curve #2662

y² + xy + y = x³ + x² − 109043304x − 27354134679

a-invariants: [1, 1, 1, -109043304, -27354134679]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 659022
discriminant (Δ): 82658507783312370783654144
Faltings height: 3.6626
naive height: 67.1354
primes of bad reduction: 2, 3, 7, 13, 17, 71
regulator: 11.6407403859762630711447686822206296024438
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:16:28 UTC
last updated: 2026-09-26 20:16:28 UTC

Witness: 2 independent points log in to add more points →

(1185853/49, 1159463915/343)
(232909/16, -78066685/64)

Commentary

2-isogenous to curve#1471 via the rational 2-torsion point x=5157. 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 20:16:28 UTC · history