curve #2553

y² + xy = x³ − 11420x − 450288

a-invariants: [1, 0, 0, -11420, -450288]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/6ℤ
conductor (N): 4290
discriminant (Δ): 8097103872000
Faltings height: 1.2362
naive height: 39.6430
primes of bad reduction: 2, 3, 5, 11, 13
regulator: 2.145205242224710692465142794551165664586
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:08:47 UTC
last updated: 2026-09-26 20:08:47 UTC

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

(-68, -80)

Commentary

2-isogenous to curve#1054 via the rational 2-torsion point x=575/4. 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 20:08:47 UTC · history