curve #2542

y² = x³ + x² − 8x − 8

a-invariants: [0, 1, 0, -8, -8]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ
conductor (N): 224
discriminant (Δ): 25088
Faltings height: -0.4572
naive height: 17.9744
primes of bad reduction: 2, 7
regulator: 0.3935482296911246208047523735113536041983
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:08:05 UTC
last updated: 2026-09-26 20:08:05 UTC

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

(-2, 2)

Commentary

2-isogenous to curve#1796 via the rational 2-torsion point x=0. 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 20:08:05 UTC · history