Elliptic curves by rank › curves from searches
Rank 15 record curves
The ten smallest curves of rank 15 in this collection, in each of four categories. The same curve often heads more than one list. Every curve here has proven rank 15, is given by its global minimal model, and carries 15 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 | [1,1,0,-1661237516922,1018021144936251600] |
265121998882424427980422961463765954 |
81.565498000 | 96.451932000 | 6.04151980 | 87.93196861 |
| 2 | [1,-1,0,-438546442624,120392125493108044] |
431793384450914672704925243339122174 |
82.053255000 | 92.182205000 | 5.63797596 | 82.74640245 |
| 3 | [1,-1,0,-1407918189274,648619542235505344] |
1566351503089209175204588574733288574 |
83.341812000 | 95.550390000 | 5.82133555 | 84.03495956 |
| 4 | [1,1,0,-3452523650433,2558284848943524873] |
6450751441436292258960621122114716590 |
84.757260000 | 98.294884000 | 6.11279221 | 88.15845736 |
| 5 | [1,-1,0,-2210571130630,1328597747095485400] |
7121083963624023427016681231107700210 |
84.856123000 | 96.984456000 | 6.01869637 | 87.15870840 |
| 6 | [0,0,0,-1336053036892,648846883908105865] |
7309765093248775744134541632103899692 |
84.882274000 | 95.551092000 | 5.92651892 | 86.26856885 |
| 7 | [1,1,0,-2785429754167,905599396205211145] |
15588198294282902850412499840899939902 |
85.639577000 | 97.579873000 | 6.18212550 | 89.82923220 |
| 8 | [1,-1,0,-2671180080340,1519287911839041556] |
22264540822862075051759146026785848030 |
85.996059000 | 97.454227000 | 6.09289010 | 88.29864376 |
| 9 | [1,-1,0,-1053711230239,573871088239158649] |
33696601705258235525930879596769745214 |
86.410460000 | 95.305507000 | 5.96302701 | 87.10360752 |
| 10 | [0,1,1,-2799321745670,2434072577271351660] |
39847210354556971174387718855720678327 |
86.578116000 | 98.195341000 | 6.20126783 | 89.94541158 |
generators for these ten
1. [1,1,0,-1661237516922,1018021144936251600] N = 265121998882424427980422961463765954
E = ellinit([1,1,0,-1661237516922,1018021144936251600]);
generators:
[1077288,-692374848]
[2543346,-3640617486]
[1839126,-2046263406]
[2736491/4,-3595771303/8]
[-574525,-1334930105]
[982014,-578133216]
[307302,732334962]
[134642,-892698084]
[-673077,1353568455]
[-1406307,757658295]
[-545619,-1327128201]
[1925183/4,4593480663/8]
[-150150,1124384130]
[2141475,2697290055]
[-131429,1110959815]
2. [1,-1,0,-438546442624,120392125493108044] N = 431793384450914672704925243339122174
E = ellinit([1,-1,0,-438546442624,120392125493108044]);
generators:
[337505,-104214372]
[830308,572896950]
[384631,-93015561]
[756838,-471550080]
[-349194,480747530]
[633826,-311861496]
[997802,821832750]
[225627,-181579850]
[458692,-125697522]
[690406,382676864]
[-528813,-451866130]
[161302,-232137750]
[-226338,456245570]
[-743271,189393268]
[1954172,2592469090]
3. [1,-1,0,-1407918189274,648619542235505344] N = 1566351503089209175204588574733288574
E = ellinit([1,-1,0,-1407918189274,648619542235505344]);
generators:
[701256,78120580]
[341518,455485742]
[595038,-147061580]
[1227790,-878591698]
[2056000,2537658312]
[740875,110041937]
[548729,-203444262]
[-1255762,-659954780]
[669157,-78629242]
[1823826,2035626070]
[726368,95510640]
[186495,626433832]
[10621477/16,5150482685/64]
[550173,201102142]
[-75050,-868214212]
4. [1,1,0,-3452523650433,2558284848943524873] N = 6450751441436292258960621122114716590
E = ellinit([1,1,0,-3452523650433,2558284848943524873]);
generators:
[1112104,-307384667]
[494436,985707363]
[1586154,-1036473567]
[-720557,2161820587]
[1093029,-301267587]
[1631799,1125934143]
[235424,1325976643]
[770379,-596825742]
[889754,-437221367]
[1918659,-1732184862]
[1272554,474263713]
[2168829,2295029013]
[1074804,-299063037]
[-81916,-1685352797]
[4380084,8451712713]
5. [1,-1,0,-2210571130630,1328597747095485400] N = 7121083963624023427016681231107700210
E = ellinit([1,-1,0,-2210571130630,1328597747095485400]);
generators:
[-28805,1179950565]
[1742263,-1663941876]
[666510,388661740]
[1655100,-1485343480]
[978733,-320777286]
[278010,857488000]
[392950,-721742730]
[-1682309,535864224]
[1148990,-553334820]
[-1461275,-1198665870]
[760343,-295973891]
[-759257,1603282973]
[696490,-356470170]
[-49332,-1198945552]
[-504337,1521826788]
6. [0,0,0,-1336053036892,648846883908105865] N = 7309765093248775744134541632103899692
E = ellinit([0,0,0,-1336053036892,648846883908105865]);
generators:
[341734,481851179]
[264036,560792347]
[-448705,-1076104090]
[-1262558,568425317]
[697324,237205259]
[722,804911333]
[34176,776676157]
[960464,-501632861]
[782170,-286966885]
[530696,-298786163]
[1049884,-635127979]
[733606,252033323]
[691058,235752421]
[1439756,-1307563723]
[819054,322504619]
7. [1,1,0,-2785429754167,905599396205211145] N = 15588198294282902850412499840899939902
E = ellinit([1,1,0,-2785429754167,905599396205211145]);
generators:
[1907988,-1593722545]
[331985,-132332725]
[-1722314,771558835]
[4545766,-9067446341]
[1594136,717797435]
[339014,16044779]
[9030796,26683686439]
[315848,239291627]
[3251293,5118772540]
[-1253753,1558533232]
[-1765946,564180367]
[336187,-84848024]
[-17463,-976841324]
[-1752167,638710195]
[3210531,5003939845]
8. [1,-1,0,-2671180080340,1519287911839041556] N = 22264540822862075051759146026785848030
E = ellinit([1,-1,0,-2671180080340,1519287911839041556]);
generators:
[1345643,-601889654]
[665977,188666415]
[1175928,64623206]
[-581855,-1695744769]
[1492778,925694766]
[662653,200165516]
[-1853939,316102167]
[-1845382,-404422904]
[520103,-520539309]
[651678,-235476134]
[303398,858210136]
[2899298,4258365766]
[530893,-501072489]
[480648,-588824114]
[2315130,-2783935106]
9. [1,-1,0,-1053711230239,573871088239158649] N = 33696601705258235525930879596769745214
E = ellinit([1,-1,0,-1053711230239,573871088239158649]);
generators:
[230856,585477299]
[302220,531847253]
[653186,404993559]
[1139236,-923614395]
[-805619,949031270]
[-964879,832516150]
[-1217484,228884519]
[698995,422564927]
[887066,580227619]
[476964,423784343]
[208421,602647125]
[-240254,901874775]
[-12689756/25,123645594993/125]
[1426125,1403439718]
[805140,497008613]
10. [0,1,1,-2799321745670,2434072577271351660] N = 39847210354556971174387718855720678327
E = ellinit([0,1,1,-2799321745670,2434072577271351660]);
generators:
[760344,863248524]
[24237,1538258643]
[-1996425,-255999690]
[1523759,1306334590]
[2900560,4326385539]
[462641,-1112660744]
[2800697,-4069696049]
[-10691919/16,-128100759823/64]
[-552656,-1952520900]
[1618106,-1463253044]
[-327678,1821034076]
[1231837,924652931]
[336393,1237120352]
[1156397,862173523]
[819330,-830976861]
Smallest naive height
| # | a-invariants | conductor N | log N | naive h | Faltings h | log abs(disc) |
|---|---|---|---|---|---|---|
| 1 | [1,-1,0,-438546442624,120392125493108044] |
431793384450914672704925243339122174 |
82.053255000 | 92.182205000 | 5.63797596 | 82.74640245 |
| 2 | [1,-1,0,-1053711230239,573871088239158649] |
33696601705258235525930879596769745214 |
86.410460000 | 95.305507000 | 5.96302701 | 87.10360752 |
| 3 | [1,-1,0,-1036327194109,592685546138283889] |
40259950941709401913212369600884639134 |
86.588421000 | 95.370025000 | 5.97449020 | 87.28156773 |
| 4 | [1,-1,0,-1407918189274,648619542235505344] |
1566351503089209175204588574733288574 |
83.341812000 | 95.550390000 | 5.82133555 | 84.03495956 |
| 5 | [0,0,0,-1336053036892,648846883908105865] |
7309765093248775744134541632103899692 |
84.882274000 | 95.551092000 | 5.92651892 | 86.26856885 |
| 6 | [1,1,0,-1661237516922,1018021144936251600] |
265121998882424427980422961463765954 |
81.565498000 | 96.451932000 | 6.04151980 | 87.93196861 |
| 7 | [1,-1,0,-2210571130630,1328597747095485400] |
7121083963624023427016681231107700210 |
84.856123000 | 96.984456000 | 6.01869637 | 87.15870840 |
| 8 | [1,-1,0,-1705142089864,1478421014988866524] |
313470185465711365174722663519489654214 |
88.640768000 | 97.198158000 | 6.13877537 | 89.33391478 |
| 9 | [0,0,1,-2193487560853,1645739038058040708] |
98923079663225083409518579325988101695 |
87.487406000 | 97.412588000 | 6.13250601 | 89.09684384 |
| 10 | [1,-1,0,-2671180080340,1519287911839041556] |
22264540822862075051759146026785848030 |
85.996059000 | 97.454227000 | 6.09289010 | 88.29864376 |
generators for these ten
1. [1,-1,0,-438546442624,120392125493108044] N = 431793384450914672704925243339122174
E = ellinit([1,-1,0,-438546442624,120392125493108044]);
generators:
[337505,-104214372]
[830308,572896950]
[384631,-93015561]
[756838,-471550080]
[-349194,480747530]
[633826,-311861496]
[997802,821832750]
[225627,-181579850]
[458692,-125697522]
[690406,382676864]
[-528813,-451866130]
[161302,-232137750]
[-226338,456245570]
[-743271,189393268]
[1954172,2592469090]
2. [1,-1,0,-1053711230239,573871088239158649] N = 33696601705258235525930879596769745214
E = ellinit([1,-1,0,-1053711230239,573871088239158649]);
generators:
[230856,585477299]
[302220,531847253]
[653186,404993559]
[1139236,-923614395]
[-805619,949031270]
[-964879,832516150]
[-1217484,228884519]
[698995,422564927]
[887066,580227619]
[476964,423784343]
[208421,602647125]
[-240254,901874775]
[-12689756/25,123645594993/125]
[1426125,1403439718]
[805140,497008613]
3. [1,-1,0,-1036327194109,592685546138283889] N = 40259950941709401913212369600884639134
E = ellinit([1,-1,0,-1036327194109,592685546138283889]);
generators:
[-306556,-938765627]
[-787889,-958823836]
[-667785,993781957]
[435366,473094685]
[737192,-479264745]
[-1180731,-411987772]
[691291,454228785]
[781492,509593653]
[832631,-554535996]
[-502992,-993072313]
[-1081656,669957463]
[-1225557,-147671263]
[-803144,-951934921]
[1252991,1122473949]
[1099288,-884789263]
4. [1,-1,0,-1407918189274,648619542235505344] N = 1566351503089209175204588574733288574
E = ellinit([1,-1,0,-1407918189274,648619542235505344]);
generators:
[701256,78120580]
[341518,455485742]
[595038,-147061580]
[1227790,-878591698]
[2056000,2537658312]
[740875,110041937]
[548729,-203444262]
[-1255762,-659954780]
[669157,-78629242]
[1823826,2035626070]
[726368,95510640]
[186495,626433832]
[10621477/16,5150482685/64]
[550173,201102142]
[-75050,-868214212]
5. [0,0,0,-1336053036892,648846883908105865] N = 7309765093248775744134541632103899692
E = ellinit([0,0,0,-1336053036892,648846883908105865]);
generators:
[341734,481851179]
[264036,560792347]
[-448705,-1076104090]
[-1262558,568425317]
[697324,237205259]
[722,804911333]
[34176,776676157]
[960464,-501632861]
[782170,-286966885]
[530696,-298786163]
[1049884,-635127979]
[733606,252033323]
[691058,235752421]
[1439756,-1307563723]
[819054,322504619]
6. [1,1,0,-1661237516922,1018021144936251600] N = 265121998882424427980422961463765954
E = ellinit([1,1,0,-1661237516922,1018021144936251600]);
generators:
[1077288,-692374848]
[2543346,-3640617486]
[1839126,-2046263406]
[2736491/4,-3595771303/8]
[-574525,-1334930105]
[982014,-578133216]
[307302,732334962]
[134642,-892698084]
[-673077,1353568455]
[-1406307,757658295]
[-545619,-1327128201]
[1925183/4,4593480663/8]
[-150150,1124384130]
[2141475,2697290055]
[-131429,1110959815]
7. [1,-1,0,-2210571130630,1328597747095485400] N = 7121083963624023427016681231107700210
E = ellinit([1,-1,0,-2210571130630,1328597747095485400]);
generators:
[-28805,1179950565]
[1742263,-1663941876]
[666510,388661740]
[1655100,-1485343480]
[978733,-320777286]
[278010,857488000]
[392950,-721742730]
[-1682309,535864224]
[1148990,-553334820]
[-1461275,-1198665870]
[760343,-295973891]
[-759257,1603282973]
[696490,-356470170]
[-49332,-1198945552]
[-504337,1521826788]
8. [1,-1,0,-1705142089864,1478421014988866524] N = 313470185465711365174722663519489654214
E = ellinit([1,-1,0,-1705142089864,1478421014988866524]);
generators:
[-328619,-1415206776]
[-1325583,1187866228]
[6565876,16529784810]
[8001964,22361397918]
[1101510,967270442]
[597371,820061854]
[701164,-792531322]
[-1601612,-317008078]
[596682,-820925842]
[-740044,-1527702126]
[992903,-874704278]
[315700,985525818]
[-1205964,1335094330]
[2830914,-4398966922]
[397164,-929632922]
9. [0,0,1,-2193487560853,1645739038058040708] N = 98923079663225083409518579325988101695
E = ellinit([0,0,1,-2193487560853,1645739038058040708]);
generators:
[878506,629884182]
[1380386,-1117209663]
[-458128,1598275515]
[-1685679,743891792]
[1137746,789227982]
[-1647752,-886720413]
[1187621,-846037608]
[1509123,1331334687]
[1708898,-1699365378]
[1031473,-693280368]
[1044307,702824255]
[-377489,1555623687]
[982171,-662434993]
[325373,-983099113]
[380327,930865335]
10. [1,-1,0,-2671180080340,1519287911839041556] N = 22264540822862075051759146026785848030
E = ellinit([1,-1,0,-2671180080340,1519287911839041556]);
generators:
[1345643,-601889654]
[665977,188666415]
[1175928,64623206]
[-581855,-1695744769]
[1492778,925694766]
[662653,200165516]
[-1853939,316102167]
[-1845382,-404422904]
[520103,-520539309]
[651678,-235476134]
[303398,858210136]
[2899298,4258365766]
[530893,-501072489]
[480648,-588824114]
[2315130,-2783935106]
Smallest Faltings height
| # | a-invariants | conductor N | log N | naive h | Faltings h | log abs(disc) |
|---|---|---|---|---|---|---|
| 1 | [1,-1,0,-438546442624,120392125493108044] |
431793384450914672704925243339122174 |
82.053255000 | 92.182205000 | 5.63797596 | 82.74640245 |
| 2 | [1,-1,0,-1407918189274,648619542235505344] |
1566351503089209175204588574733288574 |
83.341812000 | 95.550390000 | 5.82133555 | 84.03495956 |
| 3 | [0,0,0,-1336053036892,648846883908105865] |
7309765093248775744134541632103899692 |
84.882274000 | 95.551092000 | 5.92651892 | 86.26856885 |
| 4 | [1,-1,0,-1053711230239,573871088239158649] |
33696601705258235525930879596769745214 |
86.410460000 | 95.305507000 | 5.96302701 | 87.10360752 |
| 5 | [1,-1,0,-1036327194109,592685546138283889] |
40259950941709401913212369600884639134 |
86.588421000 | 95.370025000 | 5.97449020 | 87.28156773 |
| 6 | [1,-1,0,-2210571130630,1328597747095485400] |
7121083963624023427016681231107700210 |
84.856123000 | 96.984456000 | 6.01869637 | 87.15870840 |
| 7 | [1,1,0,-1661237516922,1018021144936251600] |
265121998882424427980422961463765954 |
81.565498000 | 96.451932000 | 6.04151980 | 87.93196861 |
| 8 | [1,-1,0,-2671180080340,1519287911839041556] |
22264540822862075051759146026785848030 |
85.996059000 | 97.454227000 | 6.09289010 | 88.29864376 |
| 9 | [1,1,0,-3452523650433,2558284848943524873] |
6450751441436292258960621122114716590 |
84.757260000 | 98.294884000 | 6.11279221 | 88.15845736 |
| 10 | [1,0,1,-3847814251363,2824924562370598842] |
99300204089004822267342053284482380746 |
87.491211000 | 98.549182000 | 6.12351029 | 88.18435815 |
generators for these ten
1. [1,-1,0,-438546442624,120392125493108044] N = 431793384450914672704925243339122174
E = ellinit([1,-1,0,-438546442624,120392125493108044]);
generators:
[337505,-104214372]
[830308,572896950]
[384631,-93015561]
[756838,-471550080]
[-349194,480747530]
[633826,-311861496]
[997802,821832750]
[225627,-181579850]
[458692,-125697522]
[690406,382676864]
[-528813,-451866130]
[161302,-232137750]
[-226338,456245570]
[-743271,189393268]
[1954172,2592469090]
2. [1,-1,0,-1407918189274,648619542235505344] N = 1566351503089209175204588574733288574
E = ellinit([1,-1,0,-1407918189274,648619542235505344]);
generators:
[701256,78120580]
[341518,455485742]
[595038,-147061580]
[1227790,-878591698]
[2056000,2537658312]
[740875,110041937]
[548729,-203444262]
[-1255762,-659954780]
[669157,-78629242]
[1823826,2035626070]
[726368,95510640]
[186495,626433832]
[10621477/16,5150482685/64]
[550173,201102142]
[-75050,-868214212]
3. [0,0,0,-1336053036892,648846883908105865] N = 7309765093248775744134541632103899692
E = ellinit([0,0,0,-1336053036892,648846883908105865]);
generators:
[341734,481851179]
[264036,560792347]
[-448705,-1076104090]
[-1262558,568425317]
[697324,237205259]
[722,804911333]
[34176,776676157]
[960464,-501632861]
[782170,-286966885]
[530696,-298786163]
[1049884,-635127979]
[733606,252033323]
[691058,235752421]
[1439756,-1307563723]
[819054,322504619]
4. [1,-1,0,-1053711230239,573871088239158649] N = 33696601705258235525930879596769745214
E = ellinit([1,-1,0,-1053711230239,573871088239158649]);
generators:
[230856,585477299]
[302220,531847253]
[653186,404993559]
[1139236,-923614395]
[-805619,949031270]
[-964879,832516150]
[-1217484,228884519]
[698995,422564927]
[887066,580227619]
[476964,423784343]
[208421,602647125]
[-240254,901874775]
[-12689756/25,123645594993/125]
[1426125,1403439718]
[805140,497008613]
5. [1,-1,0,-1036327194109,592685546138283889] N = 40259950941709401913212369600884639134
E = ellinit([1,-1,0,-1036327194109,592685546138283889]);
generators:
[-306556,-938765627]
[-787889,-958823836]
[-667785,993781957]
[435366,473094685]
[737192,-479264745]
[-1180731,-411987772]
[691291,454228785]
[781492,509593653]
[832631,-554535996]
[-502992,-993072313]
[-1081656,669957463]
[-1225557,-147671263]
[-803144,-951934921]
[1252991,1122473949]
[1099288,-884789263]
6. [1,-1,0,-2210571130630,1328597747095485400] N = 7121083963624023427016681231107700210
E = ellinit([1,-1,0,-2210571130630,1328597747095485400]);
generators:
[-28805,1179950565]
[1742263,-1663941876]
[666510,388661740]
[1655100,-1485343480]
[978733,-320777286]
[278010,857488000]
[392950,-721742730]
[-1682309,535864224]
[1148990,-553334820]
[-1461275,-1198665870]
[760343,-295973891]
[-759257,1603282973]
[696490,-356470170]
[-49332,-1198945552]
[-504337,1521826788]
7. [1,1,0,-1661237516922,1018021144936251600] N = 265121998882424427980422961463765954
E = ellinit([1,1,0,-1661237516922,1018021144936251600]);
generators:
[1077288,-692374848]
[2543346,-3640617486]
[1839126,-2046263406]
[2736491/4,-3595771303/8]
[-574525,-1334930105]
[982014,-578133216]
[307302,732334962]
[134642,-892698084]
[-673077,1353568455]
[-1406307,757658295]
[-545619,-1327128201]
[1925183/4,4593480663/8]
[-150150,1124384130]
[2141475,2697290055]
[-131429,1110959815]
8. [1,-1,0,-2671180080340,1519287911839041556] N = 22264540822862075051759146026785848030
E = ellinit([1,-1,0,-2671180080340,1519287911839041556]);
generators:
[1345643,-601889654]
[665977,188666415]
[1175928,64623206]
[-581855,-1695744769]
[1492778,925694766]
[662653,200165516]
[-1853939,316102167]
[-1845382,-404422904]
[520103,-520539309]
[651678,-235476134]
[303398,858210136]
[2899298,4258365766]
[530893,-501072489]
[480648,-588824114]
[2315130,-2783935106]
9. [1,1,0,-3452523650433,2558284848943524873] N = 6450751441436292258960621122114716590
E = ellinit([1,1,0,-3452523650433,2558284848943524873]);
generators:
[1112104,-307384667]
[494436,985707363]
[1586154,-1036473567]
[-720557,2161820587]
[1093029,-301267587]
[1631799,1125934143]
[235424,1325976643]
[770379,-596825742]
[889754,-437221367]
[1918659,-1732184862]
[1272554,474263713]
[2168829,2295029013]
[1074804,-299063037]
[-81916,-1685352797]
[4380084,8451712713]
10. [1,0,1,-3847814251363,2824924562370598842] N = 99300204089004822267342053284482380746
E = ellinit([1,0,1,-3847814251363,2824924562370598842]);
generators:
[-101315,1792737438]
[1753114,1210446732]
[742393,-614783340]
[965830,97206528]
[-746684,2298573090]
[-1797357,-1982652054]
[-1942613,1723995646]
[-2133101,-1150817502]
[-1062829,2390911290]
[968424,-83193202]
[753573,593970740]
[-319251,-2005034802]
[5863805,13483520478]
[2492115,-2953084902]
[944275,-183496094]
Smallest absolute discriminant
| # | a-invariants | conductor N | log N | naive h | Faltings h | log abs(disc) |
|---|---|---|---|---|---|---|
| 1 | [1,-1,0,-438546442624,120392125493108044] |
431793384450914672704925243339122174 |
82.053255000 | 92.182205000 | 5.63797596 | 82.74640245 |
| 2 | [1,-1,0,-1407918189274,648619542235505344] |
1566351503089209175204588574733288574 |
83.341812000 | 95.550390000 | 5.82133555 | 84.03495956 |
| 3 | [0,0,0,-1336053036892,648846883908105865] |
7309765093248775744134541632103899692 |
84.882274000 | 95.551092000 | 5.92651892 | 86.26856885 |
| 4 | [1,-1,0,-1053711230239,573871088239158649] |
33696601705258235525930879596769745214 |
86.410460000 | 95.305507000 | 5.96302701 | 87.10360752 |
| 5 | [1,-1,0,-2210571130630,1328597747095485400] |
7121083963624023427016681231107700210 |
84.856123000 | 96.984456000 | 6.01869637 | 87.15870840 |
| 6 | [1,-1,0,-1036327194109,592685546138283889] |
40259950941709401913212369600884639134 |
86.588421000 | 95.370025000 | 5.97449020 | 87.28156773 |
| 7 | [1,1,0,-1661237516922,1018021144936251600] |
265121998882424427980422961463765954 |
81.565498000 | 96.451932000 | 6.04151980 | 87.93196861 |
| 8 | [1,1,0,-3452523650433,2558284848943524873] |
6450751441436292258960621122114716590 |
84.757260000 | 98.294884000 | 6.11279221 | 88.15845736 |
| 9 | [1,0,1,-3847814251363,2824924562370598842] |
99300204089004822267342053284482380746 |
87.491211000 | 98.549182000 | 6.12351029 | 88.18435815 |
| 10 | [1,-1,0,-2671180080340,1519287911839041556] |
22264540822862075051759146026785848030 |
85.996059000 | 97.454227000 | 6.09289010 | 88.29864376 |
generators for these ten
1. [1,-1,0,-438546442624,120392125493108044] N = 431793384450914672704925243339122174
E = ellinit([1,-1,0,-438546442624,120392125493108044]);
generators:
[337505,-104214372]
[830308,572896950]
[384631,-93015561]
[756838,-471550080]
[-349194,480747530]
[633826,-311861496]
[997802,821832750]
[225627,-181579850]
[458692,-125697522]
[690406,382676864]
[-528813,-451866130]
[161302,-232137750]
[-226338,456245570]
[-743271,189393268]
[1954172,2592469090]
2. [1,-1,0,-1407918189274,648619542235505344] N = 1566351503089209175204588574733288574
E = ellinit([1,-1,0,-1407918189274,648619542235505344]);
generators:
[701256,78120580]
[341518,455485742]
[595038,-147061580]
[1227790,-878591698]
[2056000,2537658312]
[740875,110041937]
[548729,-203444262]
[-1255762,-659954780]
[669157,-78629242]
[1823826,2035626070]
[726368,95510640]
[186495,626433832]
[10621477/16,5150482685/64]
[550173,201102142]
[-75050,-868214212]
3. [0,0,0,-1336053036892,648846883908105865] N = 7309765093248775744134541632103899692
E = ellinit([0,0,0,-1336053036892,648846883908105865]);
generators:
[341734,481851179]
[264036,560792347]
[-448705,-1076104090]
[-1262558,568425317]
[697324,237205259]
[722,804911333]
[34176,776676157]
[960464,-501632861]
[782170,-286966885]
[530696,-298786163]
[1049884,-635127979]
[733606,252033323]
[691058,235752421]
[1439756,-1307563723]
[819054,322504619]
4. [1,-1,0,-1053711230239,573871088239158649] N = 33696601705258235525930879596769745214
E = ellinit([1,-1,0,-1053711230239,573871088239158649]);
generators:
[230856,585477299]
[302220,531847253]
[653186,404993559]
[1139236,-923614395]
[-805619,949031270]
[-964879,832516150]
[-1217484,228884519]
[698995,422564927]
[887066,580227619]
[476964,423784343]
[208421,602647125]
[-240254,901874775]
[-12689756/25,123645594993/125]
[1426125,1403439718]
[805140,497008613]
5. [1,-1,0,-2210571130630,1328597747095485400] N = 7121083963624023427016681231107700210
E = ellinit([1,-1,0,-2210571130630,1328597747095485400]);
generators:
[-28805,1179950565]
[1742263,-1663941876]
[666510,388661740]
[1655100,-1485343480]
[978733,-320777286]
[278010,857488000]
[392950,-721742730]
[-1682309,535864224]
[1148990,-553334820]
[-1461275,-1198665870]
[760343,-295973891]
[-759257,1603282973]
[696490,-356470170]
[-49332,-1198945552]
[-504337,1521826788]
6. [1,-1,0,-1036327194109,592685546138283889] N = 40259950941709401913212369600884639134
E = ellinit([1,-1,0,-1036327194109,592685546138283889]);
generators:
[-306556,-938765627]
[-787889,-958823836]
[-667785,993781957]
[435366,473094685]
[737192,-479264745]
[-1180731,-411987772]
[691291,454228785]
[781492,509593653]
[832631,-554535996]
[-502992,-993072313]
[-1081656,669957463]
[-1225557,-147671263]
[-803144,-951934921]
[1252991,1122473949]
[1099288,-884789263]
7. [1,1,0,-1661237516922,1018021144936251600] N = 265121998882424427980422961463765954
E = ellinit([1,1,0,-1661237516922,1018021144936251600]);
generators:
[1077288,-692374848]
[2543346,-3640617486]
[1839126,-2046263406]
[2736491/4,-3595771303/8]
[-574525,-1334930105]
[982014,-578133216]
[307302,732334962]
[134642,-892698084]
[-673077,1353568455]
[-1406307,757658295]
[-545619,-1327128201]
[1925183/4,4593480663/8]
[-150150,1124384130]
[2141475,2697290055]
[-131429,1110959815]
8. [1,1,0,-3452523650433,2558284848943524873] N = 6450751441436292258960621122114716590
E = ellinit([1,1,0,-3452523650433,2558284848943524873]);
generators:
[1112104,-307384667]
[494436,985707363]
[1586154,-1036473567]
[-720557,2161820587]
[1093029,-301267587]
[1631799,1125934143]
[235424,1325976643]
[770379,-596825742]
[889754,-437221367]
[1918659,-1732184862]
[1272554,474263713]
[2168829,2295029013]
[1074804,-299063037]
[-81916,-1685352797]
[4380084,8451712713]
9. [1,0,1,-3847814251363,2824924562370598842] N = 99300204089004822267342053284482380746
E = ellinit([1,0,1,-3847814251363,2824924562370598842]);
generators:
[-101315,1792737438]
[1753114,1210446732]
[742393,-614783340]
[965830,97206528]
[-746684,2298573090]
[-1797357,-1982652054]
[-1942613,1723995646]
[-2133101,-1150817502]
[-1062829,2390911290]
[968424,-83193202]
[753573,593970740]
[-319251,-2005034802]
[5863805,13483520478]
[2492115,-2953084902]
[944275,-183496094]
10. [1,-1,0,-2671180080340,1519287911839041556] N = 22264540822862075051759146026785848030
E = ellinit([1,-1,0,-2671180080340,1519287911839041556]);
generators:
[1345643,-601889654]
[665977,188666415]
[1175928,64623206]
[-581855,-1695744769]
[1492778,925694766]
[662653,200165516]
[-1853939,316102167]
[-1845382,-404422904]
[520103,-520539309]
[651678,-235476134]
[303398,858210136]
[2899298,4258365766]
[530893,-501072489]
[480648,-588824114]
[2315130,-2783935106]