curve #2637

y² + xy + y = x³ + x² − 43323070x − 81451564105

a-invariants: [1, 1, 1, -43323070, -81451564105]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 308490
discriminant (Δ): 2339232164953982451562500
Faltings height: 3.3850
naive height: 64.3662
primes of bad reduction: 2, 3, 5, 7, 13, 113
regulator: 5.34385037846615349708486300991640982157832
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:14:24 UTC
last updated: 2026-09-26 20:14:24 UTC

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

(80173, -22662687)
(12373, -1136187)

Commentary

2-isogenous to curve#2068 via the rational 2-torsion point x=2641. 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 20:14:24 UTC · history