curve #2714

y² + xy + y = x³ − x² − 12855x + 115022

a-invariants: [1, -1, 1, -12855, 115022]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 457025
discriminant (Δ): 130544906640625
Faltings height: 1.3989
naive height: 39.9980
primes of bad reduction: 5, 101, 181
regulator: 29.132411229804974879362056813140444227035609
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:18:58 UTC
last updated: 2026-09-26 20:18:58 UTC

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

(14314/121, -730580/1331)
(22734, -3439055)
(13354/81, -1203020/729)

Commentary

2-isogenous to curve#1525 via the rational 2-torsion point x=-69/4. 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 20:18:58 UTC · history