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Torsion Z/3: record curves

The curves of this collection with torsion subgroup Z/3, 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 appears in the corresponding rank_r file as well. 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)
4 110 16.238707 41.861849 31.037773
5 358 21.625343 50.133939 40.494169
6 4,295 26.966490 59.982325 50.262399
7 2,321 36.084600 84.190609 68.928403
8 92 42.561401 98.821628 83.606141
9 1 61.898802 135.715458 126.976008

Rank 4

# a-invariants conductor N log N naive h log abs(disc) torsion generators
1 [1,0,1,-1402210,638980920] 11281858 16.238706507 54.074282000 32.60579418 [[690,-55]]
2 [1,0,0,-59867,10816849] 15913354 16.582669189 45.917299000 38.14590800 [[30,2993]]
3 [1,-1,0,-29301,1919681] 16064082 16.592096406 42.469753000 31.03777281 [[127,421]]
4 [1,-1,0,-52251,2965013] 19378602 16.779680026 44.205057000 36.21876580 [[271,2806]]
5 [1,0,1,-2958745,1969597352] 32080998 17.283774450 56.325586000 44.36951806 [[784,11096]]
6 [1,0,1,-121870,17419212] 34906762 17.368191122 46.870480000 37.27265049 [[114,2181]]
7 [0,1,0,-283945,57744600] 35374580 17.381504041 49.283214000 37.53217966 [[385,2375]]
8 [1,0,1,-28280,2631530] 35662926 17.389622220 43.091088000 34.97671799 [[30,1330]]
9 [1,0,1,-100721,12290520] 38083486 17.455291308 46.173918000 31.49503442 [[200,295]]
10 [1,0,1,-325580,71396382] 45171154 17.625969255 49.693689000 36.14904020 [[374,1219]]
generators for these ten

1. [1,0,1,-1402210,638980920] N = 11281858

E = ellinit([1,0,1,-1402210,638980920]);
generators:
  [55309/81,-271333/729]
  [109,-22133]
  [684,-352]
  [6973/16,-687357/64]
torsion generators:
  [690,-55]

2. [1,0,0,-59867,10816849] N = 15913354

E = ellinit([1,0,0,-59867,10816849]);
generators:
  [-158,-3963]
  [124,-2365]
  [312,4591]
  [6286/9,-484693/27]
torsion generators:
  [30,2993]

3. [1,-1,0,-29301,1919681] N = 16064082

E = ellinit([1,-1,0,-29301,1919681]);
generators:
  [-196,421]
  [1096,35305]
  [-26,1645]
  [32,991]
torsion generators:
  [127,421]

4. [1,-1,0,-52251,2965013] N = 19378602

E = ellinit([1,-1,0,-52251,2965013]);
generators:
  [-206,2329]
  [-47,2329]
  [6154,479329]
  [-173,2695]
torsion generators:
  [271,2806]

5. [1,0,1,-2958745,1969597352] N = 32080998

E = ellinit([1,0,1,-2958745,1969597352]);
generators:
  [10795/4,923599/8]
  [15439/49,11158568/343]
  [1189,10934]
  [23761,3641462]
torsion generators:
  [784,11096]

6. [1,0,1,-121870,17419212] N = 34906762

E = ellinit([1,0,1,-121870,17419212]);
generators:
  [-293,5437]
  [5503/9,345415/27]
  [-370,3633]
  [3777,229287]
torsion generators:
  [114,2181]

7. [0,1,0,-283945,57744600] N = 35374580

E = ellinit([0,1,0,-283945,57744600]);
generators:
  [-565,6175]
  [-835/4,83125/8]
  [2760,142500]
  [-615,375]
torsion generators:
  [385,2375]

8. [1,0,1,-28280,2631530] N = 35662926

E = ellinit([1,0,1,-28280,2631530]);
generators:
  [-177,1537]
  [-87,2149]
  [-108,2158]
  [-777/4,7949/8]
torsion generators:
  [30,1330]

9. [1,0,1,-100721,12290520] N = 38083486

E = ellinit([1,0,1,-100721,12290520]);
generators:
  [-139,4928]
  [-365,860]
  [426,6623]
  [116,1415]
torsion generators:
  [200,295]

10. [1,0,1,-325580,71396382] N = 45171154

E = ellinit([1,0,1,-325580,71396382]);
generators:
  [3187,175625]
  [-1317/4,96955/8]
  [-305,12083]
  [6000,459738]
torsion generators:
  [374,1219]

Rank 5

# a-invariants conductor N log N naive h log abs(disc) torsion generators
1 [1,0,0,-22297742,98226074116] 2464716938 21.625342805 64.144258000 56.50294463 [[444,297122]]
2 [1,-1,0,-324141,89192321] 3123097398 21.862091102 50.133939000 41.67031943 [[127,7012]]
3 [1,0,0,-83296293,293440629889] 8306144278 22.840261352 66.333075000 53.71316396 [[4370,111367]]
4 [1,0,0,-127702,333062436] 8982023266 22.918491002 52.770890000 45.31338561 [[4,18234]]
5 [1,0,1,-40932715,100783384482] 16619239546 23.533826870 64.195924000 48.37068527 [[3924,22289]]
6 [1,-1,0,-16036386,24883806968] 18135416754 23.621132590 61.397789000 49.59940697 [[1801,42013]]
7 [1,0,0,-24393911,46686479785] 22406086870 23.832598494 62.656674000 50.89294847 [[2214,58325]]
8 [0,1,1,-30379967,64440778455] 27716849069 24.045306335 63.301485000 40.49416948 [[3201,1865]]
9 [1,0,0,-199700187,1086437663569] 29709620122 24.114736740 68.951027000 53.76839118 [[7550,91537]]
10 [1,0,0,-30606263,79323080617] 41399070350 24.446524262 63.716800000 55.13816745 [[1302,203509]]
generators for these ten

1. [1,0,0,-22297742,98226074116] N = 2464716938

E = ellinit([1,0,0,-22297742,98226074116]);
generators:
  [-6020,122594]
  [21452,-3091630]
  [85436/25,30896026/125]
  [13372,1473570]
  [372124,226798914]
torsion generators:
  [444,297122]

2. [1,-1,0,-324141,89192321] N = 3123097398

E = ellinit([1,-1,0,-324141,89192321]);
generators:
  [4844,332485]
  [-674,1405]
  [-668,3037]
  [14659/4,1740065/8]
  [-10976/25,1541597/125]
torsion generators:
  [127,7012]

3. [1,0,0,-83296293,293440629889] N = 8306144278

E = ellinit([1,0,0,-83296293,293440629889]);
generators:
  [2866,278311]
  [6786,198343]
  [143074/25,7731083/125]
  [-1670,654967]
  [231474,111165223]
torsion generators:
  [4370,111367]

4. [1,0,0,-127702,333062436] N = 8982023266

E = ellinit([1,0,0,-127702,333062436]);
generators:
  [380,18234]
  [192,17670]
  [-748,3570]
  [1884,81402]
  [-654,12030]
torsion generators:
  [4,18234]

5. [1,0,1,-40932715,100783384482] N = 16619239546

E = ellinit([1,0,1,-40932715,100783384482]);
generators:
  [2741,94452]
  [31585/9,463756/27]
  [2325,133686]
  [726,266936]
  [243609/25,98385538/125]
torsion generators:
  [3924,22289]

6. [1,-1,0,-16036386,24883806968] N = 18135416754

E = ellinit([1,-1,0,-16036386,24883806968]);
generators:
  [26323,4210753]
  [-57011/16,12387283/64]
  [14062,1599160]
  [193,147538]
  [73634/25,6882338/125]
torsion generators:
  [1801,42013]

7. [1,0,0,-24393911,46686479785] N = 22406086870

E = ellinit([1,0,0,-24393911,46686479785]);
generators:
  [3088,26861]
  [-1662,288301]
  [1427/4,1558663/8]
  [138202/49,5682363/343]
  [-914,261645]
torsion generators:
  [2214,58325]

8. [0,1,1,-30379967,64440778455] N = 27716849069

E = ellinit([0,1,1,-30379967,64440778455]);
generators:
  [12517/4,41037/8]
  [3565,38174]
  [1479,150818]
  [32561/16,6726961/64]
  [62409/16,4659987/64]
torsion generators:
  [3201,1865]

9. [1,0,0,-199700187,1086437663569] N = 29709620122

E = ellinit([1,0,0,-199700187,1086437663569]);
generators:
  [8838,104417]
  [10658,405445]
  [4974,462481]
  [2398,787057]
  [-738,1110961]
torsion generators:
  [7550,91537]

10. [1,0,0,-30606263,79323080617] N = 41399070350

E = ellinit([1,0,0,-30606263,79323080617]);
generators:
  [-6122,196085]
  [8726,686069]
  [82966,23804405]
  [10582,964469]
  [3622,124629]
torsion generators:
  [1302,203509]

Rank 6

# a-invariants conductor N log N naive h log abs(disc) torsion generators
1 [0,1,1,-9687757,12256549127] 514514775019 26.966490109 59.982325000 50.26239908 [[1045,57228]]
2 [0,1,1,-925753397,10841851921227] 3524484976529 28.890755436 73.552072000 57.01766418 [[16725,193176]]
3 [1,0,1,-6571364219,204874375164626] 5998023791070 29.422451163 79.431565000 65.52434342 [[52404,2076193]]
4 [1,0,1,-9641629029,364396545204956] 7155067330810 29.598841939 80.581678000 61.22287564 [[55624,412228]]
5 [1,0,1,-5350645921,150644230655160] 7213783166674 29.607014641 78.815052000 60.36480231 [[43320,365639]]
6 [1,0,0,-30023595887,2002298360220601] 7323725565118 29.622140271 83.989351000 66.79868654 [[103974,2103997]]
7 [1,0,1,-1052379025,13115318303120] 7566702958578 29.654778548 73.936561000 60.90656984 [[21760,709520]]
8 [1,-1,1,-374703419,2783803557547] 8217534692466 29.737291364 70.838539000 58.22798782 [[13267,377618]]
9 [1,0,0,-107483887227,14193121444682769] 9730454816874 29.906281755 87.906214000 78.00724818 [[114270,58278417]]
10 [1,0,0,-9156295527,333195140370889] 10278979796806 29.961122129 80.426726000 69.23347573 [[72230,6940533]]
generators for these ten

1. [0,1,1,-9687757,12256549127] N = 514514775019

E = ellinit([0,1,1,-9687757,12256549127]);
generators:
  [2207,40379]
  [-1279,150188]
  [181337/64,44523517/512]
  [-23297/9,3817945/27]
  [-13747/4,564007/8]
  [-925,142923]
torsion generators:
  [1045,57228]

2. [0,1,1,-925753397,10841851921227] N = 3524484976529

E = ellinit([0,1,1,-925753397,10841851921227]);
generators:
  [17407,44159]
  [-108715/4,31926803/8]
  [70093/4,213927/8]
  [628357/36,7715699/216]
  [4667953/256,640184873/4096]
  [17693,38296]
torsion generators:
  [16725,193176]

3. [1,0,1,-6571364219,204874375164626] N = 5998023791070

E = ellinit([1,0,1,-6571364219,204874375164626]);
generators:
  [14523,10599418]
  [-61239,19463572]
  [261527/4,58917009/8]
  [2886657/64,238404581/512]
  [2100597/49,471526714/343]
  [75381,11703556]
torsion generators:
  [52404,2076193]

4. [1,0,1,-9641629029,364396545204956] N = 7155067330810

E = ellinit([1,0,1,-9641629029,364396545204956]);
generators:
  [96558,18218518]
  [56679,7108]
  [117025,28902292]
  [61454617/1089,3021152236/35937]
  [54033,1061098]
  [4682319/100,3926391433/1000]
torsion generators:
  [55624,412228]

5. [1,0,1,-5350645921,150644230655160] N = 7213783166674

E = ellinit([1,0,1,-5350645921,150644230655160]);
generators:
  [308401/25,1161902034/125]
  [264634,131272870]
  [37584,1604615]
  [4688435/121,1601534784/1331]
  [-24741,16379420]
  [138681,45491468]
torsion generators:
  [43320,365639]

6. [1,0,0,-30023595887,2002298360220601] N = 7323725565118

E = ellinit([1,0,0,-30023595887,2002298360220601]);
generators:
  [12230,40452989]
  [99462,151805]
  [889894/9,14513935/27]
  [2798954,4672504337]
  [99180,352589]
  [1044350,1052893901]
torsion generators:
  [103974,2103997]

7. [1,0,1,-1052379025,13115318303120] N = 7566702958578

E = ellinit([1,0,1,-1052379025,13115318303120]);
generators:
  [2023,3314804]
  [106513,33254672]
  [17818,135959]
  [1984801/25,2587038934/125]
  [-37451,38462]
  [61234,13321463]
torsion generators:
  [21760,709520]

8. [1,-1,1,-374703419,2783803557547] N = 8217534692466

E = ellinit([1,-1,1,-374703419,2783803557547]);
generators:
  [9659,251338]
  [10561,61016]
  [12365,-208682]
  [-791,1755302]
  [10427,96458]
  [1339,-1512118]
torsion generators:
  [13267,377618]

9. [1,0,0,-107483887227,14193121444682769] N = 9730454816874

E = ellinit([1,0,0,-107483887227,14193121444682769]);
generators:
  [445722,-234393699]
  [245214,-50928879]
  [157038,-34528143]
  [144278,41023817]
  [1734702,-2247596319]
  [179742,26000721]
torsion generators:
  [114270,58278417]

10. [1,0,0,-9156295527,333195140370889] N = 10278979796806

E = ellinit([1,0,0,-9156295527,333195140370889]);
generators:
  [164028,56878645]
  [18612,12999367]
  [46002,3032561]
  [50152,-389363]
  [94308,17515895]
  [-90450,-20482667]
torsion generators:
  [72230,6940533]

Rank 7

# a-invariants conductor N log N naive h log abs(disc) torsion generators
1 [1,0,1,-955060908095,359247468378682722] 4691836355650202 36.084600448 94.368726000 74.52563575 [[573344,11573566]]
2 [1,0,1,-16447594952910,25674479247623857532] 6645836912878238 36.432767025 102.907204000 80.17259065 [[2355874,36970104]]
3 [1,0,1,-810107314098,278171511728355256] 10190734612809870 36.860255331 93.874901000 82.37861718 [[663170,180198852]]
4 [0,1,1,-37352633327,2777874222289905] 15554489496586229 37.283125705 84.644611000 69.64992578 [[120801,5337419]]
5 [0,0,0,-97351728669,3227101284680901] 18292854230884044 37.445286899 87.518392000 79.98442321 [[426387,198083949]]
6 [1,0,1,-82065445090,9018653912336840] 18526405288385514 37.457973422 87.005952000 74.53651322 [[197890,22883540]]
7 [1,0,0,-2035462515005,1117701559690439025] 18666601961882610 37.465512331 96.638836000 79.72033215 [[859210,55398295]]
8 [1,0,0,-1483566759815,696274364523822217] 24699665118479890 37.745566080 95.692186000 82.10445171 [[615174,127866613]]
9 [1,-1,0,-15337250279766,23119028050726262088] 28939884625000854 37.903997129 102.697521000 80.90924932 [[2242081,48324113]]
10 [1,-1,0,-32988023466,2176913384690696] 30395824543282302 37.953081643 84.271834000 74.60002542 [[160777,31999861]]
generators for these ten

1. [1,0,1,-955060908095,359247468378682722] N = 4691836355650202

E = ellinit([1,0,1,-955060908095,359247468378682722]);
generators:
  [343939,267130736]
  [-1081573,356899580]
  [12314836/25,11369425501/125]
  [528882,45231300]
  [563411,336032]
  [559667,5583040]
  [296829755/529,-51514362808/12167]
torsion generators:
  [573344,11573566]

2. [1,0,1,-16447594952910,25674479247623857532] N = 6645836912878238

E = ellinit([1,0,1,-16447594952910,25674479247623857532]);
generators:
  [3338227,-2824624185]
  [1032305992/441,-10164163073/9261]
  [19760596/9,10298959357/27]
  [2163847,463718107]
  [47108614/25,-146554022523/125]
  [115293599/49,-10804169419/343]
  [2338417,-9102093]
torsion generators:
  [2355874,36970104]

3. [1,0,1,-810107314098,278171511728355256] N = 10190734612809870

E = ellinit([1,0,1,-810107314098,278171511728355256]);
generators:
  [-720205,698964477]
  [307445,-241335273]
  [1506455/4,-1303618059/8]
  [1064795,-789725523]
  [-1000705,295006227]
  [24733895,-122941559523]
  [3023045,-5046924273]
torsion generators:
  [663170,180198852]

4. [0,1,1,-37352633327,2777874222289905] N = 15554489496586229

E = ellinit([0,1,1,-37352633327,2777874222289905]);
generators:
  [58873,27979844]
  [79431,17665679]
  [113315,520375]
  [89393825/841,-71005228780/24389]
  [146589301/961,747416374925/29791]
  [-26504427/841,1527724233871/24389]
  [-1372591/16,4681594207/64]
torsion generators:
  [120801,5337419]

5. [0,0,0,-97351728669,3227101284680901] N = 18292854230884044

E = ellinit([0,0,0,-97351728669,3227101284680901]);
generators:
  [-224135,117419221]
  [-107532,111589071]
  [40977/4,377857617/8]
  [-306443,65441719]
  [941895,864378039]
  [349855,109498159]
  [-141243,118994169]
torsion generators:
  [426387,198083949]

6. [1,0,1,-82065445090,9018653912336840] N = 18526405288385514

E = ellinit([1,0,1,-82065445090,9018653912336840]);
generators:
  [146647,11661323]
  [311947,117208679]
  [116608,32109047]
  [31048,-80641921]
  [111934,35089292]
  [2669125,4335188615]
  [154912,4746824]
torsion generators:
  [197890,22883540]

7. [1,0,0,-2035462515005,1117701559690439025] N = 18666601961882610

E = ellinit([1,0,0,-2035462515005,1117701559690439025]);
generators:
  [-1568090,-672791705]
  [611086,319154107]
  [1479520,-1160409305]
  [819190,-3030905]
  [58810,-999128705]
  [817810,6090895]
  [10955965/16,13552641955/64]
torsion generators:
  [859210,55398295]

8. [1,0,0,-1483566759815,696274364523822217] N = 24699665118479890

E = ellinit([1,0,0,-1483566759815,696274364523822217]);
generators:
  [704494,27202973]
  [-1152746,935806053]
  [-1382346,325621093]
  [858774,235294213]
  [1240414,873777933]
  [6799366/9,2193386951/27]
  [-1132656,961581523]
torsion generators:
  [615174,127866613]

9. [1,-1,0,-15337250279766,23119028050726262088] N = 28939884625000854

E = ellinit([1,-1,0,-15337250279766,23119028050726262088]);
generators:
  [2127492,343390788]
  [276496554/121,-85041402438/1331]
  [-2611431,6736463649]
  [653166162/289,-23492695968/4913]
  [2260174,2373924]
  [2209287,-135469860]
  [1077894,-2800441476]
torsion generators:
  [2242081,48324113]

10. [1,-1,0,-32988023466,2176913384690696] N = 30395824543282302

E = ellinit([1,-1,0,-32988023466,2176913384690696]);
generators:
  [80476,6544444]
  [74015,11827696]
  [4103926/49,-440842352/343]
  [-1201715/16,4165287571/64]
  [1306,46192780]
  [137606,-15662886]
  [223099,76840540]
torsion generators:
  [160777,31999861]

Rank 8

# a-invariants conductor N log N naive h log abs(disc) torsion generators
1 [1,0,1,-16785799414680,26477982529328587642] 3049169315882817126 42.561400872 102.968836000 88.04381986 [[2173454,510777666]]
2 [1,0,1,-47141264881100,124579627387755672990] 8105786479173935734 43.539109861 106.066113000 87.39433808 [[4058870,324953539]]
3 [1,0,1,-4213613959455,3328416232976793662] 8682358926885363538 43.607824931 98.821628000 83.60614108 [[1275964,170749461]]
4 [1,0,1,-270178372266703,1711728668715982411506] 18634368691081768030 44.371539329 111.306727000 97.97727711 [[8198880,6903196497]]
5 [1,0,1,-28403376865544,58189065087724781826] 53669457456992966810 45.429375751 104.546191000 91.13278013 [[3513254,1326671818]]
6 [1,0,1,-2868867248090800,59144422102587499373742] 60043617650386502762 45.541602933 118.391684000 92.49739784 [[30857754,621908694]]
7 [1,0,1,-13693841992220,19491670055901696510] 72865681816774464982 45.735149445 102.357505000 88.27329481 [[2377190,609044710]]
8 [0,1,0,-9421065891357,11092061421425521756] 137823647696020728596 46.372506627 101.235511000 88.79274072 [[2123525,813592241]]
9 [1,0,1,-629556267118220,6080889056715818968350] 312377498811002040962 47.190744062 113.842021000 98.30563614 [[13523510,6343838150]]
10 [1,0,0,-618120167801113,5915031717724666018617] 325040992823102890550 47.230482980 113.786715000 93.13431657 [[14531002,1153650579]]
generators for these ten

1. [1,0,1,-16785799414680,26477982529328587642] N = 3049169315882817126

E = ellinit([1,0,1,-16785799414680,26477982529328587642]);
generators:
  [2593187,621167445]
  [2682392,-868698783]
  [8714852,23278113405]
  [480343985/64,-9207631871829/512]
  [2458817,263806965]
  [2330351,126247257]
  [376735577/121,2789067617595/1331]
  [765541466/289,3801238377003/4913]
torsion generators:
  [2173454,510777666]

2. [1,0,1,-47141264881100,124579627387755672990] N = 8105786479173935734

E = ellinit([1,0,1,-47141264881100,124579627387755672990]);
generators:
  [3506067,1546648169]
  [18514107/4,18816616671/8]
  [1604964,-7284608967]
  [3573840,-1324876006]
  [50902708/9,-168429467309/27]
  [15716871/4,-947138639/8]
  [36167923/9,4980960193/27]
  [-71340842/9,11901995041/27]
torsion generators:
  [4058870,324953539]

3. [1,0,1,-4213613959455,3328416232976793662] N = 8682358926885363538

E = ellinit([1,0,1,-4213613959455,3328416232976793662]);
generators:
  [137177,1659144070]
  [960817,408055152]
  [-563615,2350650576]
  [19130981/25,92832380906/125]
  [75289747/121,1295169509390/1331]
  [5344925,11551633378]
  [-1439605,2532681298]
  [1245950,111922021]
torsion generators:
  [1275964,170749461]

4. [1,0,1,-270178372266703,1711728668715982411506] N = 18634368691081768030

E = ellinit([1,0,1,-270178372266703,1711728668715982411506]);
generators:
  [10371555,5016590372]
  [7474655,10477246872]
  [-19868330/9,-1294116481456/27]
  [2044195,34174605732]
  [758873945/64,6774777910839/512]
  [84493720/9,44239841419/27]
  [-8659605,58330941572]
  [134938255,-1556426994128]
torsion generators:
  [8198880,6903196497]

5. [1,0,1,-28403376865544,58189065087724781826] N = 53669457456992966810

E = ellinit([1,0,1,-28403376865544,58189065087724781826]);
generators:
  [-5372555,-7461393283]
  [50688453/16,-2946036603/64]
  [-1575427,-9950410687]
  [25026589/9,22694079359/27]
  [-11935745/9,-261094507241/27]
  [-3549724,10692180646]
  [353296791/121,-515434582409/1331]
  [10521527/4,-10369555931/8]
torsion generators:
  [3513254,1326671818]

6. [1,0,1,-2868867248090800,59144422102587499373742] N = 60043617650386502762

E = ellinit([1,0,1,-2868867248090800,59144422102587499373742]);
generators:
  [32488005,-15207647377]
  [29241741,-16069530469]
  [-2983179,-260145040693]
  [56534405,278623009071]
  [-6845035,-280105838517]
  [-52636251,253636575179]
  [57179342805/1849,-2646547957759/79507]
  [772785561/25,13268528419/125]
torsion generators:
  [30857754,621908694]

7. [1,0,1,-13693841992220,19491670055901696510] N = 72865681816774464982

E = ellinit([1,0,1,-13693841992220,19491670055901696510]);
generators:
  [-3924703,-3573311611]
  [-1016137,5688855229]
  [19862385,87073333985]
  [10716283,33211939307]
  [2082259,-77259727]
  [-4117311,2466971573]
  [976207587/484,-2965313601639/10648]
  [-537075360/169,12219000475170/2197]
torsion generators:
  [2377190,609044710]

8. [0,1,0,-9421065891357,11092061421425521756] N = 137823647696020728596

E = ellinit([0,1,0,-9421065891357,11092061421425521756]);
generators:
  [1641967,223202133]
  [1870503,120058939]
  [1982043,453379069]
  [1929651,312815699]
  [1685745,31498271]
  [-546933,4010130467]
  [7327185,18315061919]
  [1650465,-197100449]
torsion generators:
  [2123525,813592241]

9. [1,0,1,-629556267118220,6080889056715818968350] N = 312377498811002040962

E = ellinit([1,0,1,-629556267118220,6080889056715818968350]);
generators:
  [15777394,-8699147137]
  [84767984601/5329,-3724621783454311/389017]
  [56639083801/3249,3719913537840941/185193]
  [-28331349545/2601,14315952628729519/132651]
  [918616711612/66049,-66457799650161743/16974593]
  [-272072007/64,-47701226345369/512]
  [6427765137/169,-423534182399067/2197]
  [26257190279/25,-4253596162807577/125]
torsion generators:
  [13523510,6343838150]

10. [1,0,0,-618120167801113,5915031717724666018617] N = 325040992823102890550

E = ellinit([1,0,0,-618120167801113,5915031717724666018617]);
generators:
  [14330982,-139478721]
  [14370986,-89673741]
  [14430992,-506815451]
  [9330482,30978632779]
  [14395098,251607507]
  [776420282/49,3411284199861/343]
  [14342372,-27927741]
  [12430792,-12341998851]
torsion generators:
  [14531002,1153650579]

Rank 9

# a-invariants conductor N log N naive h log abs(disc) torsion generators
1 [1,0,0,-829248587546232242,341761829044265374567063684] 762619546977047970820027222 61.898801511 135.715458000 126.97600788 [[229591260,12785652649478]]
generators for these ten

1. [1,0,0,-829248587546232242,341761829044265374567063684] N = 762619546977047970820027222

E = ellinit([1,0,0,-829248587546232242,341761829044265374567063684]);
generators:
  [-189916826,-22189995004600]
  [832446100,-15110490503778]
  [-195069021338/361,172444749469472198/6859]
  [133172679624/25,47938500341854022/125]
  [5694975884,424641641525726]
  [504268770228/121,350300094688740170/1331]
  [15040050644,-1841196335033074]
  [2200557492,95774937817822]
  [5965919830,455776283293592]
torsion generators:
  [229591260,12785652649478]