curve #2681

y² = x³ − 147756x + 18460240

a-invariants: [0, 0, 0, -147756, 18460240]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 614592
discriminant (Δ): 59233061162778624
Faltings height: 1.9397
naive height: 47.3236
primes of bad reduction: 2, 3, 11, 97
regulator: 7.9502588463747533890877956705870931903227276
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:17:30 UTC
last updated: 2026-09-26 20:17:30 UTC

Witness: 3 independent points log in to add more points →

(3833/4, -220077/8)
(8306/25, -307296/125)
(1698, -68288)

Commentary

2-isogenous to curve#1529 via the rational 2-torsion point x=-292. Independent witness points are the images of that curve's witnesses under the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-character independence is certified.

last edited by Natanael Wildner Fraga at 2026-09-26 20:17:30 UTC · history