curve #2863

y² = x³ − x² − 1687836033x + 26459881991937

a-invariants: [0, -1, 0, -1687836033, 26459881991937]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 18648177600
discriminant (Δ): 5289346367855366169600000000
Faltings height: 4.1383
naive height: 75.3537
primes of bad reduction: 2, 3, 5, 13, 37, 41, 197
regulator: 188.117617641314234045263744304859554107135364806
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:25:52 UTC
last updated: 2026-09-26 20:25:52 UTC

Witness: 5 independent points log in to add more points →

(473553/16, -99779121/64)
(1291977/49, -183688128/343)
(623473/9, -420004000/27)
(3715537/121, -2520024000/1331)
(645507, -517596300)

Commentary

2-isogenous to curve#1689 via the rational 2-torsion point x=-43793. 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 20:25:52 UTC · history