548342,50673229484108760] 526690672052975273468079853842 68.436410927 90.453891000 76.96276206
7 [0,0,0,-340886586292,76573524415850080] 551053262698111037872189081408 68.481628981 91.278050000 76.75138593
8 [1,-1,0,-276974959803684,1754083542285026429084] 588103262338544296786091980638 68.546700060 111.378448000 100.13288344
9 [1,1,1,-2096627564613,3098853501920019531] 616169217431040468495992549850 68.593319140 98.678274000 91.07018557
10 [1,-1,1,-11553946872669,14916846931835238117] 647907577800435646171387398454 68.643545570 101.847748000 90.75130549
generators for these ten

1. [1,-1,1,-2971687864242,1881785334032062641] N = 146265588369231452805642705490

E = ellinit([1,-1,1,-2971687864242,1881785334032062641]);
generators:
  [4482561,8865152879]
  [7477988089/9,-646671546785147/27]
  [7061131/4,11687528957/8]
  [2507509,-3194443949]
  [733871,309774689]
  [381704961/841,19299105149571/24389]
  [-289838819/361,13285400615601/6859]
  [458039321/10201,-1362376735634861/1030301]
  [-118509351/1369,-74068790044333/50653]
  [471521,764882639]
  [1210721,241529039]
  [1231521,299162639]
  [1403521,689017839]

2. [1,-1,1,-1079779952922,432109467195771225] N = 343444999462279087088765280122

E = ellinit([1,-1,1,-1079779952922,432109467195771225]);
generators:
  [868001,-386222953]
  [506023285/9,-11381802818335/27]
  [-941807,783841767]
  [435761,210326567]
  [525309797/961,2141121865045/29791]
  [-567624423/1681,-60001804972025/68921]
  [1411245899/2500,-6231750703207/125000]
  [1679525209/2601,8461206527245/132651]
  [2544618441/3481,37464333159093/205379]
  [579457,31137655]
  [581809,28464295]
  [595377,16393127]
  [742761,199296671]

3. [1,-1,1,-822040310517,288067415917133325] N = 369848615542101461913873714338

E = ellinit([1,-1,1,-822040310517,288067415917133325]);
generators:
  [1757055,2065071504]
  [42728143,-279259050416]
  [37910279/25,198671194832/125]
  [107822051/25,-1096900761616/125]
  [222917,-340549130]
  [-3116802905/3721,141651432697360/226981]
  [-5224172257/5329,151756017877840/389017]
  [-1740436577/3969,-187766601727760/250047]
  [-47310867833/95481,-22340261952071600/29503629]
  [-1029089,210726672]
  [522771,34324892]
  [648175,165686224]
  [843495,440954544]

4. [1,-1,1,-1997181598887,1111190865312138975] N = 393047963291423116150164292118

E = ellinit([1,-1,1,-1997181598887,1111190865312138975]);
generators:
  [1047179,-410527250]
  [382305147/4,-7474639037643/8]
  [35803/9,28359535034/27]
  [1811418921/4096,146940884979083/262144]
  [653855095/729,3997017110170/19683]
  [1093992195/961,16647185734610/29791]
  [3586921413/2704,125365005316325/140608]
  [7836785251/4761,496158023957558/328509]
  [274692667/81,4208076989630/729]
  [567535,400366834]
  [810547,157389550]
  [835429,160105120]
  [40789347/49,54630725906/343]

5. [0,0,0,-2954299893412,1958242043083352260] N = 416331338827329267393795115976

E = ellinit([0,0,0,-2954299893412,1958242043083352260]);
generators:
  [6804914,17232778306]
  [339948345/4,-6266589594445/8]
  [5398105,11971169725]
  [5736616,-13183151942]
  [1941074430/2401,-36875045165090/117649]
  [-5062670/81,1067094607310/729]
  [-35397506/25,227165850278/125]
  [-29060554/25,-244364338006/125]
  [-12169739976/10201,-2004403553914114/1030301]
  [-7431,1407194029]
  [1038032,100371938]
  [26969912786/14641,2946787620339182/1771561]
  [37056214394/80089,18832239232807094/22665187]

6. [1,1,0,-259000548342,50673229484108760] N = 526690672052975273468079853842

E = ellinit([1,1,0,-259000548342,50673229484108760]);
generators:
  [5716812,-13619266164]
  [-77364,265081164]
  [1744479,-2216197653]
  [15116481/49,-3998274468/343]
  [306882,-9736374]
  [2719783/9,-39451703/27]
  [19836513/64,6646899477/512]
  [218155926/529,1437022130958/12167]
  [537243489/961,8449410784332/29791]
  [-470164,261987864]
  [-485205/4,2267543385/8]
  [317534,21010624]
  [1803494,2333535874]

7. [0,0,0,-340886586292,76573524415850080] N = 551053262698111037872189081408

E = ellinit([0,0,0,-340886586292,76573524415850080]);
generators:
  [624618,-327632216]
  [39418858,-247462095016]
  [-637402,186790784]
  [202690,125723440]
  [430831762/1369,1089845689952/50653]
  [686194/9,-6099027904/27]
  [344637,5053423]
  [635083978/1681,2850991283464/68921]
  [157431186/361,714495829072/6859]
  [-427806,379619104]
  [352262,14275952]
  [380078,43770184]
  [407406,72906712]

8. [1,-1,0,-276974959803684,1754083542285026429084] N = 588103262338544296786091980638

E = ellinit([1,-1,0,-276974959803684,1754083542285026429084]);
generators:
  [7783204,-8359959602]
  [483365353,-10621086883625]
  [2478645817/289,15087128972336/4913]
  [57213823279/5476,352407109696907/405224]
  [7705282075/529,346194711627701/12167]
  [3486961783/196,136000760273993/2744]
  [6030610310/289,349455025503774/4913]
  [4540845766/81,293764161962926/729]
  [133077578,1523630001522]
  [-42634157/4,473016162569/8]
  [5074582,21888759598]
  [10597442,2996591268]
  [10737316,4239683230]

9. [1,1,1,-2096627564613,3098853501920019531] N = 616169217431040468495992549850

E = ellinit([1,1,1,-2096627564613,3098853501920019531]);
generators:
  [683262535,17859616611932]
  [288296611,-4895157233032]
  [7407149815/49,637439985561476/343]
  [201394315/9,-2852764946836/27]
  [2444898535/361,-118733847946012/6859]
  [4973701615/1369,333741895623596/50653]
  [851011031/625,25987472156604/15625]
  [5385161815/9409,-1318545067992964/912673]
  [31768615/289,-8322996362084/4913]
  [-1563065,1599901532]
  [-1403705,1810690652]
  [-1200665,1971723932]
  [581575,1440616412]

10. [1,-1,1,-11553946872669,14916846931835238117] N = 647907577800435646171387398454

E = ellinit([1,-1,1,-11553946872669,14916846931835238117]);
generators:
  [235365247,3610391543784]
  [45664505,-307771240612]
  [3368691591/25,195450266247624/125]
  [6173361,-13376915758]
  [455452163/169,-4025711969752/2197]
  [493348189/225,1188303798308/3375]
  [15918703/9,3205450496/27]
  [2124017159/1849,-141386196947656/79507]
  [13566381/16,-153224611837/64]
  [538095,2975555048]
  [7101723/4,45821997/8]
  [2145519,62133992]
  [3880287,5337370728]

Rank 14

# a-invariants conductor N log N naive h log abs(disc)
1 [1,-1,1,-213052086519005,1343673148929618519397] 625353740210974601185343420435550 75.515870264 110.822533000 101.79018666
2 [1,-1,0,-1684202952742,760174043166111016] 1836678033333873749496674545041850 76.593266592 96.070544000 86.92038656
3 [0,1,1,-33809307174946,75926969868538036360] 1923929779410106546772100007492755 76.639677923 105.075753000 92.63821778
4 [1,-1,1,-278227287557022,1785956181254759086125] 2049815854451697632132410185685814 76.703058031 111.391981000 95.99144197
5 [0,1,0,-3080764689305,2067263364126837739] 2721113685537741251345170277399464 76.986349309 97.882200000 86.11851190
6 [1,-1,0,-584282168617939,5442676050888382468969] 2779061468451421649901151652229142 77.007421338 113.620261000 100.14964280
7 [1,-1,0,-758385334271139,8150391984971115451889] 3706404056674879434550378287528762 77.295370218 114.427851000 103.36978893
8 [0,0,0,-890565484228,325628388845214052] 3765942921545589838460939994650360 77.311306343 94.172212000 82.38648016
9 [1,-1,1,-12234946757089727,522282753360625288065895] 3775206800801566325462893754646906 77.313763232 122.748138000 110.05380316
10 [1,0,1,-4934088730268,4171303846141087502] 4345716756680987001591104606225802 77.454498775 99.295170000 88.03515655
generators for these ten

1. [1,-1,1,-213052086519005,1343673148929618519397] N = 625353740210974601185343420435550

E = ellinit([1,-1,1,-213052086519005,1343673148929618519397]);
generators:
  [2866374349/361,-84758354771350/6859]
  [7665031039,-671077333502440]
  [8822959,-12282156760]
  [6098819611/169,-443011095502780/2197]
  [4106046871/289,169065860809600/4913]
  [75266809549/4761,14416691103416950/328509]
  [1894039255/81,69713613614024/729]
  [14040387703/121,1651104417096760/1331]
  [973929731599/7921,954660463835688280/704969]
  [-14549777,36931570280]
  [-12157601,46232625080]
  [4626619,21375195260]
  [4901359,20422418600]
  [22475029,88916054780]

2. [1,-1,0,-1684202952742,760174043166111016] N = 1836678033333873749496674545041850

E = ellinit([1,-1,0,-1684202952742,760174043166111016]);
generators:
  [-1442506,434362668]
  [19411798934,-2704582502363252]
  [-17405214/25,-157836656906/125]
  [317659538/121,-5058224219472/1331]
  [17814333/16,-32994695333/64]
  [245262491/484,-2046550045781/10648]
  [197592618/361,327684681656/6859]
  [10829761/9,18609544651/27]
  [150779700/121,1027085074424/1331]
  [513339,175471253]
  [988858,247861758]
  [1015284,310595768]
  [1448299,1164973728]
  [1632594,1536066368]

3. [0,1,1,-33809307174946,75926969868538036360] N = 1923929779410106546772100007492755

E = ellinit([0,1,1,-33809307174946,75926969868538036360]);
generators:
  [339163595,-6245258752166]
  [54969047,-405353825906]
  [-5370628,10128954655]
  [-19078495/16,684967423495/64]
  [617226509/196,2274579419153/2744]
  [356738365331/105625,17666793356132146/34328125]
  [488952140699/133225,54983085041745482/48627125]
  [35848051/9,56979520334/27]
  [200391158/49,844264688065/343]
  [-6627961,2974615582]
  [3177479,761333662]
  [3388874,520491007]
  [3968357,2062208644]
  [35721064,210827184967]

4. [1,-1,1,-278227287557022,1785956181254759086125] N = 2049815854451697632132410185685814

E = ellinit([1,-1,1,-278227287557022,1785956181254759086125]);
generators:
  [140887583/4,-1511313370165/8]
  [222461361,-3309082989933]
  [-779681811/49,16033649006481/343]
  [6326741,16697996731]
  [387274749/49,3079451749821/343]
  [7663725,-10192542901]
  [1390630309/169,-16107785453501/2197]
  [62834178453/6889,-1520455157203335/571787]
  [90142123/9,54097417595/27]
  [9432151,895337397]
  [9472761,625090371]
  [10751821,6112989991]
  [13876745,24431334035]
  [14902473,30802899939]

5. [0,1,0,-3080764689305,2067263364126837739] N = 2721113685537741251345170277399464

E = ellinit([0,1,0,-3080764689305,2067263364126837739]);
generators:
  [1597859,1106443602]
  [215778031,-3169542035006]
  [12469231/9,18280530746/27]
  [4362961782/529,-282126747457895/12167]
  [3464775974/2401,-93127388912937/117649]
  [350583669/289,-1667461899022/4913]
  [22465179/25,19560641942/125]
  [3444223261/3721,21163669009786/226981]
  [559898971/625,-2535436778606/15625]
  [511995,790026142]
  [797731,342488494]
  [921355,104498558]
  [1080975,12717058]
  [1081627,20977246]

6. [1,-1,0,-584282168617939,5442676050888382468969] N = 2779061468451421649901151652229142

E = ellinit([1,-1,0,-584282168617939,5442676050888382468969]);
generators:
  [1174245310/81,-3188249424937/729]
  [117021216,-1240846039315]
  [12935699,7003385098]
  [27413016004/2025,339101893559827/91125]
  [881685873/64,1443161169451/512]
  [773195614/49,4225731459977/343]
  [35929953972/961,5640976087999433/29791]
  [222745774408/4489,94445822962739039/300763]
  [476735570296/6241,314344829682008931/493039]
  [-22182722,86545030307]
  [3937749,56592887138]
  [13655535,3216147943]
  [14195412,3003436405]
  [14739758,5725413835]

7. [1,-1,0,-758385334271139,8150391984971115451889] N = 3706404056674879434550378287528762

E = ellinit([1,-1,0,-758385334271139,8150391984971115451889]);
generators:
  [2174879536,101417641647895]
  [2347441138,-113727842009933]
  [10959306316/25,1145055790593599/125]
  [183315797,-2455574362790]
  [125466923410/5329,-22507243119654749/389017]
  [137949214666/7225,15419064412137259/614125]
  [141791006098/7921,12421236928564355/704969]
  [16066001,-10641489750]
  [17430308845/1296,-913861638737767/46656]
  [-22717445,116865529747]
  [-13501966,126215446323]
  [-491878,92321998735]
  [8137561,50174148445]
  [9636058,41675988775]

8. [0,0,0,-890565484228,325628388845214052] N = 3765942921545589838460939994650360

E = ellinit([0,0,0,-890565484228,325628388845214052]);
generators:
  [55236746,-410467861030]
  [488154136/25,-10773012863366/125]
  [-52634522/49,70973199254/343]
  [171894,421455302]
  [14619224474/30625,516416757022118/5359375]
  [4456714/9,2101198690/27]
  [92769128/169,102488039386/2197]
  [73746592/81,378452351078/729]
  [2264385016/1521,89950285855630/59319]
  [110062,478481162]
  [486898,86270390]
  [520398,55776310]
  [540906,46626970]
  [673432,176922818]

9. [1,-1,1,-12234946757089727,522282753360625288065895] N = 3775206800801566325462893754646906

E = ellinit([1,-1,1,-12234946757089727,522282753360625288065895]);
generators:
  [4693272499/289,2813156868745846/4913]
  [113673131155,-38325442061818090]
  [-15973841,844783640330]
  [-8834055053/289,4576593586671286/4913]
  [-121225525229/961,-7195187080674838/29791]
  [16776534403/529,-4959851933354150/12167]
  [162978971,1690277868302]
  [365595040603/1369,204497957552813630/50653]
  [201821996899/625,85925265844795718/15625]
  [-68207209,1019582606342]
  [-6666029,776884953302]
  [65671123,44907928022]
  [404844271,7868886384326]
  [-2162723772413/18769,1630755915635913766/2571353]

10. [1,0,1,-4934088730268,4171303846141087502] N = 4345716756680987001591104606225802

E = ellinit([1,0,1,-4934088730268,4171303846141087502]);
generators:
  [131498481/121,404397049823/1331]
  [12241698495,-1354454666535437]
  [3690759273/4096,177088565897515/262144]
  [-218809617/5476,846954951858845/405224]
  [-293032974/361,18963404321077/6859]
  [-1647802671/841,-61274294944483/24389]
  [-22279521/49,-862262174411/343]
  [10117741512/2401,897352701867469/117649]
  [86863205283/10609,24737074412460517/1092727]
  [-2504766,904308382]
  [210516,1772443378]
  [758886,929105155]
  [1137081,175607905]
  [1428891,195342355]

Rank 15

# a-invariants conductor N log N naive h log abs(disc)
1 [0,1,0,-2176181004084740,38634864427450373637984] 2900836471454746643444186032359612504 83.958062482 117.562647000 106.30758942
2 [0,0,0,-6444421059559,6276680644075449226] 3425148201540012310824333672243640232 84.124208089 100.096311000 87.58994399
3 [0,0,1,-207242089946857,1148141454762714130566] 15459554382087158087678575436367936383 85.631290567 110.508329000 95.00875425
4 [1,-1,0,-1871334218805892,30990402608130412495516] 17399038455669600535830935804330341450 85.749478291 117.109887000 105.12272866
5 [1,1,1,-23071149566978913,1338645488637948810320031] 22289397489264490553116463505910081350 85.997174464 124.645681000 112.99261548
6 [1,1,1,-54097496892045,201832371761861463171] 27616402753065013663845267238419134118 86.211473247 107.031084000 98.71889416
7 [1,-1,0,-2780765160676384,50673295072696834664140] 27920388764832770364990215814812715970 86.222420550 118.298111000 109.20316754
8 [1,0,1,-1288158765513114,18255142829604704331112] 36430565911780606913115971672433708630 86.488471493 116.040613000 105.58532196
9 [0,0,1,-72207531729307,146901717978901791450] 44849853616257127472030900696938178795 86.696383672 107.345299000 99.40133587
10 [0,0,1,-303753802926397,1585920252682476900486] 45796689754878855399649023421714308587 86.717275160 111.655319000 103.26980108
generators for these ten

1. [0,1,0,-2176181004084740,38634864427450373637984] N = 2900836471454746643444186032359612504

E = ellinit([0,1,0,-2176181004084740,38634864427450373637984]);
generators:
  [95389144,-836065261512]
  [-11292200279/256,904846690877931/4096]
  [6006181438/121,-306180601257330/1331]
  [29707596241/784,-2258093405000511/21952]
  [896169346/25,-10222972115694/125]
  [3575322136/121,-15234908231016/1331]
  [288474214/9,1149496610678/27]
  [137835633646/1849,42865256373910686/79507]
  [5075789926/49,329841082639074/343]
  [-53406074,50307852114]
  [-46033670,203131905678]
  [-27716033,278673840666]
  [-12474209,252665670114]
  [37848940,102415465728]
  [1183641478,40690944816210]

2. [0,0,0,-6444421059559,6276680644075449226] N = 3425148201540012310824333672243640232

E = ellinit([0,0,0,-6444421059559,6276680644075449226]);
generators:
  [205667647/169,1068132770548/2197]
  [84604237,-777848164214]
  [-14153239/25,390184488866/125]
  [963817501/625,-1207268773126/15625]
  [2331968545/1521,794748466234/59319]
  [60611982/49,-152544160448/343]
  [2546179477/1849,9285299324558/79507]
  [122634570795/1681,42920007952631444/68921]
  [9321347773/121,899466761884954/1331]
  [-2881287,961767266]
  [1545435,91194044]
  [1917925,985763326]
  [2015847,1215478724]
  [2107297,1433264326]
  [4071833,6895386046]

3. [0,0,1,-207242089946857,1148141454762714130566] N = 15459554382087158087678575436367936383

E = ellinit([0,0,1,-207242089946857,1148141454762714130566]);
generators:
  [18570632,60860073189]
  [264270378,-4289838564517]
  [49149833/4,170991163287/8]
  [21473330,-81236690628]
  [5788422097/576,-123931800606439/13824]
  [306191833/36,188314243831/216]
  [66603478978/7921,159655606556427/704969]
  [34367609/4,-10729065873/8]
  [23872597202/2809,-124161029317284/148877]
  [-7234352,47631793266]
  [7158514,5606179971]
  [7939866,1791053300]
  [32651401/4,4822352919/8]
  [8817493,2515916333]
  [417037434/49,309849249900/343]

4. [1,-1,0,-1871334218805892,30990402608130412495516] N = 17399038455669600535830935804330341450

E = ellinit([1,-1,0,-1871334218805892,30990402608130412495516]);
generators:
  [200289730/9,516700688782/27]
  [82920331724,-23877686245612062]
  [-60203007636/1681,15728847373574938/68921]
  [3549888879/121,-48758427486422/1331]
  [126057361114/4761,678087611732842/328509]
  [10105627386/1849,-11501549477995924/79507]
  [1027224665/121,-166862459691259/1331]
  [107964379774/2601,20900790368928788/132651]
  [36188465095/729,4837832217483058/19683]
  [-49896806,11702275428]
  [-41324781,194316825203]
  [7303974,133082330588]
  [17211599,62285033563]
  [29076374,34058733838]
  [41178724,154114045838]

5. [1,1,1,-23071149566978913,1338645488637948810320031] N = 22289397489264490553116463505910081350

E = ellinit([1,1,1,-23071149566978913,1338645488637948810320031]);
generators:
  [-147755895,-1233524944378]
  [7517998059,-651730202050648]
  [1641665,-1140515973858]
  [53493939735/361,-7431407469586912/6859]
  [8223014665/64,-360409447024241/512]
  [84360012615/1156,-8212134390696457/39304]
  [52658255755/676,2089863784415497/17576]
  [750355329681/7744,77304692446879061/681472]
  [100142047921/1024,4357913745529351/32768]
  [-175199465,54648075032]
  [-135391745,1407346218272]
  [-126949265,1490560681232]
  [76227055,151361635472]
  [80911135,40288046432]
  [100553415,188250345392]

6. [1,1,1,-54097496892045,201832371761861463171] N = 27616402753065013663845267238419134118

E = ellinit([1,1,1,-54097496892045,201832371761861463171]);
generators:
  [5478553,-8362922878]
  [150702183,-1847957605468]
  [4522315159/625,-214993869640348/15625]
  [11270999,-32004319404]
  [1588960599/841,251511024611244/24389]
  [-12699778053/1681,923202048955944/68921]
  [-2405802545/289,42650446902796/4913]
  [1685925295/361,48989312567708/6859]
  [2580751671/529,89400441719532/12167]
  [-8594737,5652063492]
  [-4504937,18820141844]
  [-662153,15406916468]
  [1127503,11927161772]
  [1544799,11042285604]
  [5752695,8997280532]

7. [1,-1,0,-2780765160676384,50673295072696834664140] N = 27920388764832770364990215814812715970

E = ellinit([1,-1,0,-2780765160676384,50673295072696834664140]);
generators:
  [-458244626/9,6628720351414/27]
  [43243201386,-8992438550589368]
  [-540605786/9,845447151584/27]
  [2403656164/9,-115687706955926/27]
  [315226383591/3481,-151135130218551122/205379]
  [1328562381/121,-195009477320783/1331]
  [68232339/4,-724600580879/8]
  [373093743771/7921,109636172501910838/704969]
  [21747291321/361,2187986471977313/6859]
  [-19433939,312058982907]
  [10246166,152496667722]
  [16310406,98261538592]
  [19610066,60681621672]
  [20747111,43703377207]
  [39226236,44157963682]

8. [1,0,1,-1288158765513114,18255142829604704331112] N = 36430565911780606913115971672433708630

E = ellinit([1,0,1,-1288158765513114,18255142829604704331112]);
generators:
  [68022881,-495392856741]
  [452196449,-9586759395645]
  [-672993994/121,211493434867479/1331]
  [255214901/16,2689196918301/64]
  [4988089484/289,167538924668592/4913]
  [35029826993/1681,1478795446155987/68921]
  [598173041/25,4203363821499/125]
  [91009857374/1225,24725876407370487/42875]
  [2542013264/25,121091642247528/125]
  [10315646,77870815749]
  [19316096,24073600599]
  [21778811,23024484009]
  [24098849,34737266475]
  [25583426,45200921049]
  [28748411,70571440809]

9. [0,0,1,-72207531729307,146901717978901791450] N = 44849853616257127472030900696938178795

E = ellinit([0,0,1,-72207531729307,146901717978901791450]);
generators:
  [-29377223/4,134121776671/8]
  [1269516438,-45232207082913]
  [-1503459103/169,20279951898539/2197]
  [314372861/25,-4379194784141/125]
  [29206633727/2809,-3395511825473516/148877]
  [7232663,-1731994213]
  [4635303127/529,166364559251004/12167]
  [2372458807/169,95759216447799/2197]
  [11616234427/729,1085637852622396/19683]
  [-9016872,8054824782]
  [-5598937,19382237412]
  [-4098412,19339001637]
  [10920813,25705997712]
  [13873373,42606976367]
  [45145553,298159605567]

10. [0,0,1,-303753802926397,1585920252682476900486] N = 45796689754878855399649023421714308587

E = ellinit([0,0,1,-303753802926397,1585920252682476900486]);
generators:
  [-433017551/25,-5078789186082/125]
  [7372149979,-632980061346154]
  [-6829233377/729,-1182513204400150/19683]
  [4111515831/121,-232439138194925/1331]
  [60680069813/2209,-12271184932318350/103823]
  [1303064299/225,15468581042407/3375]
  [17674448819/4225,5412512068075878/274625]
  [8099507889/400,489082843847287/8000]
  [21942080647/729,2763420186495203/19683]
  [-19385816,13749718181]
  [-10583848,60126737450]
  [6956697/4,260817175839/8]
  [17921069,43565380673]
  [49652604,330024762153]
  [125291281/9,200680226387/27]

Rank 16

# a-invariants conductor N log N naive h log abs(disc)
1 [1,-1,1,-80616432047323437,8848311542285694409453845] 1306046612716079154116875733335056508018 90.067823348 128.407683000 116.19770714
2 [1,1,0,-214690684828225,1234522870323369723625] 6686283657824244240901969615219363968150 91.700876840 110.653089000 99.93038796
3 [1,-1,1,-11787619440588782,492945352107197232466685] 6872032306498553291336308079119666264818 91.728278513 122.632516000 108.63014858
4 [1,1,0,-356181280978227,2579091857646540795945] 27175971268218999870987545081109578626254 93.103151800 112.132986000 99.62229909
5 [1,0,0,-69283937711206345,7369712716702797558539801] 29109434091169948293553656515843844039762 93.171880944 128.041987000 118.21018944
6 [0,1,1,-71144170500499672,7306006044364626753567322] 37096807484877365829693257492215827538671 93.414349541 128.024624000 113.09294391
7 [1,-1,1,-1074165304813047,14616391394613548743119] 40531433402643104717643452250340307599810 93.502896433 115.596007000 106.17897271
8 [0,0,1,-28153341138661675,1814372863373355693034056] 45610300416068014360512834699213194395225 93.620952204 125.242930000 112.31831670
9 [1,-1,0,-114590917776624,496524101894893328804] 62979444499453069527560665784219464167354 93.943627022 108.831473000 99.03122336
10 [0,0,0,-311207933239563412,67086737262927137217359140] 64327933600498682703332055234381017134072 93.964812590 132.459203000 120.15796038
generators for these ten

1. [1,-1,1,-80616432047323437,8848311542285694409453845] N = 1306046612716079154116875733335056508018

E = ellinit([1,-1,1,-80616432047323437,8848311542285694409453845]);
generators:
  [2777261111/25,-140517901928456/125]
  [1292362947791,-1469186496066928168]
  [3901741699/25,-32614473273192/125]
  [71633986999/441,-1835490305856040/9261]
  [-895098551/9,107603371694182/27]
  [-116504398401/625,65175853629211832/15625]
  [-11257916641/49,1339159208859368/343]
  [2915376603767/10201,3116684883829586680/1030301]
  [4838515494191/12769,8251907239193308120/1442897]
  [-171458977,4198911813512]
  [-103137009,4008262618776]
  [114717485,1053456252550]
  [153989839,292739066200]
  [235520739,1710382049220]
  [1422371527/9,6329453307464/27]
  [3939647479/25,30010707010232/125]

2. [1,1,0,-214690684828225,1234522870323369723625] N = 6686283657824244240901969615219363968150

E = ellinit([1,1,0,-214690684828225,1234522870323369723625]);
generators:
  [406502199,8190402784351]
  [692610779315/289,-576408276155132990/4913]
  [12134778060/121,1323158291626595/1331]
  [920863064890/25281,-821335966829761205/4019679]
  [6789246536160/243049,-15640202749761377615/119823157]
  [14481553564/1225,800284420586267/42875]
  [-20934868781910/2948089,248049014947112412785/5061868813]
  [-163089752790/14641,-83907277253653355/1771561]
  [-259240643990/17689,-82599261913293215/2352637]
  [-16414310,18339113605]
  [2979880,24923012035]
  [5809435,13538035570]
  [6430831,10943665591]
  [8691105,5006538310]
  [9215344,6213520051]
  [38050795/4,58231918805/8]

3. [1,-1,1,-11787619440588782,492945352107197232466685] N = 6872032306498553291336308079119666264818

E = ellinit([1,-1,1,-11787619440588782,492945352107197232466685]);
generators:
  [17040590065/9,-2220918337766527/27]
  [718498105,-19051361441325]
  [-1664956895/81,621394136708275/729]
  [2671041745/441,6014436967097399/9261]
  [358423237/9,7948129076633/27]
  [4822324777/81,34065514060795/729]
  [9513112513/121,303947321239049/1331]
  [17274894849/169,1310875269646639/2197]
  [127711263,1034598196429]
  [-124808543,141401557435]
  [3187677,674833659847]
  [57632265,70840364755]
  [61375455,25909564819]
  [906456721,27103248364587]
  [5716344945/121,271136707073129/1331]
  [10577575011/169,41332223651965/2197]

4. [1,1,0,-356181280978227,2579091857646540795945] N = 27175971268218999870987545081109578626254

E = ellinit([1,1,0,-356181280978227,2579091857646540795945]);
generators:
  [89683656,-831895364115]
  [975497418,-30462493578273]
  [-539772204/25,-1785822408021/125]
  [25501515/4,190541064885/8]
  [1192833888/121,6760691702025/1331]
  [10388261,-222241536]
  [1145688279/100,-1488003406353/1000]
  [24515737506/961,2992813648007805/29791]
  [155527883352/5329,50780192942651715/389017]
  [-21741707,6773781355]
  [10027808,3962366157]
  [11394978,26617347]
  [11436336,1193905539]
  [11724008,3829819435]
  [12782957,10709402307]
  [103040476/9,37069519493/27]

5. [1,0,0,-69283937711206345,7369712716702797558539801] N = 29109434091169948293553656515843844039762

E = ellinit([1,0,0,-69283937711206345,7369712716702797558539801]);
generators:
  [1346476346,48530143705763]
  [6102869144,-476328541126339]
  [106124746346/121,33175165369333753/1331]
  [276942260,-3069781319629]
  [2333150986/9,-70569818073295/27]
  [785946521930/4489,-234210822742610767/300763]
  [800219262026/5041,-218203324958181707/357911]
  [91329479834/625,-9450357524178373/15625]
  [69559027097/1024,-56536946495389133/32768]
  [-130452742,3766755858659]
  [-30673834,3076710999263]
  [42194234,2126349210275]
  [152482394,591938921411]
  [169517690,704302845731]
  [244713530,2251453751459]
  [269575346,2877841135763]

6. [0,1,1,-71144170500499672,7306006044364626753567322] N = 37096807484877365829693257492215827538671

E = ellinit([0,1,1,-71144170500499672,7306006044364626753567322]);
generators:
  [41348686516,-8407823065766567]
  [193333166,-881946689534]
  [90321730408/729,12344009388980347/19683]
  [37117496441/256,806873503852723/4096]
  [1498178718628/9801,50067871774808707/970299]
  [287655483827/1849,4512794570094271/79507]
  [11638177409/64,316453922863841/512]
  [730569066266/3721,216073940389063393/226981]
  [1669327609967/6889,1184980496613801491/571787]
  [-171287239,3803504146636]
  [139389395,312275472061]
  [151982762,62704623730]
  [158211527,101750260009]
  [715164125,17950038866383]
  [-9652294462/49,1268482754178667/343]
  [-3988104319/25,477553268917004/125]

7. [1,-1,1,-1074165304813047,14616391394613548743119] N = 40531433402643104717643452250340307599810

E = ellinit([1,-1,1,-1074165304813047,14616391394613548743119]);
generators:
  [4216009983/169,-127090566061018/2197]
  [151957383859,-59235663718540818]
  [5944152523/169,-313428028238538/2197]
  [17906711123/484,-1701119523485957/10648]
  [-261954463229/6889,-12529943037771726/571787]
  [-1786655953/49,-24978963423266/343]
  [-19661034323/841,-4003623464424046/24389]
  [124339818183/2209,37788052188504598/103823]
  [7804101104979/14641,21760728444439072238/1771561]
  [-21157693,166959829886]
  [2034777,111529826586]
  [15711427,40217391486]
  [17337627,34697072286]
  [24997277,58168926136]
  [26150067,66387166046]
  [151372843/9,976149321322/27]

8. [0,0,1,-28153341138661675,1814372863373355693034056] N = 45610300416068014360512834699213194395225

E = ellinit([0,0,1,-28153341138661675,1814372863373355693034056]);
generators:
  [6484729345/64,22964009980929/512]
  [42007214289/4,-8608564247333691/8]
  [9053728745/361,7272071962671863/6859]
  [7549763446/81,3606917581754/729]
  [1371153905/16,-11281432672087/64]
  [334387348480/9801,-917207068192023592/970299]
  [299465006545/1936,91768697484640263/85184]
  [1637438438219/3025,2004667692337981703/166375]
  [18684442096/25,2494489206349144/125]
  [-189928820,556964658932]
  [88674505,123092605317]
  [93125315,14036850782]
  [93166391,10476218798]
  [109110830,203768928317]
  [129211365,577840375157]
  [271304225,3761099108357]

9. [1,-1,0,-114590917776624,496524101894893328804] N = 62979444499453069527560665784219464167354

E = ellinit([1,-1,0,-114590917776624,496524101894893328804]);
generators:
  [-1334654,-25437215966]
  [6794357778751/25,-17710182423527493214/125]
  [453226801/256,-70853714286161/4096]
  [8709978254/169,-796713184890180/2197]
  [198795941938/6889,-83300531904674380/571787]
  [2868102763/484,-53870864149481/10648]
  [-2968975298219/286225,3653768928934294741/153130375]
  [14200374826/841,1416814579345346/24389]
  [88906699874/3025,24962984449107822/166375]
  [-12325466,6044477788]
  [-7108502,30856358572]
  [-2927984,28408199074]
  [5053447,6816305983]
  [6518032,5147828578]
  [7047982,6240765478]
  [238988374/49,2511522954340/343]

10. [0,0,0,-311207933239563412,67086737262927137217359140] N = 64327933600498682703332055234381017134072

E = ellinit([0,0,0,-311207933239563412,67086737262927137217359140]);
generators:
  [271155938,-1624113824066]
  [230174631966,-110429450671948562]
  [292625561,-1037682878933]
  [11184942718/9,-1079920003564486/27]
  [2505004634306/3025,-3231471655940317454/166375]
  [87996987616/225,-7692724001118086/3375]
  [-613448983366/5329,3917037166077763294/389017]
  [3134903728/9,26281526980814/27]
  [3439312806334/9801,1013633882782748794/970299]
  [-629073894,3730096228978]
  [327645170,542323542110]
  [336047522,674711700418]
  [359203358,1283258781934]
  [446121094,4127848331614]
  [3334310832,189997506921418]
  [7821916161/25,73431470677159/125]

Rank 17

# a-invariants conductor N log N naive h log abs(disc)
1 [0,0,0,-143352735666059647,20308350490107193886372290] 837877902601733961103246999529573248471046104 103.439446295 130.125857000 119.77058409
2 [0,1,0,-9825556066930749980,11729178538780483196526641904] 1581722370777087577044826670736769612479144504 104.074843546 142.808158000 131.49182928
3 [1,-1,1,-417021599588606487,103355942904397210370672175] 2046819555713424945668705479118862619827345878 104.332616337 133.329346000 120.71470446
4 [1,0,0,-503897620966323620,151217417043830260627562256] 2206369951742974882400755286879288413262834238 104.407677794 134.084667000 124.86424636
5 [0,-1,0,-2569048307069387108,1622434557263521518889966212] 2713126118888294398313627472411615188672713800 104.614430704 138.830596000 128.29052027
6 [1,0,0,-20041798012414773644650,1091040202112161863735130035418532] 4111423344469783039462650315957622792007824170 105.030098466 165.669924000 151.94787206
7 [1,-1,1,-17647330988340345402,28400013493631012572109825145] 4190506510606183610086555829247330835129764106 105.049150797 144.564952000 132.44186331
8 [1,0,0,-5514848603805151010,4968573874922595458725358916] 4417713314635932233592727617217483889651187474 105.101951397 141.075531000 128.58534282
9 [1,-1,1,-685990640466912207377,6868986816410030691695751537025] 4611183920987854374283972944656606152532275998 105.144813825 155.545790000 143.77967821
10 [1,0,0,-22838565855447084625,41855387033877832055344377641] 5240227668680445150085901505663732024266517078 105.272694130 145.338550000 132.96957277
generators for these ten

1. [0,0,0,-143352735666059647,20308350490107193886372290] N = 837877902601733961103246999529573248471046104

E = ellinit([0,0,0,-143352735666059647,20308350490107193886372290]);
generators:
  [64691739533/361,4194967326506266/6859]
  [8638785114,-802173562805774]
  [169948966,924271589272]
  [362536742198/961,-132954938600871284/29791]
  [344876473955/1369,-21646811490452600/50653]
  [-66646890227/2601,-649376911062102374/132651]
  [368659519105/3249,-434443881559264370/185193]
  [12724521729823/6561,44581225013874726616/531441]
  [21704078576389/8649,100022351135707123714/804357]
  [-181418186,6351708994076]
  [271402042,1180401152198]
  [439985993,6512374354426]
  [1025145645,30833434172810]
  [1316329261,45961316037002]
  [3835135961,236386839806198]
  [1038932313/4,6180366347291/8]
  [1090269381/25,470032742809346/125]

2. [0,1,0,-9825556066930749980,11729178538780483196526641904] N = 1581722370777087577044826670736769612479144504

E = ellinit([0,1,0,-9825556066930749980,11729178538780483196526641904]);
generators:
  [25873381585/16,531760400746047/64]
  [516299164312,-370974576290472396]
  [338916255310/361,395935173861573918/6859]
  [4041003897070/1849,-2094983694559514286/79507]
  [567636640510/289,13687326089777574/4913]
  [5603822114530/2809,1220828128491111354/148877]
  [14206042748770/3721,39225026388754449738/226981]
  [5714756752315/361,13411534833860978232/6859]
  [10214446450078/289,32521133790849449658/4913]
  [222441304,97747508716308]
  [888492910,60832848037302]
  [1323753142,32283278684514]
  [1358667670,29792340963198]
  [1460007370,22270550032698]
  [1644786382,4232600886294]
  [2061958324,15364314566172]
  [2821020727,80381650463334]

3. [1,-1,1,-417021599588606487,103355942904397210370672175] N = 2046819555713424945668705479118862619827345878

E = ellinit([1,-1,1,-417021599588606487,103355942904397210370672175]);
generators:
  [13618911113,-1587579791136518]
  [235058115115/4,-113956120507500103/8]
  [-5531142222173/8649,8378753474241730678/804357]
  [-273727804921/1444,727128101828618189/54872]
  [-55504839701/1849,855754346499038874/79507]
  [84443357189/289,-12480001600674134/4913]
  [244658263411/625,-4846130276349234/15625]
  [3615739036259/6889,3082418380588634354/571787]
  [14181005639199/15625,42452495157615844582/1953125]
  [-471626029,13969125605806]
  [-278934565,14070509729534]
  [287646331,2683358670726]
  [395688243,545681931902]
  [435423251,2080267808366]
  [-14468988836363/58081,193847542942556056810/13997521]
  [49712645723/121,1559333745622474/1331]
  [603721730043/1369,115658088293130950/50653]

4. [1,0,0,-503897620966323620,151217417043830260627562256] N = 2206369951742974882400755286879288413262834238

E = ellinit([1,0,0,-503897620966323620,151217417043830260627562256]);
generators:
  [-193706366816/4225,3624885400727474372/274625]
  [42253105720,-8684166653830244]
  [-136476213812/169,12332387459519548/2197]
  [512863041832/841,-205098352444218004/24389]
  [749702024641/1600,-271418487280602059/64000]
  [46253709574/625,-167072182141200968/15625]
  [6068695111360/10201,8111897954078304404/1030301]
  [861962257804/1225,516332685739014488/42875]
  [2957428636894/3481,3766535517767942504/205379]
  [-813698456,4742154722716]
  [-264387848,16308438884764]
  [-107911400,14294706820684]
  [324300388,4680664208908]
  [373632808,3886254383164]
  [476912488,4401347439004]
  [519152152,5434740818764]
  [697112536,11777468780428]

5. [0,-1,0,-2569048307069387108,1622434557263521518889966212] N = 2713126118888294398313627472411615188672713800

E = ellinit([0,-1,0,-2569048307069387108,1622434557263521518889966212]);
generators:
  [293329333,29901438124586]
  [3658721751842,-6998323787696249400]
  [-139813143752/2209,4386177725162992150/103823]
  [28371858317/4,-4666464893246457/8]
  [278507781193/144,-107753672975689475/1728]
  [-181856253343/1936,-3676680723630035625/85184]
  [457630773857/256,214500837640263825/4096]
  [2378340437,94686078450750]
  [2911042190068/1089,4230241193556718550/35937]
  [-1756677472,26729481432066]
  [-1509205408,45410764598850]
  [359420092,27303806932850]
  [588021262,17751029707600]
  [721845092,12004353042150]
  [960473237,6401364197550]
  [6738067262,538730651436600]
  [23130358562,3509594452371000]

6. [1,0,0,-20041798012414773644650,1091040202112161863735130035418532] N = 4111423344469783039462650315957622792007824170

E = ellinit([1,0,0,-20041798012414773644650,1091040202112161863735130035418532]);
generators:
  [-130573977196,38493547337746598]
  [68197162001804,-563181712878156877402]
  [-152815103813956/961,477655205467285192418/29791]
  [1552676481202796/1849,-60363169608172912817014/79507]
  [23685191803169/256,-21959197471520058457/4096]
  [7174385321524/81,-2389955796251228458/729]
  [585866243202956/6889,742038827805038482426/571787]
  [2840799181284689/10816,132836607878046476313547/1124864]
  [150104707896551/484,1673631056955890802419/10648]
  [-103059437416,45408385826334278]
  [41077334804,18359943801826598]
  [49573934804,14809468030438598]
  [69591695924,5773210447737158]
  [77414194244,1860211677889718]
  [83859215204,282108551537798]
  [84035997524,523442602488518]
  [85147414004,1363288817801798]

7. [1,-1,1,-17647330988340345402,28400013493631012572109825145] N = 4190506510606183610086555829247330835129764106

E = ellinit([1,-1,1,-17647330988340345402,28400013493631012572109825145]);
generators:
  [433624867889/121,-140748355475504395/1331]
  [26132313447363,-133587808394463064243]
  [12647045258489/3025,-27689699968178292223/166375]
  [12340590597649/529,-42692197259537722543/12167]
  [-11141979068607/6889,131276711176987915549/571787]
  [-2148070474463/961,-7092359957392389383/29791]
  [-12143925905509/8836,-185831212923264246361/830584]
  [18508411072177/9409,-32877763610095486233/912673]
  [207614941242493/11664,2914715444549641249949/1259712]
  [-4372082703,148268077800455]
  [-3263910659,226338807016767]
  [2278548809,4408313301655]
  [2573995793,5453011398727]
  [3070927305,56274685848735]
  [4299866625,178934838587495]
  [6199369265,396548237679815]
  [20145888073/9,287619014350685/27]

8. [1,0,0,-5514848603805151010,4968573874922595458725358916] N = 4417713314635932233592727617217483889651187474

E = ellinit([1,0,0,-5514848603805151010,4968573874922595458725358916]);
generators:
  [-27356441891/16,6204912683086675/64]
  [1010800485070,-1016242158296919806]
  [-280469284136/121,96880198110210926/1331]
  [-11028316272095/4096,4529624980760925841/262144]
  [-959279324,-96829831448114]
  [542366276377/256,216511973929855189/4096]
  [2127110104606/729,2305415804755252240/19683]
  [57112607887015/7396,413608361297973271379/636056]
  [77118090890905/7744,659874938142961390393/681472]
  [811481584,32057952508846]
  [844584292,30220108094734]
  [1244133328,5754442522414]
  [1279997380,2591894199214]
  [1288309348,1414516993678]
  [1289822524,1095273952750]
  [2497004836,82259788286926]
  [466452452356/361,1008217375914394/6859]

9. [1,-1,1,-685990640466912207377,6868986816410030691695751537025] N = 4611183920987854374283972944656606152532275998

E = ellinit([1,-1,1,-685990640466912207377,6868986816410030691695751537025]);
generators:
  [735709022803,-630649048859436556]
  [1752836841367,-2320407132328855948]
  [-30214918889,-108106754430988]
  [-458905034201/49,1211336657070286508/343]
  [5268567615871/729,29777477104487033180/19683]
  [15406939417471/1681,-80125798643229214988/68921]
  [1750803102517/144,-986311354207590943/1728]
  [14091139399,23159030189060]
  [75583624818511/4489,91261835934874275260/300763]
  [-20946338857,3471003365857012]
  [13459388983,272407663877972]
  [55942661935/4,820914226840687/8]
  [40905425911,6874091101731476]
  [-15767189247385/529,11129728879796086028/12167]
  [-1349917105865/49,756051585904477052/343]
  [11409652727591/625,10242936137797276564/15625]
  [32214123009955/1849,36067100650817766908/79507]

10. [1,0,0,-22838565855447084625,41855387033877832055344377641] N = 5240227668680445150085901505663732024266517078

E = ellinit([1,0,0,-22838565855447084625,41855387033877832055344377641]);
generators:
  [539892509438/169,-85034263784439217/2197]
  [1504429856,104408809677293]
  [568095244931/196,-8166492954795083/2744]
  [2908821818,5856925181243]
  [53887589165/16,3585869909279339/64]
  [1142004372122/961,-3814351974253718491/29791]
  [291923399834/169,-191015191227781129/2197]
  [2287595232769/64,3430467667563062291/512]
  [15175587715370/361,58751161020657962249/6859]
  [663374780,164306658990281]
  [1194584714,127582696090715]
  [2189786570,48415747746011]
  [3921260426,112220291518043]
  [4675242626,193053370309043]
  [36214031618,6834299050276043]
  [37939057514,7333725097634171]
  [185459371082/289,814186655234607019/4913]

Rank 18

# a-invariants conductor N log N naive h log abs(disc)
1 [0,1,0,-60644523341955931815220,5753484063464912298436438516620224] 12812290006126708208219509600625580071112139117656 113.074489331 168.993373000 155.22936150
2 [1,0,1,-51645574017006922559,114359963314028339882885488382] 47290188619362468646572850422665780847445759150230 114.380387309 147.786412000 139.30769259
3 [1,-1,1,-337872973491959196267,749512428602757726556083220155] 55035751703278323680294108487782527741865489894062 114.532067469 153.421208000 145.86300277
4 [1,-1,0,-714621165290271150,167336948819766456647608400] 82254192485037013616681222384133359549202218288370 114.933898825 134.945190000 126.76083179
5 [1,-1,1,-15793126247508684444,24154450924865994000420817119] 133189757005333373984927132272779327740156243097818 115.415859320 144.231922000 128.46101330
6 [1,-1,1,-1317837124555501486862,17527825124158781768840206873885] 174117693036610424661072980305410965823814139317254 115.683815931 157.504439000 147.68422810
7 [1,-1,0,-175794244176026716639,924139424489542810017330367009] 795674228819300344739553923797214936788267268052782 117.203274306 151.520466000 141.21151727
8 [1,0,1,-1464301595298229270658,21196941319954761614647613982056] 809089619733908209365281749844742217326645985963890 117.219994153 157.820599000 146.98569817
9 [1,0,0,-227781760006021270350,1239644962466450800403457742596] 921696670794521859371340115713061536866663911815042 117.350300643 152.238362000 142.68243847
10 [0,0,0,-170364434238838852687,811783598798924467766606521810] 11263947205505276370500249815376820412893317391816209656 126.761202134 151.367018000 141.61374457
generators for these ten

1. [0,1,0,-60644523341955931815220,5753484063464912298436438516620224] N = 12812290006126708208219509600625580071112139117656

E = ellinit([0,1,0,-60644523341955931815220,5753484063464912298436438516620224]);
generators:
  [4609209354050,-9881700823460124918]
  [10259268069134,-32851149625767207798]
  [-976915759771/4,619518203958630753/8]
  [-1825797824914/25,12369911958907021134/125]
  [85010462037872/1849,4399870667972140620000/79507]
  [171071671284794/1369,-569886995316475831302/50653]
  [16502842308500/121,-5854866999737710608/1331]
  [1372452821908/9,194183433347980832/27]
  [85579781514626/361,470209074065342384094/6859]
  [25459047152,65007952580096736]
  [115576342490,16978458180296718]
  [133206345524,6233206925444688]
  [147640154690,4256823643486218]
  [170398200434,19166933193484902]
  [192733879394,34994136972983958]
  [209547173444,47400588064096008]
  [-78975260122066/289,215211700462079579958/4913]
  [285243641333/4,338609052585253863/8]

2. [1,0,1,-51645574017006922559,114359963314028339882885488382] N = 47290188619362468646572850422665780847445759150230

E = ellinit([1,0,1,-51645574017006922559,114359963314028339882885488382]);
generators:
  [521919121685,-377019761317563264]
  [-7939868019,154528343569744]
  [4576271198505/289,-8880248580832860016/4913]
  [1317007745541/121,-1221118204436658586/1331]
  [38855996247/4,-5820307586737999/8]
  [824992430001/121,-374549184415055536/1331]
  [1624056619269/289,196368877377720992/4913]
  [766302664763/121,270457332234645474/1331]
  [356268514214/49,120401657086780812/343]
  [-7156266672,342730352678629]
  [-2542480077,478783783494382]
  [2499295350,29902125796261]
  [7443542721,377293638469984]
  [-49752809484/169,790733140933279705/2197]
  [-156987616335/64,243555557722881707/512]
  [89878404765/16,2482007489612179/64]
  [1068330592209/64,1011579564770551163/512]
  [998147735805/169,272262010596584146/2197]

3. [1,-1,1,-337872973491959196267,749512428602757726556083220155] N = 55035751703278323680294108487782527741865489894062

E = ellinit([1,-1,1,-337872973491959196267,749512428602757726556083220155]);
generators:
  [4763161247519/169,-8106725263999451198/2197]
  [141136094523235,-1676706924842794056846]
  [97565402831799/2809,-827789307921061985678/148877]
  [291095861974393/1089,-4954887310935042826096/35937]
  [-12594940831767/1849,131486569038666368264/79507]
  [-108406391086077/7921,-1181775485788121765894/704969]
  [194204908172737/9216,1529078127305135809777/884736]
  [2020029797607591/11449,90301796592633436951570/1225043]
  [3438773829822219/12769,201186759334087127654602/1442897]
  [-16856573125/4,11589028380434165/8]
  [772456758955/4,675860816159977745/8]
  [216838415657,100612957977811360]
  [847740314091,780354918896928746]
  [-58171873872413/4489,516734281720482245262/300763]
  [-12038244359757/1369,88325910754733287170/50653]
  [-10075349576047/4489,367933914174926566400/300763]
  [6280339433571/361,2537504914547948174/6859]
  [6065274144878291/2886601,1084024385005540765996654/4904335099]

4. [1,-1,0,-714621165290271150,167336948819766456647608400] N = 82254192485037013616681222384133359549202218288370

E = ellinit([1,-1,0,-714621165290271150,167336948819766456647608400]);
generators:
  [12233241730/9,-1115638088780500/27]
  [9045355870,-856614379633070]
  [-6733180838/49,5561911664780164/343]
  [54838759648/289,30510578746789292/4913]
  [113861171680/441,-1878989659788380/9261]
  [2056328224/25,-1305723404868628/125]
  [1023065990302/1369,360452213724169312/50653]
  [1213198411303/529,1252105307031888308/12167]
  [7015193432830/2809,17589316588118830400/148877]
  [8153830,12708677657650]
  [837409858,12495349220554]
  [1087203433,25989552821329]
  [1979660395,80689952971525]
  [8751641779/4,762187332858425/8]
  [-3176653326437/11236,22179212795064515389/1191016]
  [-36958844345/49,5711263073606875/343]
  [672525860827/961,94033503220714624/29791]
  [1645298972530/1681,1387869145121709050/68921]

5. [1,-1,1,-15793126247508684444,24154450924865994000420817119] N = 133189757005333373984927132272779327740156243097818

E = ellinit([1,-1,1,-15793126247508684444,24154450924865994000420817119]);
generators:
  [27303179641/9,-1742084067279137/27]
  [8111807463,-655604623260525]
  [-3431605611,194783461538981]
  [820001228921/361,5564338996067215/6859]
  [4321807695093/1936,-411613902183856751/85184]
  [4500760399789/2025,-517072383395726327/91125]
  [11480192262861/4624,4949595182490815353/314432]
  [19797931083897/6889,28602898366811705935/571787]
  [967246392751/324,350522307384405767/5832]
  [-2158417799,219516566701225]
  [1579395573,56129810696421]
  [2127915741,13536495120365]
  [2372176993,6254271643441]
  [2440528063,12127290766411]
  [48834175457,10756904214331057]
  [21638857117/9,243718978318375/27]
  [24630253459/9,1020961561645775/27]
  [169239137797/81,12150531942500573/729]

6. [1,-1,1,-1317837124555501486862,17527825124158781768840206873885] N = 174117693036610424661072980305410965823814139317254

E = ellinit([1,-1,1,-1317837124555501486862,17527825124158781768840206873885]);
generators:
  [-24835934591,-5910837774641605]
  [1186670860507753,-40878544417080981298141]
  [62855536489729/4225,-302710983660239851397/274625]
  [153482197228057/4489,-1060773087988829994199/300763]
  [175460141487761/6241,810061699172767455973/493039]
  [-8693319433,5322336260429635]
  [-379519471717427/21609,18861071469366209302885/3176523]
  [198526032702517/3481,2322396564488318707285/205379]
  [118543609996729/1849,1114697008140740897249/79507]
  [12233954209,1799026277276675]
  [30105585007,2267064914524115]
  [47284575451,7806049593553931]
  [90061517705,25086551307774019]
  [92395565641,26163687663111347]
  [1387869389593,1634464602412090259]
  [-2052063962255/64,2651497851104907853/512]
  [1167603922153/81,900722222378622811/729]
  [6310906738999/625,35803171308099248507/15625]

7. [1,-1,0,-175794244176026716639,924139424489542810017330367009] N = 795674228819300344739553923797214936788267268052782

E = ellinit([1,-1,0,-175794244176026716639,924139424489542810017330367009]);
generators:
  [1084296139136,1128988049709794799]
  [1718273689812,-2252297661457811437]
  [1695371666989/9,2202158722087378138/27]
  [16940901090960/289,-68084728724874009169/4913]
  [4783732418605/144,-9736191350229775361/1728]
  [69289682205414/4489,413283019807066511077/300763]
  [46291924693174/7569,183617934300521489257/658503]
  [1898838730537/576,-8526673033363930025/13824]
  [28270341257004/9409,-593639898628534672103/912673]
  [-3468073700,1221514910738297]
  [-727047972,1025459263994795]
  [5878674200,306366647115697]
  [8123367343,179305385056427]
  [28115475136,4266872380988049]
  [-17700175556/25,127980027937041343/125]
  [549328287809/64,111703513763142693/512]
  [596004090640/169,1296107556717154251/2197]
  [220758139722470/22201,1320217993764635493087/3307949]

8. [1,0,1,-1464301595298229270658,21196941319954761614647613982056] N = 809089619733908209365281749844742217326645985963890

E = ellinit([1,0,1,-1464301595298229270658,21196941319954761614647613982056]);
generators:
  [165919131640/9,18459888491734184/27]
  [2652838892952,-4320375628769386577]
  [227723703405/169,9633354862809880099/2197]
  [803864307651/25,-339074579857394341/125]
  [5533902558304/225,-829131066288474088/3375]
  [-20843564890485/961,-194791408431992233703/29791]
  [68864304103620/8281,-2334247420540856306543/753571]
  [11643740474895/289,25811405564504237651/4913]
  [927479217623820/16129,23096885811503776402141/2048383]
  [-35954394510,5231280556562617]
  [-25729864020,6468350039406352]
  [76534448379/4,3434192782474427/8]
  [28162022640,1514757603560392]
  [40733208735,5397714926216947]
  [62386559115,13139902381863367]
  [410054431845,261474855363871267]
  [-4157101783801905/100489,105536365081756974389201/31855013]
  [87151999885/9,76010190331916209/27]

9. [1,0,0,-227781760006021270350,1239644962466450800403457742596] N = 921696670794521859371340115713061536866663911815042

E = ellinit([1,0,0,-227781760006021270350,1239644962466450800403457742596]);
generators:
  [85127298648,-24469156392579066]
  [-41168216145/4,12633424642441533/8]
  [11306962800532/729,-23602967669242160738/19683]
  [1562342621910/121,-894051410060825646/1331]
  [74582182530940/6561,-183519656448185250046/531441]
  [261805227036/25,-6524897227941606/125]
  [593575248372/49,174209321525514414/343]
  [70767667097204/4225,400193798660554463362/274625]
  [92150992994172/5041,638689129895249540814/357911]
  [-12239036292,1481269051286178]
  [-7354380054,1586529104789958]
  [116870642,1101374336693414]
  [6858500460,4563376283634]
  [10870531476,219289059815658]
  [10908776760,230177978473506]
  [17551259796,1627380586324458]
  [403601438674/81,348379792273577960/729]
  [46219489987356/1681,273631898498883646386/68921]

10. [0,0,0,-170364434238838852687,811783598798924467766606521810] N = 11263947205505276370500249815376820412893317391816209656

E = ellinit([0,0,0,-170364434238838852687,811783598798924467766606521810]);
generators:
  [23210033101,-3059574332630582]
  [-11897904495,1074474031027250]
  [278455081273/16,-113010434425226989/64]
  [1391756770717/121,-813923822298045578/1331]
  [12277062089071/1369,-3652723704515219152/50653]
  [8733084990937/841,9829259832144645382/24389]
  [36801183951355/3481,90061895272441627640/205379]
  [12957453973,883059435837026]
  [66446041387459/5041,331198969256623656104/357911]
  [-8510633531,1282676951901646]
  [-2370317167,1096487092363726]
  [3473035313,511853069977774]
  [6075947443,31061815320424]
  [9975816913,324070669381774]
  [11654468342,639737352281888]
  [18167001257,1926813072375562]
  [18446529877,1986462697477538]
  [52180062945/4,7196794722093305/8]

Rank 19

# a-invariants conductor N log N naive h log abs(disc)
1 [1,1,1,-10958572218642024278780,441782147883394334171891116337501] 1403350426911985538403637610899460834214448220801709234 124.678457561 163.859885000 149.55041146
2 [1,-1,1,-20967825830676242381168,1049906339210514909937857261778131] 19790611384047910958418807384150866111612560217535236970 127.324802674 165.805431000 156.70496099
generators for these ten

1. [1,1,1,-10958572218642024278780,441782147883394334171891116337501] N = 1403350426911985538403637610899460834214448220801709234

E = ellinit([1,1,1,-10958572218642024278780,441782147883394334171891116337501]);
generators:
  [137845974861,39375927966972697]
  [1049351406543,-1069777833730017371]
  [2036247919749/25,1182902774435470133/125]
  [42109180193565/529,-104558848884240215761/12167]
  [1254971166117/16,-515143870777842593/64]
  [1533431535749/25,77055589868722997/125]
  [85721035194459/1444,36453130130197101359/54872]
  [112565936888829/1849,-41180755183612894061/79507]
  [169562184341319/2809,-72020779509948064801/148877]
  [-11267890083,23745142052512009]
  [-4178595123,22079418369947929]
  [54040990821,2718963082320001]
  [56494199769,1729989996855241]
  [61072869429,553242628511641]
  [66732158093,2768241826408729]
  [68328490189,3465556361794841]
  [69006390093,3764393296417177]
  [71137484941,4712829294790937]
  [356950640821/9,225153610957081507/27]

2. [1,-1,1,-20967825830676242381168,1049906339210514909937857261778131] N = 19790611384047910958418807384150866111612560217535236970

E = ellinit([1,-1,1,-20967825830676242381168,1049906339210514909937857261778131]);
generators:
  [24207049547821/81,-106830249160709075831/729]
  [3818446759197,-7456273396408679119]
  [-4932144028931/225,130669704083218426367/3375]
  [6107049522749/289,121962901422297168993/4913]
  [101059079412725/1849,651570455299632699939/79507]
  [545374707115/9,36514883625266659/27]
  [752140203101133/5041,12618573589081795933671/357911]
  [2185102423069/9,2736301854818103547/27]
  [2751765150967/9,4114451871496689797/27]
  [14954361285,27197238410591297]
  [107753411997,6453986905710641]
  [121406308541,17138996754470097]
  [337333808133,179897986581379265]
  [552605499405,397760556493770977]
  [-12255232629253915/259081,5802230249742187713125013/131872229]
  [35347527426365/289,87203955845365432161/4913]
  [80812020972725/121,710493105579315194307/1331]
  [181601058252005/361,2354179947939171149403/6859]
  [140567620846053317/175561,51887821202850956413890699/73560059]