curve #2583

y² + xy = x³ + 10134040x + 425388708672

a-invariants: [1, 0, 0, 10134040, 425388708672]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/8ℤ
conductor (N): 82110
discriminant (Δ): -78239096930039062500000000
Faltings height: 3.6475
naive height: 67.0757
primes of bad reduction: 2, 3, 5, 7, 17, 23
regulator: 4.069730484363187393043275250556656602285
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:10:53 UTC
last updated: 2026-09-26 20:10:53 UTC

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

(-44744/9, 13624616/27)

Commentary

2-isogenous to curve#1073 via the rational 2-torsion point x=3536. 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 20:10:53 UTC · history