curve #278

y² = x³ − 25876904769x + 1776132919332864

a-invariants: [0, 0, 0, -25876904769, 1776132919332864]
c-invariants: [1242091428912, -1534578842303594496]
rank (lower bound): ≥ 7
torsion subgroup: trivial
conductor (N): 2215450455430034397055968
discriminant (Δ): -253845254197855645658231020687296
Faltings height: 4.9506
naive height: 83.7496
primes of bad reduction: 2, 3, 29, 1164682969, 7853546759
regulator: 336275.0594986145591955762580908484074969345112952335
submitted by: Daksh Shami
submitted at: 2026-08-21 20:23:25 UTC
last updated: 2026-09-02 14:44:30 UTC

Witness: 7 independent points log in to add more points →

(0, 42144192)
(75081, 16016004)
(81345, 14471928)
(160863, 42144192)
(174087, 50470092)
(108489/4, 264634947/8)
(13064935/121, 20658754592/1331)

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