curve #3521

y² = x³ + x² − 4727871213189944240x + 1033371908306469912341898900

a-invariants: [0, 1, 0, -4727871213189944240, 1033371908306469912341898900]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 36102502634605680
discriminant (Δ): 6302269551326414568420783143236765728568400905278159360000
Faltings height: 9.7818
naive height: 140.6136
primes of bad reduction: 2, 3, 5, 7, 13, 17, 29, 41, 53, 71, 103, 211
regulator: 15207.1376350615921740428179107171085974594983015
submitted by: jesper-petersen
submitted at: 2026-09-27 16:05:02 UTC
last updated: 2026-09-27 16:05:02 UTC

Witness: 5 independent points log in to add more points →

(-2207677985, 26666743933830)
(130470940, 20463212606970)
(1140209898940/289, 1028135915432738970/4913)
(21900730418980/1849, 100782173742330366450/79507)
(154968841498420/755161, 5560341463857916307250/656234909)

Commentary

Discriminant-directed search in the two-parameter Dujella-Peral Z/2Z x Z/4Z family. Parameters alpha=104/7, tau=-5/14. PARI/GP rank bounds [5,5]; five independent points supplied.

last edited by jesper-petersen at 2026-09-27 16:05:02 UTC · history