curve #2645

y² + xy + y = x³ + x² − 153114x + 22539486

a-invariants: [1, 1, 1, -153114, 22539486]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 35139
discriminant (Δ): 9021336601834089
Faltings height: 1.8483
naive height: 47.4304
primes of bad reduction: 3, 13, 17, 53
regulator: 2.61709471353856531039378494479972002810721
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:15:09 UTC
last updated: 2026-09-26 20:15:09 UTC

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

(1576, -61606)
(34012, -6289318)

Commentary

2-isogenous to curve#1170 via the rational 2-torsion point x=225. 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 20:15:09 UTC · history