curve #2004

y² + xy = x³ − 88362822905136158369061583163x + 14376898779874743116748140784495810477788817

a-invariants: [1, 0, 0, -88362822905136158369061583163, 14376898779874743116748140784495810477788817]
rank (lower bound): ≥ 15
torsion subgroup: ℤ/2ℤ
conductor (N): 688038028320098121783655338615679833504856167124350
discriminant (Δ): -45136436638706580503937300260443756006438439775343511603165062830094770116377165824000000
Faltings height: 15.7137
naive height: 212.2715
primes of bad reduction: 2, 3, 5, 23, 31, 41, 67, 71, 79, 137, 197, 257, 337, 379, 439, 1063, 1129, 1993, 2089, 2671
regulator: 154770797569328503819.29106967850721628285822945027610873290038941913
submitted by: Steps Unbounded
submitted at: 2026-09-26 04:58:07 UTC
last updated: 2026-09-26 04:58:07 UTC

(-222591871118498, 4797598888213799085649)
(143551499178718/9, 97243320940020515278523/27)
(9327847205189038/121, 3770084035767392191984547/1331)
(438236076173400718/9, 290104271100269068626696523/27)
(167437740586346158/729, 49002802178984956288640467/19683)
(871560756355913518/2209, 664246477877915013701903327/103823)
(13948682164343169358/5329, 51779427782167897115268227833/389017)
(-75215511961664193458/212521, 112491810289418462465128810469/97972181)
(-30447012596940449762/113569, -165935758338047009479714951103/38272753)
(258922959469210350862/644809, 3420559380704965931580441016235/517781627)
(-40723224397270586894/133225, 174152057143161832575938434601/48627125)
(-2826595909709707322738/7890481, 5443964390127717276860327445721/22164361129)
(-8981255563593758022434/36590401, -1020974758855357182139010248835279/221335335649)
(1626133303629951604498/22024249, 296972648530755786102031219468993/103359800557)
(1084312176781826830281/287296, 35599074399778950899365392214305/153990656)

2-isogenous partner of curve#1198 (Dujella (2009)).

last edited by Steps Unbounded at 2026-09-26 21:37:14 UTC · history