curve #2561

y² + xy = x³ − 2178935510140x + 1237982811464867600

a-invariants: [1, 0, 0, -2178935510140, 1237982811464867600]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/8ℤ
conductor (N): 266910
discriminant (Δ): 757051842880264964991840000
Faltings height: 5.3743
naive height: 96.8432
primes of bad reduction: 2, 3, 5, 7, 31, 41
regulator: 11.25665795570367861784810810444688171373
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:09:20 UTC
last updated: 2026-09-26 20:09:20 UTC

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

(69048190/81, -552675950/729)

Commentary

2-isogenous to curve#1080 via the rational 2-torsion point x=-426120. Independent witness points are the images of that curve's witnesses under the degree-2 isogeny.

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