curve #278

y² = x³ − 25876904769x + 1776132919332864

a-invariants: [0, 0, 0, -25876904769, 1776132919332864]
rank (lower bound): ≥ 6
torsion subgroup: trivial
conductor (N): 2215450455430034397055968
naive height: 83.7496
Faltings height: 4.9506
discriminant (Δ): -253845254197855645658231020687296
primes of bad reduction: 2, 3, 29, 1164682969, 7853546759
regulator: 31350.737884554892910386288522170451896721726425949
submitted by: Daksh Shami
submitted at: 2026-08-21 20:23:25 UTC
last updated: 2026-08-21 20:23:25 UTC

Witness: 6 independent points

(0, 42144192)
(160863, 42144192)
(-121104, 55980324)
(75081, -16016004)
(174087, 50470092)
(117852, 19061622)

Commentary

Rank >= 6. Found during a preliminary search among rational specializations of the classical one-parameter family y^2 = x^3 - u^2*x + 1, at u = 1849/1392.

last edited by Daksh Shami at 2026-08-21 20:23:25 UTC · history