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Rank 14 record curves

The ten smallest curves of rank 14 in this collection, in each of four categories. The same curve often heads more than one list. Every curve here has proven rank 14, is given by its global minimal model, and carries 14 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 [0,0,0,-162487804927,24573741560967490] 25168869705838997533742636949448 72.303161000 89.055209000 5.32816311 78.60210994
2 [1,-1,0,-69256750159,7363244147255929] 46992227332945491709640493795458 72.927535000 86.593695000 5.15222069 76.75617640
3 [1,-1,0,-17511333709,745147974695329] 51901807229711945130373780604666 73.026906000 82.371945000 4.86321145 73.72005358
4 [1,-1,0,-33047232934,1847231190024964] 104471690210778059301300532983854 73.726469000 84.277214000 5.03201471 75.80591046
5 [1,-1,0,-51643728544,4440535775373364] 148465259769888571900096916876606 74.077903780 85.616506842 5.02339052 74.77105096
6 [0,0,0,-423412235407,107137669344845170] 165397470686678259930364352553256 74.185904000 91.948928000 5.52825680 80.59607916
7 [1,-1,0,-111652073395,14513129257645321] 191217850521411534913210243850810 74.330966000 87.950802000 5.19663402 76.63355124
8 [0,0,0,-77127840412,9288236618064820] 247041733347564921270591464408344 74.587110073 87.058195767 5.23309040 78.05284598
9 [1,-1,0,-47306953864,4103869699271524] 249940365173246666568907372690714 74.598775140 85.424553279 5.04044703 75.29192232
10 [0,0,0,-398361252247,96907515571559290] 346160210902139668624880103858904 74.924454495 91.748212479 5.43061268 78.39019040
generators for these ten

1. [0,0,0,-162487804927,24573741560967490] N = 25168869705838997533742636949448

E = ellinit([0,0,0,-162487804927,24573741560967490]);
generators:
  [-400707,159197306]
  [-366181,187010744]
  [-330563,205341062]
  [-9701,161706904]
  [29681,140631038]
  [116891,84720248]
  [161601,50356142]
  [200026,8664658]
  [200237,8132938]
  [201653,2755394]
  [262513,3026306]
  [264111,9049168]
  [272054,22448164]
  [783033/4,130751029/8]

2. [1,-1,0,-69256750159,7363244147255929] N = 46992227332945491709640493795458

E = ellinit([1,-1,0,-69256750159,7363244147255929]);
generators:
  [137266,20978759]
  [97823,38995107]
  [-814,86137615]
  [153688,18615555]
  [275565,95798518]
  [163210,20100987]
  [117601,29009945]
  [-124060,118577143]
  [7868,82572207]
  [63732,56609413]
  [-24999,95296129]
  [178410,26101187]
  [180023,-27102005]
  [55616,-60719541]

3. [1,-1,0,-17511333709,745147974695329] N = 51901807229711945130373780604666

E = ellinit([1,-1,0,-17511333709,745147974695329]);
generators:
  [-85915,40235703]
  [-1619,27812580]
  [564,27115613]
  [708,27069007]
  [2064,26626273]
  [33852,13808645]
  [102032,4491105]
  [116870,17113297]
  [124358,22088385]
  [183630,60912413]
  [26171988,133877339005]
  [-8046479/64,15891006891/512]
  [1383280/9,1106070619/27]
  [6295744/9,15519675125/27]

4. [1,-1,0,-33047232934,1847231190024964] N = 104471690210778059301300532983854

E = ellinit([1,-1,0,-33047232934,1847231190024964]);
generators:
  [-244,43073254]
  [57447,11733440]
  [17416,35725910]
  [60245,8627518]
  [177068,39246270]
  [23352,32976898]
  [156344,22328578]
  [-204032,9911870]
  [-186356,39257958]
  [-115877,-64134735]
  [217920,70561918]
  [21519,-33864152]
  [-104831,64547013]
  [218832,-71486642]

5. [1,-1,0,-51643728544,4440535775373364] N = 148465259769888571900096916876606

E = ellinit([1,-1,0,-51643728544,4440535775373364]);
generators:
  [-242917,51613422]
  [-198459,83003800]
  [-55576,84520558]
  [38578,50037050]
  [55681,41656580]
  [56610,41183338]
  [86138,25079940]
  [100385,16316452]
  [146017,3515963]
  [146727,4600858]
  [164273,19662580]
  [175946,28209810]
  [179607,30875018]
  [244075,79726142]

6. [0,0,0,-423412235407,107137669344845170] N = 165397470686678259930364352553256

E = ellinit([0,0,0,-423412235407,107137669344845170]);
generators:
  [620589,-288756946]
  [387161,35241118]
  [-241365,-441897440]
  [196949,177162326]
  [401481,43118638]
  [270457,111382142]
  [184539,-187845704]
  [337679,-51621784]
  [2078497,-2864698058]
  [-651542,-326227526]
  [-324507,-458656474]
  [444635,82330040]
  [3960022/9,-2095010452/27]
  [366521,-34434878]

7. [1,-1,0,-111652073395,14513129257645321] N = 191217850521411534913210243850810

E = ellinit([1,-1,0,-111652073395,14513129257645321]);
generators:
  [212688,19571891]
  [176798,-17394809]
  [165628,-23831739]
  [-56792,143802171]
  [127505,-48538851]
  [537563,-331681829]
  [175073,18131341]
  [-301762,144119191]
  [1828039/9,392736494/27]
  [233208,-34148579]
  [1483348,1763552741]
  [111753,58521586]
  [114846,-56671013]
  [173713,18878621]

8. [0,0,0,-77127840412,9288236618064820] N = 247041733347564921270591464408344

E = ellinit([0,0,0,-77127840412,9288236618064820]);
generators:
  [-189278,130788898]
  [-4271,98069219]
  [6042,93927902]
  [125134,39954154]
  [272074,91890334]
  [-23828236/169,289470587674/2197]
  [2802190/9,3356843410/27]
  [7262602/49,11441294542/343]
  [8912542/49,12257472058/343]
  [14545756/81,25554917638/729]
  [25949841/16,130384607033/64]
  [72130876/121,557036360702/1331]
  [29686225452/113569,3199306864889018/38272753]
  [41638380961/360000,9451725152018959/216000000]

9. [1,-1,0,-47306953864,4103869699271524] N = 249940365173246666568907372690714

E = ellinit([1,-1,0,-47306953864,4103869699271524]);
generators:
  [-2143,64848883]
  [620819/4,178307465/8]
  [-9169999241/241081,9054520800491998/118370771]
  [-383014029/8836,64745147598095/830584]
  [-30429449/121,13208082270/1331]
  [-2099/16,4103036051/64]
  [293150498/169,4979685567316/2197]
  [353764175/1369,4834685758779/50653]
  [933315266/121,28496631261150/1331]
  [1468670998/9409,20795972041220/912673]
  [2526679593/32041,168331069766545/5735339]
  [3484461968/36481,148581714279362/6967871]
  [12329516690/380689,11986140221031546/234885113]
  [29123760128/380689,7163663225597574/234885113]

10. [0,0,0,-398361252247,96907515571559290] N = 346160210902139668624880103858904

E = ellinit([0,0,0,-398361252247,96907515571559290]);
generators:
  [857,310750898]
  [2771,309521692]
  [209821,150200858]
  [360401,12239462]
  [378674,18922094]
  [617329,293681146]
  [10614446,34521886108]
  [-244629044361/491401,142799262056044724/344472101]
  [1116953/16,16864734589/64]
  [1448105/4,94160285/8]
  [7638457/36,31991205493/216]
  [16165893/49,12794018014/343]
  [30809521/64,66162104087/512]
  [99453161/289,117632374178/4913]

Smallest naive height

# a-invariants conductor N log N naive h Faltings h log abs(disc)
1 [1,-1,0,-17511333709,745147974695329] 51901807229711945130373780604666 73.026906000 82.371945000 4.86321145 73.72005358
2 [0,0,1,-21939919267,649337940785766] 493755674212808044114451600614357 75.279593598 83.048323869 4.97009006 75.27959360
3 [1,-1,0,-6935133529,1323087002140129] 367446112571792983028151976807954 74.984129465 83.160630995 4.98738590 75.67727665
4 [1,-1,0,-33047232934,1847231190024964] 104471690210778059301300532983854 73.726469000 84.277214000 5.03201471 75.80591046
5 [1,-1,0,-37987453366,3315640089106648] 620410434799344097520433283935898 75.507934040 84.997993986 5.07233051 76.20108122
6 [1,-1,0,-47306953864,4103869699271524] 249940365173246666568907372690714 74.598775140 85.424553279 5.04044703 75.29192232
7 [1,-1,0,-50804263534,2907200305341544] 2370568937196628085123918626957166 76.848438000 85.567341000 5.16492845 77.54158523
8 [1,-1,0,-51643728544,4440535775373364] 148465259769888571900096916876606 74.077903780 85.616506842 5.02339052 74.77105096
9 [1,-1,0,-52928150404,3220515266029924] 2504442201030820515043474582151246 76.903374000 85.690207000 5.17123380 77.59652128
10 [1,-1,0,-56718972634,1053347080076704] 5599299686054224830727840572630866 77.707950000 85.897727000 5.22384260 78.40109678
generators for these ten

1. [1,-1,0,-17511333709,745147974695329] N = 51901807229711945130373780604666

E = ellinit([1,-1,0,-17511333709,745147974695329]);
generators:
  [-85915,40235703]
  [-1619,27812580]
  [564,27115613]
  [708,27069007]
  [2064,26626273]
  [33852,13808645]
  [102032,4491105]
  [116870,17113297]
  [124358,22088385]
  [183630,60912413]
  [26171988,133877339005]
  [-8046479/64,15891006891/512]
  [1383280/9,1106070619/27]
  [6295744/9,15519675125/27]

2. [0,0,1,-21939919267,649337940785766] N = 493755674212808044114451600614357

E = ellinit([0,0,1,-21939919267,649337940785766]);
generators:
  [-127138,37197684]
  [-1620,26170142]
  [-120,25533717]
  [1021005,1021076132]
  [-562064484938/3508129,47271451162511756/6570725617]
  [-189408467/1369,1630693958927/50653]
  [-477486407/4096,10560152015789/262144]
  [-20211714/169,86848491956/2197]
  [-1871/36,5508966331/216]
  [1358194/9,751746968/27]
  [7972092/49,12771156999/343]
  [102341593/729,360822194945/19683]
  [393676606/12769,2150516645467/1442897]
  [462062546/49,9931108679528/343]

3. [1,-1,0,-6935133529,1323087002140129] N = 367446112571792983028151976807954

E = ellinit([1,-1,0,-6935133529,1323087002140129]);
generators:
  [-1303,36498888]
  [-788,36449693]
  [2045,36177883]
  [50040,33161593]
  [69241,34241480]
  [1250116,1394481029]
  [2850180,4808467013]
  [5094983,11496403665]
  [16819449,68969872328]
  [-1709/9,982596296/27]
  [88063/9,956813195/27]
  [3017764/9,5167680455/27]
  [15815067/121,68423558888/1331]
  [7335727690/56169,683757412791509/13312053]

4. [1,-1,0,-33047232934,1847231190024964] N = 104471690210778059301300532983854

E = ellinit([1,-1,0,-33047232934,1847231190024964]);
generators:
  [-244,43073254]
  [57447,11733440]
  [17416,35725910]
  [60245,8627518]
  [177068,39246270]
  [23352,32976898]
  [156344,22328578]
  [-204032,9911870]
  [-186356,39257958]
  [-115877,-64134735]
  [217920,70561918]
  [21519,-33864152]
  [-104831,64547013]
  [218832,-71486642]

5. [1,-1,0,-37987453366,3315640089106648] N = 620410434799344097520433283935898

E = ellinit([1,-1,0,-37987453366,3315640089106648]);
generators:
  [-227154,15070108]
  [-200594,53618268]
  [-188532,61545248]
  [-177361,66975732]
  [-49002,71154214]
  [-36843,68320690]
  [-756,57830804]
  [11551,53644836]
  [41146,42667446]
  [93548,24049764]
  [127574,23296422]
  [144714,29064032]
  [150269,31555177]
  [1663949/16,1413110073/64]

6. [1,-1,0,-47306953864,4103869699271524] N = 249940365173246666568907372690714

E = ellinit([1,-1,0,-47306953864,4103869699271524]);
generators:
  [-2143,64848883]
  [620819/4,178307465/8]
  [-9169999241/241081,9054520800491998/118370771]
  [-383014029/8836,64745147598095/830584]
  [-30429449/121,13208082270/1331]
  [-2099/16,4103036051/64]
  [293150498/169,4979685567316/2197]
  [353764175/1369,4834685758779/50653]
  [933315266/121,28496631261150/1331]
  [1468670998/9409,20795972041220/912673]
  [2526679593/32041,168331069766545/5735339]
  [3484461968/36481,148581714279362/6967871]
  [12329516690/380689,11986140221031546/234885113]
  [29123760128/380689,7163663225597574/234885113]

7. [1,-1,0,-50804263534,2907200305341544] N = 2370568937196628085123918626957166

E = ellinit([1,-1,0,-50804263534,2907200305341544]);
generators:
  [-231868,47245300]
  [-2219,54954945]
  [-1260,54509452]
  [-94,53962774]
  [42100,29012688]
  [60627,7035808]
  [477636,295746184]
  [8385559,24269851253]
  [-2202780/49,24503382856/343]
  [-1790636/9,1938299600/27]
  [-3995019/16,332450885/64]
  [685093/16,1820494703/64]
  [678325/49,16109687159/343]
  [51568290/961,544875973432/29791]

8. [1,-1,0,-51643728544,4440535775373364] N = 148465259769888571900096916876606

E = ellinit([1,-1,0,-51643728544,4440535775373364]);
generators:
  [-242917,51613422]
  [-198459,83003800]
  [-55576,84520558]
  [38578,50037050]
  [55681,41656580]
  [56610,41183338]
  [86138,25079940]
  [100385,16316452]
  [146017,3515963]
  [146727,4600858]
  [164273,19662580]
  [175946,28209810]
  [179607,30875018]
  [244075,79726142]

9. [1,-1,0,-52928150404,3220515266029924] N = 2504442201030820515043474582151246

E = ellinit([1,-1,0,-52928150404,3220515266029924]);
generators:
  [-4634,-58867750]
  [61409,-14237217]
  [284970,-106346698]
  [4891817,-10810075160]
  [-106462,-87403538]
  [190022,-5030400]
  [191234,-9704882]
  [61702,13740410]
  [-175950,84266768]
  [63630,10471408]
  [612942,-448702910]
  [208313,-35239025]
  [-59034,-78324416]
  [-154290,-87751358]

10. [1,-1,0,-56718972634,1053347080076704] N = 5599299686054224830727840572630866

E = ellinit([1,-1,0,-56718972634,1053347080076704]);
generators:
  [-44502,59092720]
  [-239378,-30109132]
  [-127082,78860382]
  [-47624,-60362580]
  [284677,89172870]
  [-188658,71081108]
  [-24773,49441553]
  [-231994,-41423970]
  [228265,167018]
  [283203,87632540]
  [11664,19827568]
  [18542,-2844492]
  [346677,151666870]
  [-206130,63241172]

Smallest Faltings height

# a-invariants conductor N log N naive h Faltings h log abs(disc)
1 [1,-1,0,-17511333709,745147974695329] 51901807229711945130373780604666 73.026906000 82.371945000 4.86321145 73.72005358
2 [0,0,1,-21939919267,649337940785766] 493755674212808044114451600614357 75.279593598 83.048323869 4.97009006 75.27959360
3 [1,-1,0,-6935133529,1323087002140129] 367446112571792983028151976807954 74.984129465 83.160630995 4.98738590 75.67727665
4 [1,-1,0,-51643728544,4440535775373364] 148465259769888571900096916876606 74.077903780 85.616506842 5.02339052 74.77105096
5 [1,-1,0,-33047232934,1847231190024964] 104471690210778059301300532983854 73.726469000 84.277214000 5.03201471 75.80591046
6 [1,-1,0,-47306953864,4103869699271524] 249940365173246666568907372690714 74.598775140 85.424553279 5.04044703 75.29192232
7 [1,-1,0,-37987453366,3315640089106648] 620410434799344097520433283935898 75.507934040 84.997993986 5.07233051 76.20108122
8 [1,-1,0,-69256750159,7363244147255929] 46992227332945491709640493795458 72.927535000 86.593695000 5.15222069 76.75617640
9 [1,-1,0,-50804263534,2907200305341544] 2370568937196628085123918626957166 76.848438000 85.567341000 5.16492845 77.54158523
10 [1,-1,0,-52928150404,3220515266029924] 2504442201030820515043474582151246 76.903374000 85.690207000 5.17123380 77.59652128
generators for these ten

1. [1,-1,0,-17511333709,745147974695329] N = 51901807229711945130373780604666

E = ellinit([1,-1,0,-17511333709,745147974695329]);
generators:
  [-85915,40235703]
  [-1619,27812580]
  [564,27115613]
  [708,27069007]
  [2064,26626273]
  [33852,13808645]
  [102032,4491105]
  [116870,17113297]
  [124358,22088385]
  [183630,60912413]
  [26171988,133877339005]
  [-8046479/64,15891006891/512]
  [1383280/9,1106070619/27]
  [6295744/9,15519675125/27]

2. [0,0,1,-21939919267,649337940785766] N = 493755674212808044114451600614357

E = ellinit([0,0,1,-21939919267,649337940785766]);
generators:
  [-127138,37197684]
  [-1620,26170142]
  [-120,25533717]
  [1021005,1021076132]
  [-562064484938/3508129,47271451162511756/6570725617]
  [-189408467/1369,1630693958927/50653]
  [-477486407/4096,10560152015789/262144]
  [-20211714/169,86848491956/2197]
  [-1871/36,5508966331/216]
  [1358194/9,751746968/27]
  [7972092/49,12771156999/343]
  [102341593/729,360822194945/19683]
  [393676606/12769,2150516645467/1442897]
  [462062546/49,9931108679528/343]

3. [1,-1,0,-6935133529,1323087002140129] N = 367446112571792983028151976807954

E = ellinit([1,-1,0,-6935133529,1323087002140129]);
generators:
  [-1303,36498888]
  [-788,36449693]
  [2045,36177883]
  [50040,33161593]
  [69241,34241480]
  [1250116,1394481029]
  [2850180,4808467013]
  [5094983,11496403665]
  [16819449,68969872328]
  [-1709/9,982596296/27]
  [88063/9,956813195/27]
  [3017764/9,5167680455/27]
  [15815067/121,68423558888/1331]
  [7335727690/56169,683757412791509/13312053]

4. [1,-1,0,-51643728544,4440535775373364] N = 148465259769888571900096916876606

E = ellinit([1,-1,0,-51643728544,4440535775373364]);
generators:
  [-242917,51613422]
  [-198459,83003800]
  [-55576,84520558]
  [38578,50037050]
  [55681,41656580]
  [56610,41183338]
  [86138,25079940]
  [100385,16316452]
  [146017,3515963]
  [146727,4600858]
  [164273,19662580]
  [175946,28209810]
  [179607,30875018]
  [244075,79726142]

5. [1,-1,0,-33047232934,1847231190024964] N = 104471690210778059301300532983854

E = ellinit([1,-1,0,-33047232934,1847231190024964]);
generators:
  [-244,43073254]
  [57447,11733440]
  [17416,35725910]
  [60245,8627518]
  [177068,39246270]
  [23352,32976898]
  [156344,22328578]
  [-204032,9911870]
  [-186356,39257958]
  [-115877,-64134735]
  [217920,70561918]
  [21519,-33864152]
  [-104831,64547013]
  [218832,-71486642]

6. [1,-1,0,-47306953864,4103869699271524] N = 249940365173246666568907372690714

E = ellinit([1,-1,0,-47306953864,4103869699271524]);
generators:
  [-2143,64848883]
  [620819/4,178307465/8]
  [-9169999241/241081,9054520800491998/118370771]
  [-383014029/8836,64745147598095/830584]
  [-30429449/121,13208082270/1331]
  [-2099/16,4103036051/64]
  [293150498/169,4979685567316/2197]
  [353764175/1369,4834685758779/50653]
  [933315266/121,28496631261150/1331]
  [1468670998/9409,20795972041220/912673]
  [2526679593/32041,168331069766545/5735339]
  [3484461968/36481,148581714279362/6967871]
  [12329516690/380689,11986140221031546/234885113]
  [29123760128/380689,7163663225597574/234885113]

7. [1,-1,0,-37987453366,3315640089106648] N = 620410434799344097520433283935898

E = ellinit([1,-1,0,-37987453366,3315640089106648]);
generators:
  [-227154,15070108]
  [-200594,53618268]
  [-188532,61545248]
  [-177361,66975732]
  [-49002,71154214]
  [-36843,68320690]
  [-756,57830804]
  [11551,53644836]
  [41146,42667446]
  [93548,24049764]
  [127574,23296422]
  [144714,29064032]
  [150269,31555177]
  [1663949/16,1413110073/64]

8. [1,-1,0,-69256750159,7363244147255929] N = 46992227332945491709640493795458

E = ellinit([1,-1,0,-69256750159,7363244147255929]);
generators:
  [137266,20978759]
  [97823,38995107]
  [-814,86137615]
  [153688,18615555]
  [275565,95798518]
  [163210,20100987]
  [117601,29009945]
  [-124060,118577143]
  [7868,82572207]
  [63732,56609413]
  [-24999,95296129]
  [178410,26101187]
  [180023,-27102005]
  [55616,-60719541]

9. [1,-1,0,-50804263534,2907200305341544] N = 2370568937196628085123918626957166

E = ellinit([1,-1,0,-50804263534,2907200305341544]);
generators:
  [-231868,47245300]
  [-2219,54954945]
  [-1260,54509452]
  [-94,53962774]
  [42100,29012688]
  [60627,7035808]
  [477636,295746184]
  [8385559,24269851253]
  [-2202780/49,24503382856/343]
  [-1790636/9,1938299600/27]
  [-3995019/16,332450885/64]
  [685093/16,1820494703/64]
  [678325/49,16109687159/343]
  [51568290/961,544875973432/29791]

10. [1,-1,0,-52928150404,3220515266029924] N = 2504442201030820515043474582151246

E = ellinit([1,-1,0,-52928150404,3220515266029924]);
generators:
  [-4634,-58867750]
  [61409,-14237217]
  [284970,-106346698]
  [4891817,-10810075160]
  [-106462,-87403538]
  [190022,-5030400]
  [191234,-9704882]
  [61702,13740410]
  [-175950,84266768]
  [63630,10471408]
  [612942,-448702910]
  [208313,-35239025]
  [-59034,-78324416]
  [-154290,-87751358]

Smallest absolute discriminant

# a-invariants conductor N log N naive h Faltings h log abs(disc)
1 [1,-1,0,-17511333709,745147974695329] 51901807229711945130373780604666 73.026906000 82.371945000 4.86321145 73.72005358
2 [1,-1,0,-51643728544,4440535775373364] 148465259769888571900096916876606 74.077903780 85.616506842 5.02339052 74.77105096
3 [0,0,1,-21939919267,649337940785766] 493755674212808044114451600614357 75.279593598 83.048323869 4.97009006 75.27959360
4 [1,-1,0,-47306953864,4103869699271524] 249940365173246666568907372690714 74.598775140 85.424553279 5.04044703 75.29192232
5 [1,-1,0,-6935133529,1323087002140129] 367446112571792983028151976807954 74.984129465 83.160630995 4.98738590 75.67727665
6 [1,-1,0,-33047232934,1847231190024964] 104471690210778059301300532983854 73.726469000 84.277214000 5.03201471 75.80591046
7 [1,-1,0,-37987453366,3315640089106648] 620410434799344097520433283935898 75.507934040 84.997993986 5.07233051 76.20108122
8 [1,-1,0,-111652073395,14513129257645321] 191217850521411534913210243850810 74.330966000 87.950802000 5.19663402 76.63355124
9 [1,-1,0,-69256750159,7363244147255929] 46992227332945491709640493795458 72.927535000 86.593695000 5.15222069 76.75617640
10 [1,1,0,-174627385832,27982674874382580] 423821844193030172919783692430042 75.126866000 89.271364000 5.26327353 76.91862545
generators for these ten

1. [1,-1,0,-17511333709,745147974695329] N = 51901807229711945130373780604666

E = ellinit([1,-1,0,-17511333709,745147974695329]);
generators:
  [-85915,40235703]
  [-1619,27812580]
  [564,27115613]
  [708,27069007]
  [2064,26626273]
  [33852,13808645]
  [102032,4491105]
  [116870,17113297]
  [124358,22088385]
  [183630,60912413]
  [26171988,133877339005]
  [-8046479/64,15891006891/512]
  [1383280/9,1106070619/27]
  [6295744/9,15519675125/27]

2. [1,-1,0,-51643728544,4440535775373364] N = 148465259769888571900096916876606

E = ellinit([1,-1,0,-51643728544,4440535775373364]);
generators:
  [-242917,51613422]
  [-198459,83003800]
  [-55576,84520558]
  [38578,50037050]
  [55681,41656580]
  [56610,41183338]
  [86138,25079940]
  [100385,16316452]
  [146017,3515963]
  [146727,4600858]
  [164273,19662580]
  [175946,28209810]
  [179607,30875018]
  [244075,79726142]

3. [0,0,1,-21939919267,649337940785766] N = 493755674212808044114451600614357

E = ellinit([0,0,1,-21939919267,649337940785766]);
generators:
  [-127138,37197684]
  [-1620,26170142]
  [-120,25533717]
  [1021005,1021076132]
  [-562064484938/3508129,47271451162511756/6570725617]
  [-189408467/1369,1630693958927/50653]
  [-477486407/4096,10560152015789/262144]
  [-20211714/169,86848491956/2197]
  [-1871/36,5508966331/216]
  [1358194/9,751746968/27]
  [7972092/49,12771156999/343]
  [102341593/729,360822194945/19683]
  [393676606/12769,2150516645467/1442897]
  [462062546/49,9931108679528/343]

4. [1,-1,0,-47306953864,4103869699271524] N = 249940365173246666568907372690714

E = ellinit([1,-1,0,-47306953864,4103869699271524]);
generators:
  [-2143,64848883]
  [620819/4,178307465/8]
  [-9169999241/241081,9054520800491998/118370771]
  [-383014029/8836,64745147598095/830584]
  [-30429449/121,13208082270/1331]
  [-2099/16,4103036051/64]
  [293150498/169,4979685567316/2197]
  [353764175/1369,4834685758779/50653]
  [933315266/121,28496631261150/1331]
  [1468670998/9409,20795972041220/912673]
  [2526679593/32041,168331069766545/5735339]
  [3484461968/36481,148581714279362/6967871]
  [12329516690/380689,11986140221031546/234885113]
  [29123760128/380689,7163663225597574/234885113]

5. [1,-1,0,-6935133529,1323087002140129] N = 367446112571792983028151976807954

E = ellinit([1,-1,0,-6935133529,1323087002140129]);
generators:
  [-1303,36498888]
  [-788,36449693]
  [2045,36177883]
  [50040,33161593]
  [69241,34241480]
  [1250116,1394481029]
  [2850180,4808467013]
  [5094983,11496403665]
  [16819449,68969872328]
  [-1709/9,982596296/27]
  [88063/9,956813195/27]
  [3017764/9,5167680455/27]
  [15815067/121,68423558888/1331]
  [7335727690/56169,683757412791509/13312053]

6. [1,-1,0,-33047232934,1847231190024964] N = 104471690210778059301300532983854

E = ellinit([1,-1,0,-33047232934,1847231190024964]);
generators:
  [-244,43073254]
  [57447,11733440]
  [17416,35725910]
  [60245,8627518]
  [177068,39246270]
  [23352,32976898]
  [156344,22328578]
  [-204032,9911870]
  [-186356,39257958]
  [-115877,-64134735]
  [217920,70561918]
  [21519,-33864152]
  [-104831,64547013]
  [218832,-71486642]

7. [1,-1,0,-37987453366,3315640089106648] N = 620410434799344097520433283935898

E = ellinit([1,-1,0,-37987453366,3315640089106648]);
generators:
  [-227154,15070108]
  [-200594,53618268]
  [-188532,61545248]
  [-177361,66975732]
  [-49002,71154214]
  [-36843,68320690]
  [-756,57830804]
  [11551,53644836]
  [41146,42667446]
  [93548,24049764]
  [127574,23296422]
  [144714,29064032]
  [150269,31555177]
  [1663949/16,1413110073/64]

8. [1,-1,0,-111652073395,14513129257645321] N = 191217850521411534913210243850810

E = ellinit([1,-1,0,-111652073395,14513129257645321]);
generators:
  [212688,19571891]
  [176798,-17394809]
  [165628,-23831739]
  [-56792,143802171]
  [127505,-48538851]
  [537563,-331681829]
  [175073,18131341]
  [-301762,144119191]
  [1828039/9,392736494/27]
  [233208,-34148579]
  [1483348,1763552741]
  [111753,58521586]
  [114846,-56671013]
  [173713,18878621]

9. [1,-1,0,-69256750159,7363244147255929] N = 46992227332945491709640493795458

E = ellinit([1,-1,0,-69256750159,7363244147255929]);
generators:
  [137266,20978759]
  [97823,38995107]
  [-814,86137615]
  [153688,18615555]
  [275565,95798518]
  [163210,20100987]
  [117601,29009945]
  [-124060,118577143]
  [7868,82572207]
  [63732,56609413]
  [-24999,95296129]
  [178410,26101187]
  [180023,-27102005]
  [55616,-60719541]

10. [1,1,0,-174627385832,27982674874382580] N = 423821844193030172919783692430042

E = ellinit([1,1,0,-174627385832,27982674874382580]);
generators:
  [-223138,236413442]
  [1865,166303010]
  [222326,12048074]
  [263565,16178805]
  [280818,32862870]
  [285336,37091634]
  [378854,127096154]
  [490241,245103914]
  [7481258,20427651992]
  [-9659401/25,24318564697/125]
  [6422504/25,1072030498/125]
  [43376446/169,18142460064/2197]
  [195464407/361,2080488281103/6859]
  [415380146/529,7445979114568/12167]