curve #2767

y² = x³ + x² − 8336x + 296164

a-invariants: [0, 1, 0, -8336, 296164]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ
conductor (N): 7598320
discriminant (Δ): -1529389849600
Faltings height: 1.1241
naive height: 38.7392
primes of bad reduction: 2, 5, 17, 37, 151
regulator: 6.193977757394317331203224447330934756768386116
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:21:30 UTC
last updated: 2026-09-26 20:21:30 UTC

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

(90, -532)
(64, -170)
(526/9, -2960/27)
(79, -370)

Commentary

2-isogenous to curve#1588 via the rational 2-torsion point x=211. 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 20:21:31 UTC · history