curve #757

y² + xy + y = x³ − x² − 16373484384428031931307x + 780795720529750124678426853231739

a-invariants: [1, -1, 1, -16373484384428031931307, 780795720529750124678426853231739]
rank (lower bound): ≥ 15
torsion subgroup: trivial
conductor (N): 3054168934820674430483080510377005677651470
discriminant (Δ): 17568028278748740019130613693715009952376436328232487394688000000000
Faltings height: 11.6730
naive height: 165.0635
primes of bad reduction: 2, 3, 5, 11, 13, 19, 23, 73, 220373, 2391691, 5218639, 142342930229587
regulator: 192195642747.09885966199645188977448434695495390906019581825202936000
submitted by: Valery Asiryan
submitted at: 2026-09-18 01:25:10 UTC
last updated: 2026-09-18 01:25:10 UTC

Witness: 15 independent points log in to add more points →

(-94254393293, -38557997863419934)
(-78384948053, -39782087940793174)
(-65031102053, -39630284759368774)
(-54552803453, -38880116712586774)
(-37480069973, -36630907006969174)
(-22646416853, -33763608557410774)
(-21100121333, -33419805945963094)
(3196379467, -26990601964671574)
(12519267547, -24036933256144774)
(23576174287, -20195954085152074)
(24043496197, -20025476029594924)
(605177449681141/16129, -30331901332259444934244/2048383)
(196136852848507/1681, -1476285749311221318854/68921)
(246903079183/4, -18433845672924017/8)
(38361931847, -14461419460299074)

Commentary

Specialization at T = -19/165 of the rank-11 fibration of X163 described by wgxli for ICARM #718. Independently recovered polynomial sections and rational-point search yield 15 points with an exact independence certificate, proving rank >= 15.

last edited by Valery Asiryan at 2026-09-18 01:25:10 UTC · history