curve #2814

y² = x³ + x² − 7009x + 1495935

a-invariants: [0, 1, 0, -7009, 1495935]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ
conductor (N): 4594624
discriminant (Δ): -947721109700608
Faltings height: 1.5544
naive height: 41.9628
primes of bad reduction: 2, 17, 41, 103
regulator: 10.41641310513578030289719141633201079425364568
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:23:36 UTC
last updated: 2026-09-26 20:23:36 UTC

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

(154, 2023)
(-59/9, 33524/27)
(715, -19040)
(12763/81, -1516672/729)

Commentary

2-isogenous to curve#1582 via the rational 2-torsion point x=67. 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 20:23:37 UTC · history