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	95	15.298409	28.767894	20.407947
5	8,121	19.262706	40.659381	31.203562
6	307,206	24.529232	45.572845	35.074889
7	319,858	30.739101	56.114918	43.632901
8	9,640	36.438334	65.963603	55.756652
9	73	44.624558	79.644600	66.506696

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	`[0,1,0,-538960,188850900]`	`1565566960`	21.171513870	51.637984000	43.13604830	`[[-870,0]]`
10	`[0,1,0,-9188960,10717630900]`	`1565566960`	21.171513870	59.714143000	43.18120069	`[[1739,0]]`

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. [0,1,0,-538960,188850900] N = 1565566960

E = ellinit([0,1,0,-538960,188850900]);
generators:
  [130,11000]
  [380,6250]
  [730,13600]
  [1130,32000]
  [-470,18400]
torsion generators:
  [-870,0]

10. [0,1,0,-9188960,10717630900] N = 1565566960

E = ellinit([0,1,0,-9188960,10717630900]);
generators:
  [3010,101680]
  [-1910,145960]
  [-270,114800]
  [128770/9,45247600/27]
  [26570,4304040]
torsion generators:
  [1739,0]

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	`[0,-1,0,-218669600,794575772496]`	`28330377346942896`	37.882711028	69.222820000	61.24469312	`[[-16348,0]]`
4	`[0,-1,0,-3134341640,67528477424016]`	`28330377346942896`	37.882711028	77.210658000	61.93760145	`[[32697,0]]`
5	`[0,1,0,-1894949065,31743132642039]`	`29231074244902976`	37.914008725	75.700976000	60.41206737	`[[24843,0]]`
6	`[0,1,0,-677920785,6446025754639]`	`31226965890509248`	37.980058408	72.617226000	62.85703718	`[[12163,0]]`
7	`[0,1,0,-541973089,4299659003007]`	`36476637438549952`	38.135448380	71.945784000	62.95892899	`[[9531,0]]`
8	`[0,1,0,805197631,22276574524831]`	`36476637438549952`	38.135448380	74.992235000	67.68235431	`[[-19063,0]]`
9	`[0,1,0,-2674433225,53223177298039]`	`43121536946337856`	38.302798964	76.734613000	61.46505915	`[[30203,0]]`
10	`[0,0,0,-30977881347,2044310129331730]`	`49969980644578704`	38.450198833	84.083221000	73.65359965	`[[87965,0]]`

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. [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]

4. [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]

5. [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]

6. [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]

7. [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]

8. [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]

9. [0,1,0,-2674433225,53223177298039] N = 43121536946337856

E = ellinit([0,1,0,-2674433225,53223177298039]);
generators:
  [-2825,7794608]
  [29485,40208]
  [8514,5574073]
  [-13175,9282892]
  [31639,528448]
  [28891,268304]
  [44922,4871989]
  [31146,374371]
torsion generators:
  [30203,0]

10. [0,0,0,-30977881347,2044310129331730] N = 49969980644578704

E = ellinit([0,0,0,-30977881347,2044310129331730]);
generators:
  [74606,12183408]
  [261851,109026522]
  [-202639,871812]
  [15314,39667446]
  [1174497,1259290588]
  [8951387,26776397862]
  [515453,350753904]
  [248273,98268804]
torsion generators:
  [87965,0]

Rank 9

#	a-invariants	conductor N	log N	naive h	log abs(disc)	torsion generators
1	`[0,1,0,-9909839449,379470040610151]`	`23999337050845260736`	44.624557881	80.663985000	66.50669561	`[[56307,0]]`
2	`[0,1,0,-7918379009,536458061971615]`	`23999337050845260736`	44.624557881	81.355174000	73.60530266	`[[-112615,0]]`
3	`[0,1,0,-49344519305,3002551554488119]`	`45709648312790275648`	45.268841072	85.479881000	77.31894421	`[[66923,0]]`
4	`[0,1,0,130197089055,19824343466561599]`	`45709648312790275648`	45.268841072	88.574515000	81.72518370	`[[-133847,0]]`
5	`[0,-1,0,-16280580185,796131389503641]`	`55660539421203992256`	45.465803121	82.153320000	69.94026804	`[[77577,0]]`
6	`[0,-1,0,-25149767425,-167124429071039]`	`55660539421203992256`	45.465803121	83.457946000	75.99130282	`[[-155153,0]]`
7	`[0,1,0,-7054975769,224370503788711]`	`59674364161385812544`	45.535434191	79.644600000	68.75601286	`[[53459,0]]`
8	`[0,1,0,-14648601729,-343962281385953]`	`59674364161385812544`	45.535434191	81.836435000	74.08861433	`[[-106919,0]]`
9	`[0,1,0,-65346333705,4613169318282679]`	`79424842446432182848`	45.821342870	86.322505000	78.14457964	`[[77803,0]]`
10	`[0,1,0,170584954655,30311984902895679]`	`79424842446432182848`	45.821342870	89.423781000	82.55705366	`[[-155607,0]]`

generators for these ten

1. [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]

2. [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]

3. [0,1,0,-49344519305,3002551554488119] N = 45709648312790275648

E = ellinit([0,1,0,-49344519305,3002551554488119]);
generators:
  [49447,26144096]
  [181545,5272612]
  [195817,-29130044]
  [51759,-24232072]
  [-61971,76305248]
  [-90361,81997392]
  [252682,-81654349]
  [-47699,-72441104]
  [181299,-3955832]
torsion generators:
  [66923,0]

4. [0,1,0,130197089055,19824343466561599] N = 45709648312790275648

E = ellinit([0,1,0,130197089055,19824343466561599]);
generators:
  [-63654,106202009]
  [3441867,6421982344]
  [-1064237/9,-1422390952/27]
  [-56773,110678264]
  [601115,-561510968]
  [146925,-205244332]
  [-5823541/49,-17730223288/343]
  [16852859,69200751752]
  [1647515,2169375032]
torsion generators:
  [-133847,0]

5. [0,-1,0,-16280580185,796131389503641] N = 55660539421203992256

E = ellinit([0,-1,0,-16280580185,796131389503641]);
generators:
  [162743,-49566612]
  [45761,-12121896]
  [67877,-1943880]
  [842185/9,259041608/27]
  [95576,10637409]
  [-92755,38835696]
  [12005,-24544104]
  [41579,13823232]
  [81089,3023832]
torsion generators:
  [77577,0]

6. [0,-1,0,-25149767425,-167124429071039] N = 55660539421203992256

E = ellinit([0,-1,0,-25149767425,-167124429071039]);
generators:
  [-6671,593928]
  [-89599,36972456]
  [-53679,32065784]
  [434833,266673672]
  [47894905/121,-303207965064/1331]
  [-48719,30700296]
  [-122157,-32897012]
  [-325619/4,292928049/8]
  [240865,88029144]
torsion generators:
  [-155153,0]

7. [0,1,0,-7054975769,224370503788711] N = 59674364161385812544

E = ellinit([0,1,0,-7054975769,224370503788711]);
generators:
  [5221,13699592]
  [35031,4496432]
  [84943,15427160]
  [-196187/4,170159545/8]
  [-1009,15214728]
  [53730,650671]
  [3333643,6084741320]
  [67009,7246540]
  [6901530/169,4592437273/2197]
torsion generators:
  [53459,0]

8. [0,1,0,-14648601729,-343962281385953] N = 59674364161385812544

E = ellinit([0,1,0,-14648601729,-343962281385953]);
generators:
  [-34117,10774696]
  [-79107,17883116]
  [-343454/9,340968167/27]
  [3819491/25,3921449464/125]
  [289931,140643640]
  [-85381,16862296]
  [1512997/9,1190603908/27]
  [-37798,12478999]
  [240731,100401320]
torsion generators:
  [-106919,0]

9. [0,1,0,-65346333705,4613169318282679] N = 79424842446432182848

E = ellinit([0,1,0,-65346333705,4613169318282679]);
generators:
  [2418159,3739888888]
  [234441,46678124]
  [59375,-30701048]
  [289385,99685348]
  [4397,65771776]
  [225227,36340016]
  [-253901,-69547272]
  [60531,-29656024]
  [1870405/9,79572104/27]
torsion generators:
  [77803,0]

10. [0,1,0,170584954655,30311984902895679] N = 79424842446432182848

E = ellinit([0,1,0,170584954655,30311984902895679]);
generators:
  [48427,-196688776]
  [334843,-353516360]
  [1337,174757144]
  [144443,-240760120]
  [177899,257466632]
  [3034979/25,-28725538792/125]
  [56587,200364856]
  [2845947,-4854513336]
  [2840149/4,-5709789473/8]
torsion generators:
  [-155607,0]