curve #6

y² + xy + y = x³ − x² − 2063758701246626370773726978x + 32838647793306133075103747085833809114881

a-invariants: [1, -1, 1, -2063758701246626370773726978, 32838647793306133075103747085833809114881]
rank (lower bound): ≥ 19
conductor (N): 137377583765207564914008156149740232282282540648823380362307893110
naive height: 200.2966
Faltings height: 14.6599
discriminant (Δ): 96685523963347486558024309539021902393781074235837540884094505729945198887508377600
primes of bad reduction: 2, 3, 5, 11, 17, 19, 29, 181, 73589, 2898174137, 383763976916891263992296397076513746514499
regulator: 1315117024670475573.773781834878564837945549161259425446399714968525744103236
submitted by: David Renshaw
last updated: 2026-07-01 22:30:43

(-30987785091199, 258909576181697016447)
(-28889517303967, 261435145473088184895)
(-71487320458034575/7921, 158780942822372481268517943/704969)
(-5811612460699807/2401, 22879566180834025272238959/117649)
(13824498650633, 83368523385975203271)
(761787717625797737/51529, -872181661081924408957800795/11697083)
(-6768903225745, -215633697068279328993)
(-26753594302623, -262493028566521557409)
(-43702888408807, -198899103401955431409)
(-3473544815195797742755/66896041, -720367355474239205275292698047/547142719339)
(-4844597663662106466271/94965025, 67726534118909683241734294312143/925434168625)
(-50527110390373, 90106963524511847991)
(-45015432587775, 185797905595910416127)
(-385165144189, -183394325158424667243)
(12603290965505, 93970415796904223487)
(-17345672207357056815/421201, -59881991231482114022330423257/273359449)
(19374570094625, -11265860759711920353)
(-1148870915488663/169, -474033106804620147824853/2197)
(-124803550432849879/32041, 1158739203591364356910897749/5735339)

Found by Fermigier (1992). A historical rank ≥ 19 record, via Dujella's elliptic-curve rank-records tables.

last edited by David Renshaw at 2026-05-27 22:31:38 · history