curve #2757

y² + xy + y = x³ − x² − 75861932x + 25829354031

a-invariants: [1, -1, 1, -75861932, 25829354031]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 912967290
discriminant (Δ): 27653837242943681372160000
Faltings height: 3.5715
naive height: 66.0469
primes of bad reduction: 2, 3, 5, 19, 23, 139, 167
regulator: 20.34026524089422894190746455272265572079768067
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:21:04 UTC
last updated: 2026-09-26 20:21:04 UTC

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

(9081, -297331)
(8549, 40869)
(39221, -7594731)
(236321, -114922431)

Commentary

2-isogenous to curve#1602 via the rational 2-torsion point x=71003/4. 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 20:21:04 UTC · history