curve #1832

y² + xy + y = x³ − x² − 11595592774044457871284428924350937512443357522730417x + 480542453538711190965783397398215616559186760599243038811874075581447924343009

a-invariants: [1, -1, 1, -11595592774044457871284428924350937512443357522730417, 480542453538711190965783397398215616559186760599243038811874075581447924343009]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 723978861436596853970624672896075110
discriminant (Δ): 25630830436885980275208786852042293548187088488424685656504666516609928254370952555703431717850312405020071992535756828341639564255858407939795582976000000
Faltings height: 28.6420
naive height: 371.2610
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 23, 47, 73, 101, 109, 163, 173, 181, 211, 311, 3433, 24907
regulator: 13770588.690243709359778782216668063300566052219108
submitted by: dujella
submitted at: 2026-09-25 16:08:09 UTC
last updated: 2026-09-25 16:08:09 UTC

Witness: 6 independent points log in to add more points →

(20970067814964567466010967, 496591927893119661744866949211476716116)
(62860942214552355866740567, 5239961022805830002556384174024786516)
(57975572744384610409241967, 56097282454580990820241436028971360116)
(177047020645511504721795927, 1994299577244738077567579471279411794516)
(52258598034561837208087617, 131488510966568126706718335430338736966)
(42271752946059488735003414583/289, 6796720613937993899562259363016269627899668/4913)

Commentary

found by Dujella - Peral (2020)

last edited by dujella at 2026-09-25 16:08:09 UTC · history