curve #491

y² = x³ − x² − 4198748675932176x + 104677456568968316077776

a-invariants: [0, -1, 0, -4198748675932176, 104677456568968316077776]
rank (lower bound): ≥ 14
torsion subgroup: trivial
conductor (N): 3970314507697780490911215748177254887941680
discriminant (Δ): 3811501927389869271274767118250164692424012800
Faltings height: 7.7024
naive height: 119.5343
primes of bad reduction: 2, 3, 5, 95279, 113969161, 1523453235298363340578733003
regulator: 1079742013858.25297855810327235257736699511358477078737751041079411
submitted by: 7fff-zip
submitted at: 2026-09-02 00:34:04 UTC
last updated: 2026-09-02 00:34:04 UTC

(323240521/16, -10727898293955/64)
(6216777102/169, 2698671812238/2197)
(186206041/9, -4408821610300/27)
(28321208, -92086927396)
(173416475884/5929, -37898082381332760/456533)
(84007019064/2209, 105179754400740/103823)
(38022156, -117159480)
(38058881, -2290599320)
(51417078, -157232989254)
(-66972042, 292386008646)
(-73634754, 120822064170)
(-178389291/4, -3606481666365/8)
(1062965166/25, -6868184470914/125)
(9223680127340/241081, -742172924955559624/118370771)

Mestre–Fermigier paired-root quartic construction with centers [348,-600,-216,492,876,-900] and shift 12.

last edited by 7fff-zip at 2026-09-02 00:34:04 UTC · history