curve #2801

y² + xy + y = x³ − x² − 461937708617x + 120842443299742409

a-invariants: [1, -1, 1, -461937708617, 120842443299742409]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/6ℤ
conductor (N): 1317390570
discriminant (Δ): 120698679439288764366709824000000
Faltings height: 5.3096
naive height: 92.1897
primes of bad reduction: 2, 3, 5, 31, 43, 79, 139
regulator: 63.40840226037998172388202008042309394912504199
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:23:04 UTC
last updated: 2026-09-26 20:23:04 UTC

Witness: 4 independent points log in to add more points →

(393667, -1050884)
(19283133/49, -270927362/343)
(208791111/529, -29658662476/12167)
(-5302923/16, 31202745829/64)

Commentary

2-isogenous to curve#1608 via the rational 2-torsion point x=-195705. 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 20:23:04 UTC · history