Elliptic curves by rank › curves from searches
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 | [1,-1,0,-49440790849,4339950847631569] |
201089032872016134932036202654274 |
74.381301000 | 85.536419000 | 5.03414520 | 75.07444773 |
| 9 | [0,0,0,-77127840412,9288236618064820] |
247041733347564921270591464408344 |
74.587110073 | 87.058195767 | 5.23309040 | 78.05284598 |
| 10 | [1,-1,0,-47306953864,4103869699271524] |
249940365173246666568907372690714 |
74.598775140 | 85.424553279 | 5.04044703 | 75.29192232 |
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. [1,-1,0,-49440790849,4339950847631569] N = 201089032872016134932036202654274
E = ellinit([1,-1,0,-49440790849,4339950847631569]);
generators:
[188208,-41343625]
[-64780,85301823]
[161701,-24025296]
[99200,20238537]
[68068,35882367]
[69721,-35131881]
[191850,-43868287]
[120497,11430288]
[170663,29459920]
[98810,20430393]
[-253208,25115703]
[188696,-41680265]
[556791/4,-100151801/8]
[113188,-13983105]
9. [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]
10. [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]
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 | [0,1,1,-30037959982,2392378014133310] |
737993054968595410635229854049771 |
75.681487000 | 84.345282000 | 5.02497798 | 75.68148720 |
| 6 | [0,0,1,-38693986627,2411984268434796] |
1194517052272968263829637380194437 |
76.163050000 | 84.750453000 | 5.06498498 | 76.16305003 |
| 7 | [1,-1,0,-37928420014,3069701755148464] |
289370325107810280525429943057414 |
74.745260000 | 84.843853000 | 5.02798530 | 75.43840724 |
| 8 | [1,-1,0,-37987453366,3315640089106648] |
620410434799344097520433283935898 |
75.507934040 | 84.997993986 | 5.07233051 | 76.20108122 |
| 9 | [0,0,1,-19437849067,3433542675697926] |
4622912080710675041389543771628843 |
77.516333000 | 85.067883000 | 5.14360921 | 77.51633290 |
| 10 | [1,-1,0,-47306953864,4103869699271524] |
249940365173246666568907372690714 |
74.598775140 | 85.424553279 | 5.04044703 | 75.29192232 |
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. [0,1,1,-30037959982,2392378014133310] N = 737993054968595410635229854049771
E = ellinit([0,1,1,-30037959982,2392378014133310]);
generators:
[80328,22311850]
[43679,-34112829]
[147055,33989075]
[-28246,56730021]
[-202471,-13192279]
[1398964,-1642645774]
[233908,90355469]
[-137890,62550290]
[37036,36478685]
[-97476,-66288707]
[20633,-42206506]
[152038,-36605086]
[44360,33870165]
[141888,-31414811]
6. [0,0,1,-38693986627,2411984268434796] N = 1194517052272968263829637380194437
E = ellinit([0,0,1,-38693986627,2411984268434796]);
generators:
[68759,-8746614]
[269394,107418906]
[521427,352142949]
[-5618,-51275626]
[-174442,62077118]
[171945,-29022663]
[71148,4374743]
[71824,-1828909]
[162818,-20692107]
[156281,13483974]
[438289,263907078]
[228977,74547449]
[-7554,-51998535]
[210748,60146631]
7. [1,-1,0,-37928420014,3069701755148464] N = 289370325107810280525429943057414
E = ellinit([1,-1,0,-37928420014,3069701755148464]);
generators:
[-1687,55980145]
[119120,15494212]
[614343/4,234983875/8]
[-883178171/4489,16271773495635/300763]
[-678943387/9409,67291708646274/912673]
[-540896094/3481,14842399053596/205379]
[-13093681/100,76164587083/1000]
[7668559/100,24702260907/1000]
[3572706/25,2970120356/125]
[5469641/49,5146344519/343]
[30584591/49,161711510059/343]
[662763847/9604,26269251411355/941192]
[4666586058/169,318747521118460/2197]
[5068406402/1369,360251289954226/50653]
8. [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]
9. [0,0,1,-19437849067,3433542675697926] N = 4622912080710675041389543771628843
E = ellinit([0,0,1,-19437849067,3433542675697926]);
generators:
[85707,-48960801]
[-130388,-61247650]
[181610,-76768033]
[-3007,59092851]
[6843,57453023]
[9426,57018935]
[1365926,-1589139565]
[492393,336516851]
[42485,-51811293]
[512713/4,441666567/8]
[119334,-53040877]
[-59217,-66158449]
[52009,-50628852]
[-19816,61732826]
10. [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]
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 | [0,1,1,-30037959982,2392378014133310] |
737993054968595410635229854049771 |
75.681487000 | 84.345282000 | 5.02497798 | 75.68148720 |
| 6 | [1,-1,0,-37928420014,3069701755148464] |
289370325107810280525429943057414 |
74.745260000 | 84.843853000 | 5.02798530 | 75.43840724 |
| 7 | [1,-1,0,-33047232934,1847231190024964] |
104471690210778059301300532983854 |
73.726469000 | 84.277214000 | 5.03201471 | 75.80591046 |
| 8 | [1,-1,0,-49440790849,4339950847631569] |
201089032872016134932036202654274 |
74.381301000 | 85.536419000 | 5.03414520 | 75.07444773 |
| 9 | [1,-1,0,-47306953864,4103869699271524] |
249940365173246666568907372690714 |
74.598775140 | 85.424553279 | 5.04044703 | 75.29192232 |
| 10 | [0,0,1,-38693986627,2411984268434796] |
1194517052272968263829637380194437 |
76.163050000 | 84.750453000 | 5.06498498 | 76.16305003 |
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. [0,1,1,-30037959982,2392378014133310] N = 737993054968595410635229854049771
E = ellinit([0,1,1,-30037959982,2392378014133310]);
generators:
[80328,22311850]
[43679,-34112829]
[147055,33989075]
[-28246,56730021]
[-202471,-13192279]
[1398964,-1642645774]
[233908,90355469]
[-137890,62550290]
[37036,36478685]
[-97476,-66288707]
[20633,-42206506]
[152038,-36605086]
[44360,33870165]
[141888,-31414811]
6. [1,-1,0,-37928420014,3069701755148464] N = 289370325107810280525429943057414
E = ellinit([1,-1,0,-37928420014,3069701755148464]);
generators:
[-1687,55980145]
[119120,15494212]
[614343/4,234983875/8]
[-883178171/4489,16271773495635/300763]
[-678943387/9409,67291708646274/912673]
[-540896094/3481,14842399053596/205379]
[-13093681/100,76164587083/1000]
[7668559/100,24702260907/1000]
[3572706/25,2970120356/125]
[5469641/49,5146344519/343]
[30584591/49,161711510059/343]
[662763847/9604,26269251411355/941192]
[4666586058/169,318747521118460/2197]
[5068406402/1369,360251289954226/50653]
7. [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]
8. [1,-1,0,-49440790849,4339950847631569] N = 201089032872016134932036202654274
E = ellinit([1,-1,0,-49440790849,4339950847631569]);
generators:
[188208,-41343625]
[-64780,85301823]
[161701,-24025296]
[99200,20238537]
[68068,35882367]
[69721,-35131881]
[191850,-43868287]
[120497,11430288]
[170663,29459920]
[98810,20430393]
[-253208,25115703]
[188696,-41680265]
[556791/4,-100151801/8]
[113188,-13983105]
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. [0,0,1,-38693986627,2411984268434796] N = 1194517052272968263829637380194437
E = ellinit([0,0,1,-38693986627,2411984268434796]);
generators:
[68759,-8746614]
[269394,107418906]
[521427,352142949]
[-5618,-51275626]
[-174442,62077118]
[171945,-29022663]
[71148,4374743]
[71824,-1828909]
[162818,-20692107]
[156281,13483974]
[438289,263907078]
[228977,74547449]
[-7554,-51998535]
[210748,60146631]
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 | [1,-1,0,-49440790849,4339950847631569] |
201089032872016134932036202654274 |
74.381301000 | 85.536419000 | 5.03414520 | 75.07444773 |
| 4 | [0,0,1,-21939919267,649337940785766] |
493755674212808044114451600614357 |
75.279593598 | 83.048323869 | 4.97009006 | 75.27959360 |
| 5 | [1,-1,0,-47306953864,4103869699271524] |
249940365173246666568907372690714 |
74.598775140 | 85.424553279 | 5.04044703 | 75.29192232 |
| 6 | [1,-1,0,-37928420014,3069701755148464] |
289370325107810280525429943057414 |
74.745260000 | 84.843853000 | 5.02798530 | 75.43840724 |
| 7 | [1,-1,0,-6935133529,1323087002140129] |
367446112571792983028151976807954 |
74.984129465 | 83.160630995 | 4.98738590 | 75.67727665 |
| 8 | [0,1,1,-30037959982,2392378014133310] |
737993054968595410635229854049771 |
75.681487000 | 84.345282000 | 5.02497798 | 75.68148720 |
| 9 | [1,-1,0,-33047232934,1847231190024964] |
104471690210778059301300532983854 |
73.726469000 | 84.277214000 | 5.03201471 | 75.80591046 |
| 10 | [0,0,1,-38693986627,2411984268434796] |
1194517052272968263829637380194437 |
76.163050000 | 84.750453000 | 5.06498498 | 76.16305003 |
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. [1,-1,0,-49440790849,4339950847631569] N = 201089032872016134932036202654274
E = ellinit([1,-1,0,-49440790849,4339950847631569]);
generators:
[188208,-41343625]
[-64780,85301823]
[161701,-24025296]
[99200,20238537]
[68068,35882367]
[69721,-35131881]
[191850,-43868287]
[120497,11430288]
[170663,29459920]
[98810,20430393]
[-253208,25115703]
[188696,-41680265]
[556791/4,-100151801/8]
[113188,-13983105]
4. [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]
5. [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]
6. [1,-1,0,-37928420014,3069701755148464] N = 289370325107810280525429943057414
E = ellinit([1,-1,0,-37928420014,3069701755148464]);
generators:
[-1687,55980145]
[119120,15494212]
[614343/4,234983875/8]
[-883178171/4489,16271773495635/300763]
[-678943387/9409,67291708646274/912673]
[-540896094/3481,14842399053596/205379]
[-13093681/100,76164587083/1000]
[7668559/100,24702260907/1000]
[3572706/25,2970120356/125]
[5469641/49,5146344519/343]
[30584591/49,161711510059/343]
[662763847/9604,26269251411355/941192]
[4666586058/169,318747521118460/2197]
[5068406402/1369,360251289954226/50653]
7. [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]
8. [0,1,1,-30037959982,2392378014133310] N = 737993054968595410635229854049771
E = ellinit([0,1,1,-30037959982,2392378014133310]);
generators:
[80328,22311850]
[43679,-34112829]
[147055,33989075]
[-28246,56730021]
[-202471,-13192279]
[1398964,-1642645774]
[233908,90355469]
[-137890,62550290]
[37036,36478685]
[-97476,-66288707]
[20633,-42206506]
[152038,-36605086]
[44360,33870165]
[141888,-31414811]
9. [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]
10. [0,0,1,-38693986627,2411984268434796] N = 1194517052272968263829637380194437
E = ellinit([0,0,1,-38693986627,2411984268434796]);
generators:
[68759,-8746614]
[269394,107418906]
[521427,352142949]
[-5618,-51275626]
[-174442,62077118]
[171945,-29022663]
[71148,4374743]
[71824,-1828909]
[162818,-20692107]
[156281,13483974]
[438289,263907078]
[228977,74547449]
[-7554,-51998535]
[210748,60146631]