Elliptic curves by rank › curves from searches

Torsion Z/2: record curves

The curves of this collection with torsion subgroup Z/2, by rank: for each rank the ten smallest conductors, with generators of the Mordell-Weil group and of the torsion subgroup. Every curve has proven rank, is given by its global minimal model, and 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	915	15.298409	28.767894	20.407947
5	23,420	19.262706	40.659381	26.423784
6	879,377	24.529232	45.572845	35.074889
7	1,452,483	30.739101	56.114918	43.632901
8	70,125	36.438334	64.510115	54.062158
9	2,093	43.236845	77.899841	66.506696
10	80	51.717853	87.405754	79.885089

Rank 4

#	a-invariants	conductor N	log N	naive h	log abs(disc)	torsion generators
1	`[0,1,0,-3929,93415]`	`4405696`	15.298408807	36.442278000	22.59278611	`[[35,0]]`
2	`[0,1,0,-3009,139231]`	`4405696`	15.298408807	37.225282000	29.54076494	`[[-71,0]]`
3	`[0,1,0,-15249,716431]`	`4594624`	15.340397482	40.510476000	28.35351726	`[[67,0]]`
4	`[0,1,0,161,2097]`	`5360768`	15.494617806	28.767894000	21.45045518	`[[-9,0]]`
5	`[0,1,0,-1769,24871]`	`5360768`	15.494617806	34.048677000	25.03339824	`[[17,0]]`
6	`[1,1,0,-1131,14121]`	`6399618`	15.671748859	32.707557000	20.40794731	`[[18,-9]]`
7	`[0,1,0,-985,2919]`	`7440832`	15.822493229	32.292543000	24.76049980	`[[3,0]]`
8	`[0,1,0,3775,26719]`	`7440832`	15.822493229	36.321805000	28.94530451	`[[-7,0]]`
9	`[0,1,0,-134136,18864244]`	`7598320`	15.843437728	47.033439000	25.71274783	`[[211,0]]`
10	`[1,-1,0,-4398,113120]`	`7814358`	15.871473369	36.780446000	23.90350868	`[[40,-20]]`

generators for these ten

1. [0,1,0,-3929,93415] N = 4405696

E = ellinit([0,1,0,-3929,93415]);
generators:
  [-11,368]
  [127,1288]
  [-57,368]
  [219,3128]
torsion generators:
  [35,0]

2. [0,1,0,-3009,139231] N = 4405696

E = ellinit([0,1,0,-3009,139231]);
generators:
  [11,328]
  [93,820]
  [-30,451]
  [-21,440]
torsion generators:
  [-71,0]

3. [0,1,0,-15249,716431] N = 4594624

E = ellinit([0,1,0,-15249,716431]);
generators:
  [170,1751]
  [-221/9,28016/27]
  [-139,412]
  [891,26368]
torsion generators:
  [67,0]

4. [0,1,0,161,2097] N = 5360768

E = ellinit([0,1,0,161,2097]);
generators:
  [-7,26]
  [-1,44]
  [-8,19]
  [9,66]
torsion generators:
  [-9,0]

5. [0,1,0,-1769,24871] N = 5360768

E = ellinit([0,1,0,-1769,24871]);
generators:
  [-45,124]
  [3,140]
  [-14,217]
  [141,1612]
torsion generators:
  [17,0]

6. [1,1,0,-1131,14121] N = 6399618

E = ellinit([1,1,0,-1131,14121]);
generators:
  [24,27]
  [56,333]
  [-20,181]
  [-39,48]
torsion generators:
  [18,-9]

7. [0,1,0,-985,2919] N = 7440832

E = ellinit([0,1,0,-985,2919]);
generators:
  [-31,68]
  [-25,112]
  [71,544]
  [-14,119]
torsion generators:
  [3,0]

8. [0,1,0,3775,26719] N = 7440832

E = ellinit([0,1,0,3775,26719]);
generators:
  [-5,88]
  [11,264]
  [91,1064]
  [43,520]
torsion generators:
  [-7,0]

9. [0,1,0,-134136,18864244] N = 7598320

E = ellinit([0,1,0,-134136,18864244]);
generators:
  [210,-28]
  [212,-22]
  [5426/25,-18724/125]
  [215,-98]
torsion generators:
  [211,0]

10. [1,-1,0,-4398,113120] N = 7814358

E = ellinit([1,-1,0,-4398,113120]);
generators:
  [-17,436]
  [97,721]
  [-74,208]
  [103/4,923/8]
torsion generators:
  [40,-20]

Rank 5

#	a-invariants	conductor N	log N	naive h	log abs(disc)	torsion generators
1	`[0,-1,0,-16025,731481]`	`232106304`	19.262706032	40.659381000	31.20356235	`[[57,0]]`
2	`[0,1,0,-517680,160352164]`	`585882128`	20.188629181	51.311063000	42.25872245	`[[-842,0]]`
3	`[0,1,0,-8555320,9628692084]`	`585882128`	20.188629181	59.499795000	41.64682044	`[[1683,0]]`
4	`[1,-1,0,-483939,105674949]`	`672899094`	20.327105942	50.882747000	42.33868987	`[[-786,393]]`
5	`[1,-1,0,-7337079,7650982089]`	`672899094`	20.327105942	59.038957000	42.28504099	`[[6291/4,-6291/8]]`
6	`[1,1,1,-237413,44411906]`	`1049432925`	20.771515784	48.746273000	33.93909150	`[[285,-143]]`
7	`[1,1,1,-272288,30461906]`	`1049432925`	20.771515784	49.157450000	41.32792019	`[[-2285/4,2281/8]]`
8	`[0,-1,0,-358745,20266521]`	`1147880256`	20.861182823	49.984707000	42.46881141	`[[57,0]]`
9	`[1,0,0,-147143,22258702]`	`1458645725`	21.100774257	47.360734000	36.87853853	`[[-1777/4,1777/8]]`
10	`[1,0,0,-148168,21939927]`	`1458645725`	21.100774257	47.331910000	26.42378424	`[[222,-111]]`

generators for these ten

1. [0,-1,0,-16025,731481] N = 232106304

E = ellinit([0,-1,0,-16025,731481]);
generators:
  [-37,1128]
  [245,3384]
  [104,423]
  [151,1316]
  [-131,752]
torsion generators:
  [57,0]

2. [0,1,0,-517680,160352164] N = 585882128

E = ellinit([0,1,0,-517680,160352164]);
generators:
  [-166,15548]
  [3422,196144]
  [1429/4,36777/8]
  [6280/9,318734/27]
  [432,4186]
torsion generators:
  [-842,0]

3. [0,1,0,-8555320,9628692084] N = 585882128

E = ellinit([0,1,0,-8555320,9628692084]);
generators:
  [-686,123188]
  [1154,35972]
  [4052,203734]
  [190810/81,36833212/729]
  [1890,14628]
torsion generators:
  [1683,0]

4. [1,-1,0,-483939,105674949] N = 672899094

E = ellinit([1,-1,0,-483939,105674949]);
generators:
  [978,23325]
  [243,-1665]
  [537,393]
  [-345,15387]
  [222,2913]
torsion generators:
  [-786,393]

5. [1,-1,0,-7337079,7650982089] N = 672899094

E = ellinit([1,-1,0,-7337079,7650982089]);
generators:
  [3876,191535]
  [-1353,123558]
  [2877,100293]
  [1482,4803]
  [1656,5499]
torsion generators:
  [6291/4,-6291/8]

6. [1,1,1,-237413,44411906] N = 1049432925

E = ellinit([1,1,1,-237413,44411906]);
generators:
  [440,4817]
  [2535/4,95111/8]
  [-490,6832]
  [6,6553]
  [-335,9467]
torsion generators:
  [285,-143]

7. [1,1,1,-272288,30461906] N = 1049432925

E = ellinit([1,1,1,-272288,30461906]);
generators:
  [60,3757]
  [464,-2303]
  [4605,308272]
  [565,-7858]
  [-520,5897]
torsion generators:
  [-2285/4,2281/8]

8. [0,-1,0,-358745,20266521] N = 1147880256

E = ellinit([0,-1,0,-358745,20266521]);
generators:
  [2624,130917]
  [23,3468]
  [-547,7248]
  [601,4624]
  [-3709/25,1047336/125]
torsion generators:
  [57,0]

9. [1,0,0,-147143,22258702] N = 1458645725

E = ellinit([1,0,0,-147143,22258702]);
generators:
  [267,1289]
  [1834/9,20578/27]
  [-302,6410]
  [499/4,18847/8]
  [7393/49,-667423/343]
torsion generators:
  [-1777/4,1777/8]

10. [1,0,0,-148168,21939927] N = 1458645725

E = ellinit([1,0,0,-148168,21939927]);
generators:
  [217,-241]
  [223,-133]
  [221,-81]
  [242,-641]
  [-434,-1915]
torsion generators:
  [222,-111]

Rank 6

#	a-invariants	conductor N	log N	naive h	log abs(disc)	torsion generators
1	`[0,1,0,-397505,96310384]`	`44968690156`	24.529232310	50.292494000	35.07488949	`[[368,0]]`
2	`[0,1,0,-445020,71792644]`	`44968690156`	24.529232310	50.631229000	42.67169053	`[[-737,0]]`
3	`[0,1,0,-1574345,756199159]`	`73879116224`	25.025696030	54.421653000	42.30463383	`[[683,0]]`
4	`[0,1,0,-706785,1586454079]`	`73879116224`	25.025696030	55.892977000	48.41726153	`[[-1367,0]]`
5	`[1,0,0,-4172813,3280352992]`	`82820649775`	25.139943261	57.345906000	40.81710853	`[[1172,-586]]`
6	`[1,0,0,-3915438,3702705367]`	`82820649775`	25.139943261	57.587981000	49.08766246	`[[-9377/4,9377/8]]`
7	`[1,0,1,-4868976,4093135598]`	`88246450450`	25.203399310	57.808785000	46.44617595	`[[1377,-689]]`
8	`[1,0,1,-1058403,112021162]`	`121340359518`	25.521865322	53.230417000	45.70145366	`[[107,-54]]`
9	`[0,0,0,-10972227,13769230210]`	`138417695568`	25.653541730	60.246236000	49.32384949	`[[2105,0]]`
10	`[1,1,0,-82433,8186337]`	`146635526910`	25.711215936	45.572845000	36.43426303	`[[206,-103]]`

generators for these ten

1. [0,1,0,-397505,96310384] N = 44968690156

E = ellinit([0,1,0,-397505,96310384]);
generators:
  [411,1591]
  [-191,12857]
  [325,1247]
  [385,697]
  [381,-559]
  [9871,978809]
torsion generators:
  [368,0]

2. [0,1,0,-445020,71792644] N = 44968690156

E = ellinit([0,1,0,-445020,71792644]);
generators:
  [164,1802]
  [-48,9646]
  [-516,12818]
  [588,3710]
  [5080/9,23426/27]
  [-636,9898]
torsion generators:
  [-737,0]

3. [0,1,0,-1574345,756199159] N = 73879116224

E = ellinit([0,1,0,-1574345,756199159]);
generators:
  [-1203,30176]
  [1626,49979]
  [2569,116932]
  [-1433,8464]
  [269,18768]
  [4455,286672]
torsion generators:
  [683,0]

4. [0,1,0,-706785,1586454079] N = 73879116224

E = ellinit([0,1,0,-706785,1586454079]);
generators:
  [-53,40296]
  [1626,68839]
  [683,37720]
  [4619,311272]
  [3305,188048]
  [-28189/25,3854984/125]
torsion generators:
  [-1367,0]

5. [1,0,0,-4172813,3280352992] N = 82820649775

E = ellinit([1,0,0,-4172813,3280352992]);
generators:
  [1317,7679]
  [11467,1203929]
  [5043/4,34007/8]
  [1243,3177]
  [-887,79715]
  [4543/4,15757/8]
torsion generators:
  [1172,-586]

6. [1,0,0,-3915438,3702705367] N = 82820649775

E = ellinit([1,0,0,-3915438,3702705367]);
generators:
  [1607,38709]
  [1062,26719]
  [-1663,75769]
  [-1438,80469]
  [41517/16,6634091/64]
  [77683/9,21022663/27]
torsion generators:
  [-9377/4,9377/8]

7. [1,0,1,-4868976,4093135598] N = 88246450450

E = ellinit([1,0,1,-4868976,4093135598]);
generators:
  [-2098,72286]
  [-1278,91351]
  [977,15911]
  [682,32671]
  [-1403,91051]
  [6983/4,234913/8]
torsion generators:
  [1377,-689]

8. [1,0,1,-1058403,112021162] N = 121340359518

E = ellinit([1,0,1,-1058403,112021162]);
generators:
  [-1054,8073]
  [-796,21618]
  [-667,23166]
  [1913,70380]
  [2816,138105]
  [5525,400878]
torsion generators:
  [107,-54]

9. [0,0,0,-10972227,13769230210] N = 138417695568

E = ellinit([0,0,0,-10972227,13769230210]);
generators:
  [743,77634]
  [1679,8946]
  [2111,3762]
  [2786,69462]
  [3921,176152]
  [2318,28116]
torsion generators:
  [2105,0]

10. [1,1,0,-82433,8186337] N = 146635526910

E = ellinit([1,1,0,-82433,8186337]);
generators:
  [-328,431]
  [-304,2447]
  [-239,3902]
  [376,5337]
  [-202,4181]
  [-689/4,33975/8]
torsion generators:
  [206,-103]

Rank 7

#	a-invariants	conductor N	log N	naive h	log abs(disc)	torsion generators
1	`[0,1,0,-682000,55838851044]`	`22378025224048`	30.739100576	63.014625000	55.55989010	`[[-3882,0]]`
2	`[0,1,0,-223282040,1265447468404]`	`22378025224048`	30.739100576	69.285442000	58.28543240	`[[7763,0]]`
3	`[0,0,0,-114544227,471841863410]`	`24414611509584`	30.826202901	67.283018000	49.97809302	`[[6205,0]]`
4	`[0,0,0,-119353467,430063995530]`	`24414611509584`	30.826202901	67.406403000	58.62635091	`[[-12410,0]]`
5	`[0,1,0,-230853065,1349233034359]`	`42717604222528`	31.385632228	69.385479000	55.12188000	`[[8603,0]]`
6	`[0,1,0,-186847905,1879275186559]`	`42717604222528`	31.385632228	70.047026000	62.27262137	`[[-17207,0]]`
7	`[0,1,0,-4932661560,129720255016564]`	`48324055603376`	31.508950598	78.571037000	68.18963545	`[[34963,0]]`
8	`[0,1,0,-5594735,5089624849]`	`49159219350656`	31.526085521	58.225613000	43.63290121	`[[1343,0]]`
9	`[0,1,0,-4689225,6792889159]`	`49159219350656`	31.526085521	58.801890000	50.94535535	`[[-2687,0]]`
10	`[0,-1,0,-159733785,776778430041]`	`54381804383424`	31.627050736	68.280660000	53.70712885	`[[7177,0]]`

generators for these ten

1. [0,1,0,-682000,55838851044] N = 22378025224048

E = ellinit([0,1,0,-682000,55838851044]);
generators:
  [1864,247078]
  [-8,236314]
  [4074,347412]
  [-3544,117286]
  [11614,1270672]
  [3674/25,29512132/125]
  [-2009/9,6388226/27]
torsion generators:
  [-3882,0]

2. [0,1,0,-223282040,1265447468404] N = 22378025224048

E = ellinit([0,1,0,-223282040,1265447468404]);
generators:
  [20844,2380742]
  [23522,3004716]
  [-152510/9,11563604/27]
  [7636,75946]
  [10938,363220]
  [12810,712348]
  [28893/4,1375283/8]
torsion generators:
  [7763,0]

3. [0,0,0,-114544227,471841863410] N = 24414611509584

E = ellinit([0,0,0,-114544227,471841863410]);
generators:
  [5107,141642]
  [-7154,961848]
  [6571,53802]
  [6083,12566]
  [4558,210816]
  [-11363,553392]
  [6497,43508]
torsion generators:
  [6205,0]

4. [0,0,0,-119353467,430063995530] N = 24414611509584

E = ellinit([0,0,0,-119353467,430063995530]);
generators:
  [8833,254916]
  [4177,66348]
  [15041,1427452]
  [-9863,804852]
  [63097/121,807388812/1331]
  [1849,464436]
  [22849/9,10224964/27]
torsion generators:
  [-12410,0]

5. [0,1,0,-230853065,1349233034359] N = 42717604222528

E = ellinit([0,1,0,-230853065,1349233034359]);
generators:
  [237,1137776]
  [-3758,1470959]
  [8227,83096]
  [-109829/9,41383576/27]
  [-2789,1404064]
  [438279/49,2275552/343]
  [14619,1048288]
torsion generators:
  [8603,0]

6. [0,1,0,-186847905,1879275186559] N = 42717604222528

E = ellinit([0,1,0,-186847905,1879275186559]);
generators:
  [-3573,1581544]
  [10061,1008916]
  [-7381,1690072]
  [-10390,1642897]
  [11115,1084328]
  [214571,99200984]
  [11387,1108264]
torsion generators:
  [-17207,0]

7. [0,1,0,-4932661560,129720255016564] N = 48324055603376

E = ellinit([0,1,0,-4932661560,129720255016564]);
generators:
  [-75868,8201494]
  [-20701,14931868]
  [2056186/81,3329806564/729]
  [20914,5975508]
  [72650,12442508]
  [31876,2208234]
  [145794,50095612]
torsion generators:
  [34963,0]

8. [0,1,0,-5594735,5089624849] N = 49159219350656

E = ellinit([0,1,0,-5594735,5089624849]);
generators:
  [1089,17018]
  [1297,4094]
  [327,57404]
  [7047,-561844]
  [4264,242443]
  [2769,-104098]
  [9309/4,547243/8]
torsion generators:
  [1343,0]

9. [0,1,0,-4689225,6792889159] N = 49159219350656

E = ellinit([0,1,0,-4689225,6792889159]);
generators:
  [1715,61628]
  [3135,-151372]
  [-145,-86428]
  [23066/25,-7129039/125]
  [351,72044]
  [75231/49,19448036/343]
  [863,-58220]
torsion generators:
  [-2687,0]

10. [0,-1,0,-159733785,776778430041] N = 54381804383424

E = ellinit([0,-1,0,-159733785,776778430041]);
generators:
  [1163,769792]
  [7425,6696]
  [49275,10608696]
  [3333,530472]
  [6960,46221]
  [4461,391104]
  [14121,1156176]
torsion generators:
  [7177,0]

Rank 8

#	a-invariants	conductor N	log N	naive h	log abs(disc)	torsion generators
1	`[0,1,0,-1913423065,32212145083239]`	`6682940617328192`	36.438334498	75.730082000	59.58083846	`[[25443,0]]`
2	`[0,1,0,-2056755905,27106485989599]`	`6682940617328192`	36.438334498	75.946790000	67.64795055	`[[-50887,0]]`
3	`[1,1,0,-45452141,114932096265]`	`26676134520303198`	37.822545722	64.510115000	54.06215770	`[[3374,-1687]]`
4	`[0,-1,0,-218669600,794575772496]`	`28330377346942896`	37.882711028	69.222820000	61.24469312	`[[-16348,0]]`
5	`[0,-1,0,-3134341640,67528477424016]`	`28330377346942896`	37.882711028	77.210658000	61.93760145	`[[32697,0]]`
6	`[0,1,0,-1894949065,31743132642039]`	`29231074244902976`	37.914008725	75.700976000	60.41206737	`[[24843,0]]`
7	`[0,1,0,-1678071905,39286337143999]`	`29231074244902976`	37.914008725	76.126970000	68.06792347	`[[-49687,0]]`
8	`[0,1,0,-677920785,6446025754639]`	`31226965890509248`	37.980058408	72.617226000	62.85703718	`[[12163,0]]`
9	`[0,1,0,-541973089,4299659003007]`	`36476637438549952`	38.135448380	71.945784000	62.95892899	`[[9531,0]]`
10	`[0,1,0,805197631,22276574524831]`	`36476637438549952`	38.135448380	74.992235000	67.68235431	`[[-19063,0]]`

generators for these ten

1. [0,1,0,-1913423065,32212145083239] N = 6682940617328192

E = ellinit([0,1,0,-1913423065,32212145083239]);
generators:
  [-7583,6803356]
  [8930,3979633]
  [34879,2811928]
  [20725,1207808]
  [26815,-430808]
  [224269/9,2057048/27]
  [26311,288176]
  [171701,69033776]
torsion generators:
  [25443,0]

2. [0,1,0,-2056755905,27106485989599] N = 6682940617328192

E = ellinit([0,1,0,-2056755905,27106485989599]);
generators:
  [39051,2518264]
  [36349,610652]
  [-7269,6455464]
  [1771,4844536]
  [40157,3044916]
  [10112107,32155713016]
  [1563091/169,6544968136/2197]
  [-5918,6250691]
torsion generators:
  [-50887,0]

3. [1,1,0,-45452141,114932096265] N = 26676134520303198

E = ellinit([1,1,0,-45452141,114932096265]);
generators:
  [-860,392075]
  [4907,97958]
  [8708,611723]
  [-30961/4,475531/8]
  [4592,53123]
  [18193,2295258]
  [-309,359247]
  [5152,-135037]
torsion generators:
  [3374,-1687]

4. [0,-1,0,-218669600,794575772496] N = 28330377346942896

E = ellinit([0,-1,0,-218669600,794575772496]);
generators:
  [14558,834462]
  [1630,665186]
  [-5642,1359662]
  [165654,67158738]
  [80006,-22257774]
  [3236,347616]
  [15509/4,-566307/8]
  [-4244,1283024]
torsion generators:
  [-16348,0]

5. [0,-1,0,-3134341640,67528477424016] N = 28330377346942896

E = ellinit([0,-1,0,-3134341640,67528477424016]);
generators:
  [36488,1319268]
  [22216,2976604]
  [33496,348364]
  [28906,1038734]
  [32744,-60348]
  [210874,-93721102]
  [283792/9,5827436/27]
  [38384,-1941852]
torsion generators:
  [32697,0]

6. [0,1,0,-1894949065,31743132642039] N = 29231074244902976

E = ellinit([0,1,0,-1894949065,31743132642039]);
generators:
  [7367,4264144]
  [29807,1320424]
  [-14869,7525424]
  [34771,-2809624]
  [6082,4521401]
  [662717,-538365656]
  [24329,-204572]
  [24586,-126701]
torsion generators:
  [24843,0]

7. [0,1,0,-1678071905,39286337143999] N = 29231074244902976

E = ellinit([0,1,0,-1678071905,39286337143999]);
generators:
  [20731,3661736]
  [-3941,6770408]
  [-14478,7781189]
  [20856235,95247380632]
  [12922,4445239]
  [-139677/121,8545589240/1331]
  [5132275/121,8870943992/1331]
  [714309/196,15815329993/2744]
torsion generators:
  [-49687,0]

8. [0,1,0,-677920785,6446025754639] N = 31226965890509248

E = ellinit([0,1,0,-677920785,6446025754639]);
generators:
  [-12079,3587816]
  [18419,456688]
  [18810,591583]
  [2507,2182256]
  [20595,1104592]
  [-21565,3322208]
  [109131,35102416]
  [17867,193936]
torsion generators:
  [12163,0]

9. [0,1,0,-541973089,4299659003007] N = 36476637438549952

E = ellinit([0,1,0,-541973089,4299659003007]);
generators:
  [-5411,2659676]
  [-1877,2304416]
  [17002,7471]
  [6493,1026844]
  [20617,1374664]
  [17243,285344]
  [155653/9,-8524628/27]
  [17469,-403956]
torsion generators:
  [9531,0]

10. [0,1,0,805197631,22276574524831] N = 36476637438549952

E = ellinit([0,1,0,805197631,22276574524831]);
generators:
  [-3237,4431280]
  [2011,4889168]
  [-72365/9,105550928/27]
  [30538,8680175]
  [1380835/121,7640412976/1331]
  [3771,5036528]
  [13029739/529,91901526416/12167]
  [-16371/4,34790861/8]
torsion generators:
  [-19063,0]

Rank 9

#	a-invariants	conductor N	log N	naive h	log abs(disc)	torsion generators
1	`[0,-1,0,-50722837785,4393284841977561]`	`5991327633625214784`	43.236844703	85.562529000	71.72055216	`[[126937,0]]`
2	`[0,-1,0,-38802409025,6511676157345921]`	`5991327633625214784`	43.236844703	86.347888000	78.66485965	`[[-253873,0]]`
3	`[0,1,0,-17465296335,5229643552629409]`	`7623567598977423232`	43.477776123	85.909387000	78.42538340	`[[-206777,0]]`
4	`[0,1,0,-112414537633,14506038362533488]`	`16935100540754779100`	44.275920097	87.949980000	71.66908228	`[[194928,0]]`
5	`[0,1,0,-120297676508,12354729763545988]`	`16935100540754779100`	44.275920097	88.153308000	79.80250231	`[[-389857,0]]`
6	`[0,1,0,-9909839449,379470040610151]`	`23999337050845260736`	44.624557881	80.663985000	66.50669561	`[[56307,0]]`
7	`[0,1,0,-7918379009,536458061971615]`	`23999337050845260736`	44.624557881	81.355174000	73.60530266	`[[-112615,0]]`
8	`[0,1,0,-40806227465,3168820981473079]`	`24713621597826872896`	44.653886247	84.909905000	71.45387025	`[[119963,0]]`
9	`[0,1,0,-52643110305,1180828345377919]`	`24713621597826872896`	44.653886247	85.674007000	78.15259576	`[[-239927,0]]`
10	`[0,1,0,-12733181679,300724070684785]`	`25114814725829542784`	44.669989574	81.416034000	73.61077306	`[[-123185,0]]`

generators for these ten

1. [0,-1,0,-50722837785,4393284841977561] N = 5991327633625214784

E = ellinit([0,-1,0,-50722837785,4393284841977561]);
generators:
  [140949,6641688]
  [141879,7261812]
  [18005,59041144]
  [7064136/49,-3011343441/343]
  [-336475/4,718433773/8]
  [-2234459/9,1107620576/27]
  [235869,74509488]
  [1484979/25,-4984292592/125]
  [-754851/4,680929353/8]
torsion generators:
  [126937,0]

2. [0,-1,0,-38802409025,6511676157345921] N = 5991327633625214784

E = ellinit([0,-1,0,-38802409025,6511676157345921]);
generators:
  [644929,499733912]
  [72241,-63918344]
  [63997/4,-614229241/8]
  [529473,366605928]
  [4853953,10685571992]
  [1599409,2008957688]
  [294177,143369880]
  [121400,-59918589]
  [-487253/9,2482491124/27]
torsion generators:
  [-253873,0]

3. [0,1,0,-17465296335,5229643552629409] N = 7623567598977423232

E = ellinit([0,1,0,-17465296335,5229643552629409]);
generators:
  [956720,-929634103]
  [-181056,-49564367]
  [-577819/4,-550679401/8]
  [291801,158049226]
  [37934440,-233640381603]
  [53145,66719978]
  [22809961/81,109696824154/729]
  [1947192,-2711846971]
  [929481/16,4250626739/64]
torsion generators:
  [-206777,0]

4. [0,1,0,-112414537633,14506038362533488] N = 16935100540754779100

E = ellinit([0,1,0,-112414537633,14506038362533488]);
generators:
  [95173,68332175]
  [235673,33207175]
  [195473,1016425]
  [1453,119761025]
  [143453,36495775]
  [-153327,167742825]
  [205223,-8905175]
  [115903,-55080425]
  [26479183/121,26137306325/1331]
torsion generators:
  [194928,0]

5. [0,1,0,-120297676508,12354729763545988] N = 16935100540754779100

E = ellinit([0,1,0,-120297676508,12354729763545988]);
generators:
  [274388,2214150]
  [5268,108264250]
  [3426412/9,3980761750/27]
  [1807033/16,925145675/64]
  [277768,19265750]
  [4885852,10772997778]
  [8645308/81,-19709625250/729]
  [-348132,109736750]
  [-49232,-134751250]
torsion generators:
  [-389857,0]

6. [0,1,0,-9909839449,379470040610151] N = 23999337050845260736

E = ellinit([0,1,0,-9909839449,379470040610151]);
generators:
  [67841,4405988]
  [112555,-26267816]
  [58643,64240]
  [4331,18347528]
  [84631,-12122672]
  [117611,28996792]
  [52815,-1846104]
  [-12757,-22445800]
  [39041,7217188]
torsion generators:
  [56307,0]

7. [0,1,0,-7918379009,536458061971615] N = 23999337050845260736

E = ellinit([0,1,0,-7918379009,536458061971615]);
generators:
  [31387,17856248]
  [5499,22205432]
  [123613,38032708]
  [4242538/9,8604191501/27]
  [1183403,1283921832]
  [121277,36876972]
  [-99621,18347528]
  [7696771/25,20645854744/125]
  [2729,-22690728]
torsion generators:
  [-112615,0]

8. [0,1,0,-40806227465,3168820981473079] N = 24713621597826872896

E = ellinit([0,1,0,-40806227465,3168820981473079]);
generators:
  [126679,-5695168]
  [124425,-4221052]
  [79805,20507352]
  [-227590,25834773]
  [42729,-38771468]
  [1696171/25,3336737144/125]
  [200279,55043232]
  [282826,119378579]
  [89741,-15151296]
torsion generators:
  [119963,0]

9. [0,1,0,-52643110305,1180828345377919] N = 24713621597826872896

E = ellinit([0,1,0,-52643110305,1180828345377919]);
generators:
  [776475,654562888]
  [-114805,75573688]
  [453386,265538879]
  [415467,225885944]
  [-240395/9,1368209924/27]
  [227675,31576888]
  [1146699,1203591368]
  [-40637675/324,-444553398559/5832]
  [5107/9,915995240/27]
torsion generators:
  [-239927,0]

10. [0,1,0,-12733181679,300724070684785] N = 25114814725829542784

E = ellinit([0,1,0,-12733181679,300724070684785]);
generators:
  [16257,9900382]
  [-128,17388327]
  [-227935/16,-1401043495/64]
  [-21033,23648188]
  [-110416,18987503]
  [18065,8751850]
  [106657,12488082]
  [1049296/9,-540652229/27]
  [2107887,3056010872]
torsion generators:
  [-123185,0]

Rank 10

#	a-invariants	conductor N	log N	naive h	log abs(disc)	torsion generators
1	`[0,1,0,-93764325769,2791717197247671]`	`28892029830345508681664`	51.717852726	87.405754000	79.88508856	`[[-320133,0]]`
2	`[0,-1,0,-75459410575,21007795589220391]`	`168010591633224367516032`	53.478313976	88.690483000	81.08000141	`[[-364763,0]]`
3	`[0,1,0,-6080575076865,1210755392118316639]`	`319122928903483888205248`	54.119863338	99.921964000	92.42223297	`[[200443,0]]`
4	`[0,-1,0,-699947400265,185534315352193561]`	`351824891684388520040832`	54.217420538	93.436416000	84.84982312	`[[306007,0]]`
5	`[1,1,0,-551445732182,38891260836442260]`	`671251925040138068164062`	54.863431467	92.721031000	85.20349441	`[[71180,-35590]]`
6	`[0,-1,0,-2285162669176,318639106356309376]`	`825030649904725540797360`	55.069707490	96.985978000	89.47211162	`[[140656,0]]`
7	`[1,1,0,-129075833083,9551874655985737]`	`884834993897161758496110`	55.139688133	88.364601000	80.57246842	`[[77626,-38813]]`
8	`[0,-1,0,-935215007281,35046690582446881]`	`1739383412924152840357920`	55.815572922	94.305730000	86.84082250	`[[37531,0]]`
9	`[0,1,0,-343434423390,64021174864445764]`	`2014302015576706415159968`	55.962314973	91.300389000	82.69681351	`[[215593,0]]`
10	`[0,-1,0,-1510782454910,461088646585583976]`	`2585282662981525284670368`	56.211877081	95.744549000	87.75169211	`[[328707,0]]`

generators for these ten

1. [0,1,0,-93764325769,2791717197247671] N = 28892029830345508681664

E = ellinit([0,1,0,-93764325769,2791717197247671]);
generators:
  [903935,-810333016]
  [2128003,-3072410680]
  [24567,-22428480]
  [291901,-17136952]
  [3995185/9,5954946812/27]
  [-14915,-64706216]
  [-284225,80505736]
  [-1933753/49,27505528000/343]
  [5417,47790740]
  [-27521,73153000]
torsion generators:
  [-320133,0]

2. [0,-1,0,-75459410575,21007795589220391] N = 168010591633224367516032

E = ellinit([0,-1,0,-75459410575,21007795589220391]);
generators:
  [227559,124979942]
  [728215,593487054]
  [-337826,89134533]
  [7419373,-20195940852]
  [37789861/196,-320309671779/2744]
  [1581271,1963548306]
  [47638462/169,326866676319/2197]
  [-2610,145618429]
  [2629303,4242591522]
  [100164334/25,1000271042577/125]
torsion generators:
  [-364763,0]

3. [0,1,0,-6080575076865,1210755392118316639] N = 319122928903483888205248

E = ellinit([0,1,0,-6080575076865,1210755392118316639]);
generators:
  [26842029,138482964028]
  [-1568293,2624804224]
  [-8739421/25,226855683008/125]
  [14350331,53564401024]
  [-1396945885/1369,127671263464576/50653]
  [14122565/4,38989961111/8]
  [12928277763/2809,1251955148853248/148877]
  [-1712133,2569545856]
  [-2639229/25,170087296256/125]
  [6177243,14119592320]
torsion generators:
  [200443,0]

4. [0,-1,0,-699947400265,185534315352193561] N = 351824891684388520040832

E = ellinit([0,-1,0,-699947400265,185534315352193561]);
generators:
  [651589,-78101532]
  [2669893,-4165167132]
  [-7114223/9,-13361659244/27]
  [-875936,-355764843]
  [-866291/25,57247684452/125]
  [-910631,-260360532]
  [37221,399415996]
  [-632043,-612734260]
  [267609,131858732]
  [211399,216825768]
torsion generators:
  [306007,0]

5. [1,1,0,-551445732182,38891260836442260] N = 671251925040138068164062

E = ellinit([1,1,0,-551445732182,38891260836442260]);
generators:
  [-19309,222567350]
  [-72268,-279902638]
  [-669581,-328192713]
  [764929,253876544]
  [1033477,756329852]
  [735788,-177818230]
  [2965316,4946042834]
  [-705691,277134719]
  [-769492,-86764918]
  [-572659,-408229516]
torsion generators:
  [71180,-35590]

6. [0,-1,0,-2285162669176,318639106356309376] N = 825030649904725540797360

E = ellinit([0,-1,0,-2285162669176,318639106356309376]);
generators:
  [-303732,-992318404]
  [-1514884,551294820]
  [1652236,1026362820]
  [23375800,-112783388976]
  [-625704,1226176000]
  [-828242,-1281852054]
  [409342/9,12513514258/27]
  [-237239,-920552220]
  [6616024,16576942080]
  [1470838,373485546]
torsion generators:
  [140656,0]

7. [1,1,0,-129075833083,9551874655985737] N = 884834993897161758496110

E = ellinit([1,1,0,-129075833083,9551874655985737]);
generators:
  [-256539,160694552]
  [787084,628540975]
  [54571,51650497]
  [1237746,1320757807]
  [494471,-258369028]
  [360434,-99445825]
  [-245869,-162433303]
  [-350243,-108432293]
  [4550296,9674346397]
  [1174696,1215514747]
torsion generators:
  [77626,-38813]

8. [0,-1,0,-935215007281,35046690582446881] N = 1739383412924152840357920

E = ellinit([0,-1,0,-935215007281,35046690582446881]);
generators:
  [-974667,143732116]
  [1092541,563375340]
  [-8147,206555916]
  [-436459,600071340]
  [-799899,520881460]
  [-129955,392922156]
  [4316368,8741663991]
  [12736015,-45320889396]
  [2217885,2978363564]
  [3074125,5119697484]
torsion generators:
  [37531,0]

9. [0,1,0,-343434423390,64021174864445764] N = 2014302015576706415159968

E = ellinit([0,1,0,-343434423390,64021174864445764]);
generators:
  [5312,249393266]
  [582101440,14044225394958]
  [5268652425/10609,137993385981284/1092727]
  [10146447904/6561,955332802855358/531441]
  [-25083488816/1879641,674963594639299522/2576987811]
  [-3124745472/18769,877970082087998/2571353]
  [1123616684153/5987809,1152148625676563588/14652168623]
  [1926496903232/9928801,2142355182186647726/31285651951]
  [9487062955914/56896849,45807679909367016182/429172932007]
  [2417102016074/263055961,1052593364120003892122/4266504631459]
torsion generators:
  [215593,0]

10. [0,-1,0,-1510782454910,461088646585583976] N = 2585282662981525284670368

E = ellinit([0,-1,0,-1510782454910,461088646585583976]);
generators:
  [-374254,986957244]
  [1031668,-22494752]
  [3836988,7152215532]
  [-1316972,-408128392]
  [-1230529,-675928806]
  [-61102,-743755572]
  [25315925/4,125069716467/8]
  [1176382460,-40348052157924]
  [-16414636/121,-1084207179168/1331]
  [6571996/25,35816557756/125]
torsion generators:
  [328707,0]