curve #2562

y² + xy = x³ − 8184310140x + 326543733507600

a-invariants: [1, 0, 0, -8184310140, 326543733507600]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/8ℤ
conductor (N): 266910
discriminant (Δ): -10979320318525440000000000000000
Faltings height: 4.6812
naive height: 80.3623
primes of bad reduction: 2, 3, 5, 7, 31, 41
regulator: 2.814164488925919654462027026111720428432
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:09:24 UTC
last updated: 2026-09-26 20:09:24 UTC

Witness: 1 independent point log in to add more points →

(-42878280/1369, -1189453151820/50653)

Commentary

2-isogenous to curve#1080 via the rational 2-torsion point x=848959/4. 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 20:09:24 UTC · history