curve #2642

y² + xy = x³ − 2455979560x − 23092738344400

a-invariants: [1, 0, 0, -2455979560, -23092738344400]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 2607990
discriminant (Δ): 717729627963028908691406250000
Faltings height: 4.4248
naive height: 76.4790
primes of bad reduction: 2, 3, 5, 7, 11, 1129
regulator: 16.6338797735328024183330679881744832337799
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:14:49 UTC
last updated: 2026-09-26 20:14:49 UTC

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

(-12430, 2354540)
(56870, -4629010)

Commentary

2-isogenous to curve#1469 via the rational 2-torsion point x=21968. 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 20:14:49 UTC · history