curve #2586

y² + xy + y = x³ − 12x − 16

a-invariants: [1, 0, 1, -12, -16]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ
conductor (N): 82
discriminant (Δ): 3362
Faltings height: -0.5316
naive height: 18.9461
primes of bad reduction: 2, 41
regulator: 0.4494138498377561644575907202691624852156
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:11:04 UTC
last updated: 2026-09-26 20:11:04 UTC

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

(-2, 1)

Commentary

2-isogenous to curve#1794 via the rational 2-torsion point x=1. 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 20:11:04 UTC · history