curve #2105

y² + xy = x³ − 68734290168521431020x − 57037316093787781241564223600

a-invariants: [1, 0, 0, -68734290168521431020, -57037316093787781241564223600]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 3397916818895170749870
discriminant (Δ): 19377215241168646983189852993448827158168129048855880474240000
Faltings height: 10.4510
naive height: 148.6439
primes of bad reduction: 2, 3, 5, 7, 11, 17, 19, 31, 401, 449, 641, 1272881
regulator: 364347951.973390908593455914685542216943222747096186995
submitted by: Steps Unbounded
submitted at: 2026-09-26 06:57:21 UTC
last updated: 2026-09-26 06:57:21 UTC

(-1684295400, 232279634936820)
(-5929477560, -376890080921820)
(9476235630, 377589267492930)
(2126614436480955/206116, 53927462700998114407785/93576664)
(-333440782050/49, 106042799976139440/343)
(333623412285/16, -176153325550761885/64)
(-1090876079992/169, -753689376242554636/2197)
(2259685998756770200/248913729, 1017592007912291465017689140/3927111902433)

2-isogenous partner of curve#2081 (Seojun Jang).

last edited by Steps Unbounded at 2026-09-26 21:47:09 UTC · history