curve #2649

y² + xy = x³ − 84567930x + 274632178275

a-invariants: [1, 0, 0, -84567930, 274632178275]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 1330665
discriminant (Δ): 6123337821629582375390625
Faltings height: 3.4953
naive height: 66.3728
primes of bad reduction: 3, 5, 7, 19, 23, 29
regulator: 6.50721014549991701983124181992138048478267
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:15:24 UTC
last updated: 2026-09-26 20:15:24 UTC

Witness: 2 independent points log in to add more points →

(29955/4, -2010945/8)
(1583385, -1993173255)

Commentary

2-isogenous to curve#1467 via the rational 2-torsion point x=-32081/4. 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 20:15:24 UTC · history