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Rank 13 record curves

The ten smallest curves of rank 13 in this collection, in each of four categories. The same curve often heads more than one list. Every curve here has proven rank 13, is given by its global minimal model, and carries 13 independent generators, listed below each table.

Conductors are given as exact integers. All heights are natural logarithms. The naive height is log max(abs(c4)^3, c6^2); the Faltings height is -(1/2) log abs(Im(conj(w1) w2)) on the minimal model, the normalization used by the Elliptic Curve Rank Leaderboard.

Smallest conductor

# a-invariants conductor N log N naive h Faltings h log abs(disc)
1 [0,-1,1,-1876573260,32705933898332] 13048475524065056885495472921 64.738468820 75.760262570 4.24523710 65.83708111
2 [1,-1,0,-7636625866,271218848904208] 27751906366700157951398581202 65.493102047 79.991025802 4.60744226 70.26378667
3 [0,0,0,-37758892927,2824446134548930] 27921029408976004366433952184 65.499178000 84.677323000 4.76027173 68.96491356
4 [1,0,1,-104090690933,12923707417896492] 32385292333257670247550849142 65.647502000 87.719188000 5.02446526 72.33958563
5 [0,0,0,-10687932892,428567179534420] 37736703744881212022095388824 65.800431000 80.906083000 4.59564520 69.26616661
6 [0,0,0,-6529826212,195995662948900] 38252643743425234347938185256 65.814010186 79.412541531 4.53993712 69.27974609
7 [0,0,0,-39991088332,3219571125706420] 39939033574587811091814521464 65.857152000 84.939195000 5.01083149 75.02999781
8 [0,0,1,-69573490077,7061376552317536] 50809100449337709791877402759 66.097873000 86.510551000 4.93892399 71.59093444
9 [0,0,1,-13219745917,236237043476946] 56327033117154259172161550881 66.200972093 81.528535388 4.85154672 73.89582017
10 [1,-1,0,-37686930696,2815574835904308] 60154466034351804780171914478 66.266713000 84.671341000 4.76612027 69.15708496
generators for these ten

1. [0,-1,1,-1876573260,32705933898332] N = 13048475524065056885495472921

E = ellinit([0,-1,1,-1876573260,32705933898332]);
generators:
  [-50174,740983]
  [-34581,7499665]
  [-7386,6794359]
  [258,5676424]
  [10493,3764339]
  [15191,2775653]
  [15843,2636614]
  [22793,1331960]
  [25138,1190455]
  [26925,1303036]
  [28326,1508983]
  [31670,2244663]
  [41511,5131861]

2. [1,-1,0,-7636625866,271218848904208] N = 27751906366700157951398581202

E = ellinit([1,-1,0,-7636625866,271218848904208]);
generators:
  [-100864,3965436]
  [-70857,21402944]
  [-59446,22725784]
  [-48898,22996540]
  [-44873,22903433]
  [-9662,18554814]
  [557,16338798]
  [63498,6474328]
  [169238,61770214]
  [769523/4,614873529/8]
  [1105366/25,556301646/125]
  [1756288/49,2257341500/343]
  [781732416/14641,6969544831916/1771561]

3. [0,0,0,-37758892927,2824446134548930] N = 27921029408976004366433952184

E = ellinit([0,0,0,-37758892927,2824446134548930]);
generators:
  [111003,-915224]
  [103265,5143630]
  [107409,2818846]
  [118187,-3562528]
  [1015201/9,-18942578/27]
  [91711,11528792]
  [81617,-16922078]
  [49215,32944600]
  [110693,-1056274]
  [112173,-605174]
  [112283,-607576]
  [193933,52873174]
  [455809/4,9527831/8]

4. [1,0,1,-104090690933,12923707417896492] N = 32385292333257670247550849142

E = ellinit([1,0,1,-104090690933,12923707417896492]);
generators:
  [-310577,123825200]
  [2445,112556408]
  [182583,2191860]
  [759207/4,16534573/8]
  [228663,32719796]
  [1091495/4,555372253/8]
  [453848,243011875]
  [-35945032/121,176924884460/1331]
  [11203641/64,4131232039/512]
  [9243021/49,273232406/343]
  [15139469/49,34686054584/343]
  [27316382/121,40448814386/1331]
  [81174956/49,718134468421/343]

5. [0,0,0,-10687932892,428567179534420] N = 37736703744881212022095388824

E = ellinit([0,0,0,-10687932892,428567179534420]);
generators:
  [-24914,26064958]
  [-2634,21370562]
  [3362,19815962]
  [49716,4481962]
  [52002,3660262]
  [57310,2067070]
  [63810,2527130]
  [68482,4219238]
  [91194,14570266]
  [93858,15882214]
  [115842,27294362]
  [265497,127692913]
  [260793/4,23836979/8]

6. [0,0,0,-6529826212,195995662948900] N = 38252643743425234347938185256

E = ellinit([0,0,0,-6529826212,195995662948900]);
generators:
  [-61858,19058422]
  [-38214,19741382]
  [-23176,18299794]
  [-18394,17603462]
  [-6694,15472762]
  [-104,14024078]
  [2022,13520378]
  [26042,6603578]
  [37328,2064554]
  [53784,614386]
  [54654,1539254]
  [55250,1968970]
  [70414,9237226]

7. [0,0,0,-39991088332,3219571125706420] N = 39939033574587811091814521464

E = ellinit([0,0,0,-39991088332,3219571125706420]);
generators:
  [-179322,68003726]
  [-68554,75092878]
  [-1732,57348326]
  [4596,55098722]
  [46514,38210746]
  [60274,32064326]
  [105510,13216910]
  [122882,12684742]
  [135782,17113742]
  [137932,18102742]
  [175385,40006985]
  [374346,201762278]
  [3207702,5734118542]

8. [0,0,1,-69573490077,7061376552317536] N = 50809100449337709791877402759

E = ellinit([0,0,1,-69573490077,7061376552317536]);
generators:
  [-131756,118071436]
  [155146,1317469]
  [156727,2659459]
  [179261,18709004]
  [198508,32753236]
  [212140,43000852]
  [1274863,1410804211]
  [3904015,7696612147]
  [3808681/49,15804685084/343]
  [3864179/25,75505908/125]
  [34977961/196,49760617775/2744]
  [40570441/256,16244872645/4096]
  [271425706/1849,270597222391/79507]

9. [0,0,1,-13219745917,236237043476946] N = 56327033117154259172161550881

E = ellinit([0,0,1,-13219745917,236237043476946]);
generators:
  [-121053,7914354]
  [-118362,11947916]
  [-102866,22530683]
  [-12555,20005797]
  [-3338,16742979]
  [-101,15413378]
  [10364,10017026]
  [15681,5726610]
  [133799,29372453]
  [152311,41906234]
  [173046,55950524]
  [302968,155049641]
  [960493/9,172688158/27]

10. [1,-1,0,-37686930696,2815574835904308] N = 60154466034351804780171914478

E = ellinit([1,-1,0,-37686930696,2815574835904308]);
generators:
  [-706029/4,504675441/8]
  [-108786,75074124]
  [-9,53065191]
  [18957,45903003]
  [30664,41079374]
  [110541,536091]
  [237333,84966144]
  [35459871,211136228631]
  [3343357/16,4073558907/64]
  [3887601/25,3333671559/125]
  [29174217/256,3313314963/4096]
  [18287634/169,4560132186/2197]
  [321779256/2809,181141768734/148877]

Smallest naive height

# a-invariants conductor N log N naive h Faltings h log abs(disc)
1 [0,0,1,-1129201567,23953648602246] 155721986935837682842530035243 67.217870000 75.137429000 4.29745552 67.21786979
2 [0,0,1,-1141015057,26061092520366] 198333672870666343333189775723 67.459748000 75.306075000 4.31537831 67.45974834
3 [0,-1,1,-1876573260,32705933898332] 13048475524065056885495472921 64.738468820 75.760262570 4.24523710 65.83708111
4 [0,0,1,-2077523317,13064155885836] 500145136377795551079641841157 68.384696000 75.976930000 4.39134211 68.38469584
5 [0,0,1,-2217077947,28425800438316] 348398420573690733009119729797 68.023144222 76.171970810 4.37487054 68.02314422
6 [0,0,1,-2147907577,47888102069226] 356492038662688596396428055563 68.046109419 76.522921935 4.38307354 68.04610942
7 [1,-1,0,-2049670219,48898999201369] 240918419474403489984588164194 67.654256000 76.564681000 4.40046584 68.34740306
8 [1,-1,0,-2599487089,39173361400609] 230646920098311714063851989286 67.610685568 76.649343000 4.40343634 68.30383275
9 [0,-1,1,-1684944200,51357858049262] 277759817061511866219351665481 67.796554000 76.662802000 4.43254658 68.89516657
10 [0,0,1,-1726817617,57975709345266] 1122482466080847283271138480843 69.193096000 76.905236000 4.45559955 69.19309551
generators for these ten

1. [0,0,1,-1129201567,23953648602246] N = 155721986935837682842530035243

E = ellinit([0,0,1,-1129201567,23953648602246]);
generators:
  [-41321,246731]
  [-31532,5311158]
  [-18067,6201416]
  [-2305,5152107]
  [86,4884315]
  [847,4795604]
  [3304,4500981]
  [19999,3060971]
  [21377,3095720]
  [28464,3856626]
  [30009,4134216]
  [38281,6068360]
  [50563,9804491]

2. [0,0,1,-1141015057,26061092520366] N = 198333672870666343333189775723

E = ellinit([0,0,1,-1141015057,26061092520366]);
generators:
  [-30096,5756826]
  [-28332,5970441]
  [-23223,6327285]
  [-22420,6353982]
  [-10314,6060720]
  [-5762,5695991]
  [-1867,5308941]
  [-873,5201589]
  [1709,4910813]
  [10639,3889221]
  [25205,3648882]
  [28849,4141733]
  [39589,6552621]

3. [0,-1,1,-1876573260,32705933898332] N = 13048475524065056885495472921

E = ellinit([0,-1,1,-1876573260,32705933898332]);
generators:
  [-50174,740983]
  [-34581,7499665]
  [-7386,6794359]
  [258,5676424]
  [10493,3764339]
  [15191,2775653]
  [15843,2636614]
  [22793,1331960]
  [25138,1190455]
  [26925,1303036]
  [28326,1508983]
  [31670,2244663]
  [41511,5131861]

4. [0,0,1,-2077523317,13064155885836] N = 500145136377795551079641841157

E = ellinit([0,0,1,-2077523317,13064155885836]);
generators:
  [5814,1087181]
  [-46469,3043175]
  [-36326,6371598]
  [-21751,6925448]
  [-44268,-4275736]
  [24497/4,-6042957/8]
  [-7044,5229600]
  [149986,55457369]
  [1207,3249360]
  [43193,-1977897]
  [-2267,4214528]
  [-39801,5718576]
  [68828,14004671]

5. [0,0,1,-2217077947,28425800438316] N = 348398420573690733009119729797

E = ellinit([0,0,1,-2217077947,28425800438316]);
generators:
  [-1992,5730123]
  [607,5203869]
  [10905,2354862]
  [38511,399330]
  [43592,3822980]
  [47123,5347026]
  [76053,17312001]
  [102842,29801394]
  [448418,298666298]
  [-13012501/289,29872122205/4913]
  [-34298519/1296,386329606955/46656]
  [1493376/25,1305873751/125]
  [3154275529/3364,176932931836535/195112]

6. [0,0,1,-2147907577,47888102069226] N = 356492038662688596396428055563

E = ellinit([0,0,1,-2147907577,47888102069226]);
generators:
  [-219071/4,8936925/8]
  [-45112,7278558]
  [-38508,8573069]
  [-30707,9213558]
  [-9063,8161505]
  [-668,7023005]
  [606,6825444]
  [1724,6647573]
  [19378,3680016]
  [22558,3303716]
  [33568,3689433]
  [58477,11056694]
  [60591,11840190]

7. [1,-1,0,-2049670219,48898999201369] N = 240918419474403489984588164194

E = ellinit([1,-1,0,-2049670219,48898999201369]);
generators:
  [-47765,6174018]
  [-41117,7999362]
  [-40722,8072435]
  [-508,7067085]
  [33789,4251433]
  [40830,5748203]
  [77964,19013293]
  [82167,20820898]
  [531863/4,368438139/8]
  [208745,93260298]
  [381728,234096037]
  [12475639,44058514338]
  [-868995/16,7471163/64]

8. [1,-1,0,-2599487089,39173361400609] N = 230646920098311714063851989286

E = ellinit([1,-1,0,-2599487089,39173361400609]);
generators:
  [-37735,9158448]
  [-1806,6623753]
  [-177,6295600]
  [-37,6266560]
  [557,6141840]
  [2292,5763173]
  [56492,8492685]
  [124692,40603973]
  [-631661/25,1178988577/125]
  [-413012/9,212912381/27]
  [15745684/961,29247194873/29791]
  [959762629/17424,18208243461517/2299968]
  [16845344559906/1024960225,30680473388418927859/32814101603375]

9. [0,-1,1,-1684944200,51357858049262] N = 277759817061511866219351665481

E = ellinit([0,-1,1,-1684944200,51357858049262]);
generators:
  [-51668,693477]
  [-49202,3892049]
  [-39814,7438366]
  [-38185,7747171]
  [-36320,8040053]
  [-2493,7452712]
  [3014,6804910]
  [6398,6390574]
  [11431,5795756]
  [11816,5753098]
  [26316,5024026]
  [74474,18410014]
  [-429056/9,130428046/27]

10. [0,0,1,-1726817617,57975709345266] N = 1122482466080847283271138480843

E = ellinit([0,0,1,-1726817617,57975709345266]);
generators:
  [401,7568574]
  [52318,10527843]
  [-29122,9141443]
  [-33509,8843865]
  [893,7512281]
  [30523,5805593]
  [-47872,5561681]
  [-226151/9,249660170/27]
  [-207703/4,22105873/8]
  [-104487/4,73868697/8]
  [35904,6500753]
  [27267,5582409]
  [44289/4,-50731203/8]

Smallest Faltings height

# a-invariants conductor N log N naive h Faltings h log abs(disc)
1 [0,-1,1,-1876573260,32705933898332] 13048475524065056885495472921 64.738468820 75.760262570 4.24523710 65.83708111
2 [0,0,1,-1129201567,23953648602246] 155721986935837682842530035243 67.217870000 75.137429000 4.29745552 67.21786979
3 [0,0,1,-1141015057,26061092520366] 198333672870666343333189775723 67.459748000 75.306075000 4.31537831 67.45974834
4 [0,1,1,-3915257350,93169964920370] 91004323775371737344808170357 66.680704530 77.878043729 4.36269022 66.68070453
5 [0,0,1,-2217077947,28425800438316] 348398420573690733009119729797 68.023144222 76.171970810 4.37487054 68.02314422
6 [0,0,1,-2147907577,47888102069226] 356492038662688596396428055563 68.046109419 76.522921935 4.38307354 68.04610942
7 [0,0,1,-2077523317,13064155885836] 500145136377795551079641841157 68.384696000 75.976930000 4.39134211 68.38469584
8 [1,-1,0,-2049670219,48898999201369] 240918419474403489984588164194 67.654256000 76.564681000 4.40046584 68.34740306
9 [1,-1,0,-4598899594,121393996760584] 70507020932326816464044574994 66.425510000 78.383252000 4.40164549 67.11865698
10 [1,-1,0,-2599487089,39173361400609] 230646920098311714063851989286 67.610685568 76.649343000 4.40343634 68.30383275
generators for these ten

1. [0,-1,1,-1876573260,32705933898332] N = 13048475524065056885495472921

E = ellinit([0,-1,1,-1876573260,32705933898332]);
generators:
  [-50174,740983]
  [-34581,7499665]
  [-7386,6794359]
  [258,5676424]
  [10493,3764339]
  [15191,2775653]
  [15843,2636614]
  [22793,1331960]
  [25138,1190455]
  [26925,1303036]
  [28326,1508983]
  [31670,2244663]
  [41511,5131861]

2. [0,0,1,-1129201567,23953648602246] N = 155721986935837682842530035243

E = ellinit([0,0,1,-1129201567,23953648602246]);
generators:
  [-41321,246731]
  [-31532,5311158]
  [-18067,6201416]
  [-2305,5152107]
  [86,4884315]
  [847,4795604]
  [3304,4500981]
  [19999,3060971]
  [21377,3095720]
  [28464,3856626]
  [30009,4134216]
  [38281,6068360]
  [50563,9804491]

3. [0,0,1,-1141015057,26061092520366] N = 198333672870666343333189775723

E = ellinit([0,0,1,-1141015057,26061092520366]);
generators:
  [-30096,5756826]
  [-28332,5970441]
  [-23223,6327285]
  [-22420,6353982]
  [-10314,6060720]
  [-5762,5695991]
  [-1867,5308941]
  [-873,5201589]
  [1709,4910813]
  [10639,3889221]
  [25205,3648882]
  [28849,4141733]
  [39589,6552621]

4. [0,1,1,-3915257350,93169964920370] N = 91004323775371737344808170357

E = ellinit([0,1,1,-3915257350,93169964920370]);
generators:
  [-58520,11040254]
  [-799,9813141]
  [3837,8843281]
  [4705,8651754]
  [28301,2243358]
  [29377,1872138]
  [32403,571492]
  [39824,639729]
  [40642,1085841]
  [41215,1347320]
  [65150,10706345]
  [66436,11237958]
  [178900,71543654]

5. [0,0,1,-2217077947,28425800438316] N = 348398420573690733009119729797

E = ellinit([0,0,1,-2217077947,28425800438316]);
generators:
  [-1992,5730123]
  [607,5203869]
  [10905,2354862]
  [38511,399330]
  [43592,3822980]
  [47123,5347026]
  [76053,17312001]
  [102842,29801394]
  [448418,298666298]
  [-13012501/289,29872122205/4913]
  [-34298519/1296,386329606955/46656]
  [1493376/25,1305873751/125]
  [3154275529/3364,176932931836535/195112]

6. [0,0,1,-2147907577,47888102069226] N = 356492038662688596396428055563

E = ellinit([0,0,1,-2147907577,47888102069226]);
generators:
  [-219071/4,8936925/8]
  [-45112,7278558]
  [-38508,8573069]
  [-30707,9213558]
  [-9063,8161505]
  [-668,7023005]
  [606,6825444]
  [1724,6647573]
  [19378,3680016]
  [22558,3303716]
  [33568,3689433]
  [58477,11056694]
  [60591,11840190]

7. [0,0,1,-2077523317,13064155885836] N = 500145136377795551079641841157

E = ellinit([0,0,1,-2077523317,13064155885836]);
generators:
  [5814,1087181]
  [-46469,3043175]
  [-36326,6371598]
  [-21751,6925448]
  [-44268,-4275736]
  [24497/4,-6042957/8]
  [-7044,5229600]
  [149986,55457369]
  [1207,3249360]
  [43193,-1977897]
  [-2267,4214528]
  [-39801,5718576]
  [68828,14004671]

8. [1,-1,0,-2049670219,48898999201369] N = 240918419474403489984588164194

E = ellinit([1,-1,0,-2049670219,48898999201369]);
generators:
  [-47765,6174018]
  [-41117,7999362]
  [-40722,8072435]
  [-508,7067085]
  [33789,4251433]
  [40830,5748203]
  [77964,19013293]
  [82167,20820898]
  [531863/4,368438139/8]
  [208745,93260298]
  [381728,234096037]
  [12475639,44058514338]
  [-868995/16,7471163/64]

9. [1,-1,0,-4598899594,121393996760584] N = 70507020932326816464044574994

E = ellinit([1,-1,0,-4598899594,121393996760584]);
generators:
  [26346,4290074]
  [40907,1290508]
  [36887,-1412607]
  [42460,-1655992]
  [61122,8254538]
  [-34562,15478680]
  [27965,3814198]
  [50678,4273882]
  [65950,-10276822]
  [75100,-14164728]
  [52422,4910138]
  [42876,-1762516]
  [36942,1365578]

10. [1,-1,0,-2599487089,39173361400609] N = 230646920098311714063851989286

E = ellinit([1,-1,0,-2599487089,39173361400609]);
generators:
  [-37735,9158448]
  [-1806,6623753]
  [-177,6295600]
  [-37,6266560]
  [557,6141840]
  [2292,5763173]
  [56492,8492685]
  [124692,40603973]
  [-631661/25,1178988577/125]
  [-413012/9,212912381/27]
  [15745684/961,29247194873/29791]
  [959762629/17424,18208243461517/2299968]
  [16845344559906/1024960225,30680473388418927859/32814101603375]

Smallest absolute discriminant

# a-invariants conductor N log N naive h Faltings h log abs(disc)
1 [0,-1,1,-1876573260,32705933898332] 13048475524065056885495472921 64.738468820 75.760262570 4.24523710 65.83708111
2 [0,1,1,-3915257350,93169964920370] 91004323775371737344808170357 66.680704530 77.878043729 4.36269022 66.68070453
3 [1,-1,0,-4598899594,121393996760584] 70507020932326816464044574994 66.425510000 78.383252000 4.40164549 67.11865698
4 [0,0,1,-1129201567,23953648602246] 155721986935837682842530035243 67.217870000 75.137429000 4.29745552 67.21786979
5 [0,0,1,-1141015057,26061092520366] 198333672870666343333189775723 67.459748000 75.306075000 4.31537831 67.45974834
6 [1,0,1,-6489409453,202730435387172] 132452629998841421797163345894 67.056023000 79.408947000 4.47003817 67.74916976
7 [0,0,1,-6265772149,189142776829182] 288794189909830943337356727829 67.835511800 79.288706030 4.46902532 67.83551180
8 [0,0,1,-6703514287,209526656923296] 313723684682894471293495831717 67.918310124 79.491296272 4.48073556 67.91831012
9 [1,-1,0,-25949190094,1608685635288664] 165782089380280872920512734806 67.280471722 83.551821740 4.67077074 67.97361890
10 [0,0,1,-2217077947,28425800438316] 348398420573690733009119729797 68.023144222 76.171970810 4.37487054 68.02314422
generators for these ten

1. [0,-1,1,-1876573260,32705933898332] N = 13048475524065056885495472921

E = ellinit([0,-1,1,-1876573260,32705933898332]);
generators:
  [-50174,740983]
  [-34581,7499665]
  [-7386,6794359]
  [258,5676424]
  [10493,3764339]
  [15191,2775653]
  [15843,2636614]
  [22793,1331960]
  [25138,1190455]
  [26925,1303036]
  [28326,1508983]
  [31670,2244663]
  [41511,5131861]

2. [0,1,1,-3915257350,93169964920370] N = 91004323775371737344808170357

E = ellinit([0,1,1,-3915257350,93169964920370]);
generators:
  [-58520,11040254]
  [-799,9813141]
  [3837,8843281]
  [4705,8651754]
  [28301,2243358]
  [29377,1872138]
  [32403,571492]
  [39824,639729]
  [40642,1085841]
  [41215,1347320]
  [65150,10706345]
  [66436,11237958]
  [178900,71543654]

3. [1,-1,0,-4598899594,121393996760584] N = 70507020932326816464044574994

E = ellinit([1,-1,0,-4598899594,121393996760584]);
generators:
  [26346,4290074]
  [40907,1290508]
  [36887,-1412607]
  [42460,-1655992]
  [61122,8254538]
  [-34562,15478680]
  [27965,3814198]
  [50678,4273882]
  [65950,-10276822]
  [75100,-14164728]
  [52422,4910138]
  [42876,-1762516]
  [36942,1365578]

4. [0,0,1,-1129201567,23953648602246] N = 155721986935837682842530035243

E = ellinit([0,0,1,-1129201567,23953648602246]);
generators:
  [-41321,246731]
  [-31532,5311158]
  [-18067,6201416]
  [-2305,5152107]
  [86,4884315]
  [847,4795604]
  [3304,4500981]
  [19999,3060971]
  [21377,3095720]
  [28464,3856626]
  [30009,4134216]
  [38281,6068360]
  [50563,9804491]

5. [0,0,1,-1141015057,26061092520366] N = 198333672870666343333189775723

E = ellinit([0,0,1,-1141015057,26061092520366]);
generators:
  [-30096,5756826]
  [-28332,5970441]
  [-23223,6327285]
  [-22420,6353982]
  [-10314,6060720]
  [-5762,5695991]
  [-1867,5308941]
  [-873,5201589]
  [1709,4910813]
  [10639,3889221]
  [25205,3648882]
  [28849,4141733]
  [39589,6552621]

6. [1,0,1,-6489409453,202730435387172] N = 132452629998841421797163345894

E = ellinit([1,0,1,-6489409453,202730435387172]);
generators:
  [40159,2604588]
  [40170,2601123]
  [1191,13963760]
  [45438,-1317709]
  [46769,1212522]
  [53105,-2832732]
  [8362,12204451]
  [63825,6935466]
  [397012,-245561184]
  [51615,-2325412]
  [55444,3628683]
  [176375/4,-12356847/8]
  [15781,-10218240]

7. [0,0,1,-6265772149,189142776829182] N = 288794189909830943337356727829

E = ellinit([0,0,1,-6265772149,189142776829182]);
generators:
  [-46306,19493439]
  [30635,5093318]
  [34263,3831681]
  [39722,1711323]
  [41743,571761]
  [41922,380876]
  [49353,343721]
  [198473/4,5089953/8]
  [49703,707678]
  [50530,1245228]
  [50699,1338105]
  [54119,2924510]
  [621337/9,249825122/27]

8. [0,0,1,-6703514287,209526656923296] N = 313723684682894471293495831717

E = ellinit([0,0,1,-6703514287,209526656923296]);
generators:
  [-12776,17119736]
  [26713,7036878]
  [40823,1975178]
  [41468,1689228]
  [42512,1173680]
  [50836,349604]
  [53094,1811301]
  [53770,2130542]
  [75783,11693621]
  [82753,14882478]
  [218196,95577444]
  [-1076701/25,2556697218/125]
  [16501489/324,2752651765/5832]

9. [1,-1,0,-25949190094,1608685635288664] N = 165782089380280872920512734806

E = ellinit([1,-1,0,-25949190094,1608685635288664]);
generators:
  [-120149,54759245]
  [-100654,56626110]
  [-1434,40570334]
  [-308,40208088]
  [15758,34686372]
  [132103/4,224397919/8]
  [69578,11798350]
  [103747,5710205]
  [124943,17740860]
  [133006,22521764]
  [1376179/4,1460773185/8]
  [20177011/196,14458679971/2744]
  [1686891884/13225,29316901631272/1520875]

10. [0,0,1,-2217077947,28425800438316] N = 348398420573690733009119729797

E = ellinit([0,0,1,-2217077947,28425800438316]);
generators:
  [-1992,5730123]
  [607,5203869]
  [10905,2354862]
  [38511,399330]
  [43592,3822980]
  [47123,5347026]
  [76053,17312001]
  [102842,29801394]
  [448418,298666298]
  [-13012501/289,29872122205/4913]
  [-34298519/1296,386329606955/46656]
  [1493376/25,1305873751/125]
  [3154275529/3364,176932931836535/195112]