curve #2671

y² + xy + y = x³ + x² − 4180x + 77252

a-invariants: [1, 1, 1, -4180, 77252]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 5115
discriminant (Δ): 1978593890625
Faltings height: 1.0701
naive height: 36.6278
primes of bad reduction: 3, 5, 11, 31
regulator: 0.603467573678516105120115249599573304206251
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:17:00 UTC
last updated: 2026-09-26 20:17:00 UTC

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

(62, -279)
(227, -3414)

Commentary

2-isogenous to curve#1428 via the rational 2-torsion point x=-11. 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 20:17:00 UTC · history