curve #5794

y² + y = x³ + 740695839393539

a-invariants: [0, 0, 1, 0, 740695839393539]
c-invariants: [0, -639961205236017912]
rank (lower bound): ≥ 10
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 641251020813674852592574641
discriminant (Δ): -237008301045796666542773365037523
Faltings height: 4.8910
naive height: 82.0004
primes of bad reduction: 3, 13, 649306017439
regulator: 8855482781113.373831246879742236815334665017917994691326703
submitted by: jesper-petersen
submitted at: 2026-10-25 10:32:18 UTC
last updated: 2026-10-25 10:32:18 UTC

Witness: 10 independent points log in to add more points →

(-486972833439/5382400, 3775806674606191/12487168000)
(-30546417606743/358042084, 74126633368685663561/6774872313448)
(-54981923593143/1441872784, 1433225498475042395941/54750793354048)
(-227303150439/10176100, 876798668235170191/32461759000)
(55057308513/14318656, 1474653527276014993/54181794304)
(40920974213809/2831304100, 4108497464193608342877/150653691161000)
(384284982561/18490000, 2176914422148665809/79507000000)
(1120176320353/26460736, 3889535153621348463/136114025984)
(2707703066977/40551424, 8321305751823984529/258231468032)
(-101086583119837743/1949731883584, 66760383238233986328285209/2722465221541079552)

Commentary

The rationally 3-isogenous partner of the specialization t = -975/928 of the generic rank-four Burkhardt Mordell family with construction parameters (-9, 8, -2). PARI/GP 2.17.4 returned matching computational rank bounds [10,10], consistent with the independent rank lower bound of ten.

last edited by jesper-petersen at 2026-10-25 10:32:19 UTC · history