curve #2760

y² + xy + y = x³ + x² − 57516438x − 167610371094

a-invariants: [1, 1, 1, -57516438, -167610371094]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 402396225
discriminant (Δ): 44629950222102828515625
Faltings height: 3.2308
naive height: 65.2163
primes of bad reduction: 3, 5, 7, 11, 59, 1181
regulator: 221.8348657828771391093937968281392287558977405
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:21:12 UTC
last updated: 2026-09-26 20:21:12 UTC

Witness: 4 independent points log in to add more points →

(20275, 2635862)
(-40181/9, 452650/27)
(154780, -60896803)
(-18025/4, 95271/8)

Commentary

2-isogenous to curve#1508 via the rational 2-torsion point x=2265. Independent witness points are the images of that curve's witnesses under the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-character independence is certified.

last edited by Natanael Wildner Fraga at 2026-09-26 20:21:12 UTC · history