curve #3046

y² = x³ + x² − 1678071905x + 39286337143999

a-invariants: [0, 1, 0, -1678071905, 39286337143999]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
conductor (N): 29231074244902976
discriminant (Δ): -364354011624553099954124259328
Faltings height: 4.3725
naive height: 76.1270
primes of bad reduction: 2, 17, 73, 89, 137, 257, 457
regulator: 27173.9561341275043301670401132706842751403452358509094
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:34:47 UTC
last updated: 2026-09-26 20:34:47 UTC

Witness: 8 independent points log in to add more points →

(9849, 4869752)
(21069, 3644732)
(-55107/4, 61859243/8)
(-365837/9, -171477368/27)
(952057, -928115816)
(662649, -538423048)
(27095209/144, -138081689117/1728)
(-16280397/3481, -1408490977480/205379)

Commentary

2-isogenous to curve#1347 via the rational 2-torsion point x=24843. 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 20:34:47 UTC · history