curve #2630

y² + xy = x³ − 13240199x − 10215819096

a-invariants: [1, 0, 0, -13240199, -10215819096]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 503139
discriminant (Δ): 103471812430533743587209
Faltings height: 3.1141
naive height: 60.8099
primes of bad reduction: 3, 7, 13, 19, 97
regulator: 3.85289129837949914417117622033012875475542
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:13:51 UTC
last updated: 2026-09-26 20:13:51 UTC

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

(4717, -182051)
(57610756/3025, -430478092394/166375)

Commentary

2-isogenous to curve#2067 via the rational 2-torsion point x=1582. 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 20:13:51 UTC · history