curve #1831

y² + xy + y = x³ − x² − 106400353230449963598965706612473537209115813x + 422128950019755721902266808708794939178991483786699178861367557981

a-invariants: [1, -1, 1, -106400353230449963598965706612473537209115813, 422128950019755721902266808708794939178991483786699178861367557981]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 447681361499837147835850607910
discriminant (Δ): 112665616699970093081294458111328131382988750047906361119157190783261376554775842354303632543431324305317287637769850530493261414400
Faltings height: 24.0739
naive height: 315.7410
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 23, 31, 47, 61, 107, 149, 409, 503, 617, 3719
regulator: 3049007.2080081523271726671378553630423454102098827
submitted by: dujella
submitted at: 2026-09-25 16:04:04 UTC
last updated: 2026-09-25 16:04:04 UTC

(3381582657678094595391, 317798837174699492653979100463456)
(1405307609816280252915, 524765710721840000489508602178592)
(5182458350371657727295, 99515663037413274888605365739872)
(5809169908678191267135, 8373221198553485598701485793632)
(6300275580642266589471, 43095447699485136548183136831232)
(25698851534528457561883767/4489, 7540653954712106685208830187241252320/300763)

found by Dujella - Peral (2020)

last edited by dujella at 2026-09-25 16:04:04 UTC · history