curve #2700

y² + xy + y = x³ − x² − 567041x + 151026216

a-invariants: [1, -1, 1, -567041, 151026216]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 503217
discriminant (Δ): 1833741037108360809
Faltings height: 2.2437
naive height: 51.3582
primes of bad reduction: 3, 11, 13, 17, 23
regulator: 3.2363244699029097013327712527529821360470308
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:18:21 UTC
last updated: 2026-09-26 20:18:21 UTC

Witness: 3 independent points log in to add more points →

(-19851/49, 6148575/343)
(15821/16, -1541325/64)
(2054, -88485)

Commentary

2-isogenous to curve#1526 via the rational 2-torsion point x=431. 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 20:18:21 UTC · history