curve #2110

y² + xy = x³ − 656560981254063055255479497499x + 204767353732023080348214316675440461049811665

a-invariants: [1, 0, 0, -656560981254063055255479497499, 204767353732023080348214316675440461049811665]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/4ℤ
conductor (N): 1286799043897115641009631514
discriminant (Δ): 39522052277875084255186712830884656242049760657371013091318565551411679515901952
Faltings height: 15.4454
naive height: 217.5840
primes of bad reduction: 2, 3, 7, 11, 13, 17, 29, 31, 41, 47, 53, 61, 113, 193, 281, 599, 613
regulator: 103884004.383278508761412488973949128598248526783244151
submitted by: Steps Unbounded
submitted at: 2026-09-26 06:58:14 UTC
last updated: 2026-09-26 06:58:14 UTC

(511865491073310, -1675833871326014067855)
(472743136705710, -184833454152855918975)
(11783375997748206/25, -16490483435686025316819/125)
(469848887834910, -76138634819120284815)
(780430833555810, 12950123612387898869445)
(159377629979776494/289, 15850604824714164445196289/4913)
(8780483341634654334/18769, 8929925155875350566473/2571353)
(11695488413386734/25, -7085064282526192083/125)

2-isogenous partner of curve#1109 (Dujella - Peral (2016)). Isogenous to curve#2111, curve#2112 (also ours).

last edited by Steps Unbounded at 2026-09-26 21:47:35 UTC · history