curve #2564

y² + xy + y = x³ + x² − 5074x − 128689

a-invariants: [1, 1, 1, -5074, -128689]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 966
discriminant (Δ): 1439452851984
Faltings height: 1.0694
naive height: 37.2093
primes of bad reduction: 2, 3, 7, 23
regulator: 2.429046614030699609497398526925843435269
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:09:31 UTC
last updated: 2026-09-26 20:09:31 UTC

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

(131, -1281)

Commentary

2-isogenous to curve#2078 via the rational 2-torsion point x=25. 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 20:09:31 UTC · history