curve #2582

y² + xy = x³ − 49095400x + 132402324032

a-invariants: [1, 0, 0, -49095400, 132402324032]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/8ℤ
conductor (N): 82110
discriminant (Δ): 10116926999101440000
Faltings height: 2.9544
naive height: 64.7414
primes of bad reduction: 2, 3, 5, 7, 17, 23
regulator: 4.069730484363187393043275250556656602285
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:10:49 UTC
last updated: 2026-09-26 20:10:49 UTC

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

(490384/121, -1677112/1331)

Commentary

2-isogenous to curve#1073 via the rational 2-torsion point x=-32385/4. 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 20:10:49 UTC · history