curve #2644

y² + xy = x³ − 34810794x + 16188893604

a-invariants: [1, 0, 0, -34810794, 16188893604]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 1805874
discriminant (Δ): 2586479630436462323130624
Faltings height: 3.3748
naive height: 63.7099
primes of bad reduction: 2, 3, 7, 19, 31, 73
regulator: 7.98285207880755937069446362256433119612161
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:15:02 UTC
last updated: 2026-09-26 20:15:02 UTC

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

(1423530, -1699136262)
(316704, -178357338)

Commentary

2-isogenous to curve#1468 via the rational 2-torsion point x=-3745/4. 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 20:15:02 UTC · history