curve #2790

y² + xy = x³ + x² − 561x + 29055

a-invariants: [1, 1, 0, -561, 29055]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ
conductor (N): 6399618
discriminant (Δ): -359255355666
Faltings height: 0.8983
naive height: 34.0931
primes of bad reduction: 2, 3, 19, 73, 769
regulator: 40.46250522420685580279038318269407371615414759
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:22:34 UTC
last updated: 2026-09-26 20:22:34 UTC

Witness: 4 independent points log in to add more points →

(5, 160)
(53, 363)
(-17, 193)
(-19, -173)

Commentary

2-isogenous to curve#1585 via the rational 2-torsion point x=18. 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 20:22:35 UTC · history