curve #2548

y² + xy + y = x³ − x² − 232x − 1286

a-invariants: [1, -1, 1, -232, -1286]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ
conductor (N): 205
discriminant (Δ): 16015625
Faltings height: 0.1948
naive height: 27.9498
primes of bad reduction: 5, 41
regulator: 0.4006503493311752387667261273844828924598
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:08:28 UTC
last updated: 2026-09-26 20:08:28 UTC

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

(22, -74)

Commentary

2-isogenous to curve#2073 via the rational 2-torsion point x=5. 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 20:08:28 UTC · history