curve #2521

y² + xy = x³ − 3009x − 61770

a-invariants: [1, 0, 0, -3009, -61770]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ
conductor (N): 429
discriminant (Δ): 108679952667
Faltings height: 0.8877
naive height: 35.6417
primes of bad reduction: 3, 11, 13
regulator: 2.115453196439503695102406459953893088052
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:06:46 UTC
last updated: 2026-09-26 20:06:46 UTC

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

(3334/9, -195334/27)

Commentary

2-isogenous to curve#2075 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 20:06:46 UTC · history