curve #2658

y² = x³ − 2611x − 51330

a-invariants: [0, 0, 0, -2611, -51330]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 7832
discriminant (Δ): 981443584
Faltings height: 0.6782
naive height: 35.2161
primes of bad reduction: 2, 11, 89
regulator: 14.0835976124364326123417213853811849101584
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:16:07 UTC
last updated: 2026-09-26 20:16:07 UTC

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

(-269/9, -80/27)
(259, -4080)

Commentary

2-isogenous to curve#1431 via the rational 2-torsion point x=15. 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 20:16:08 UTC · history