curve #2654

y² + xy + y = x³ + x² − 10284x − 188979

a-invariants: [1, 1, 1, -10284, -188979]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 9078
discriminant (Δ): 54873248891904
Faltings height: 1.3313
naive height: 39.3286
primes of bad reduction: 2, 3, 17, 89
regulator: 1.22028694247848358479942287860700024838696
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:15:49 UTC
last updated: 2026-09-26 20:15:49 UTC

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

(559, 12725)
(3313, -192295)

Commentary

2-isogenous to curve#1432 via the rational 2-torsion point x=45. 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 20:15:49 UTC · history