curve #6227

y² + y = x³ + 56381661767805145931

a-invariants: [0, 0, 1, 0, 56381661767805145931]
c-invariants: [0, -48713755767383646084600]
rank (lower bound): ≥ 11
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 2215564848694462660775701182225
discriminant (Δ): -1373281250558045973160583115795502841641875
Faltings height: 6.7644
naive height: 104.4805
primes of bad reduction: 3, 5, 7, 13, 37, 593, 5737, 8663
regulator: 472380791.728246197283025407711908903065061567320696861468045
submitted by: jesper-petersen
submitted at: 2026-10-31 08:48:28 UTC
last updated: 2026-10-31 08:48:28 UTC

Witness: 11 independent points log in to add more points →

(-3585855, 3205224067)
(-3350165, 4333674117)
(-2287155, 6664636192)
(147889, 7508987699)
(170755, 7509103842)
(829725, 7546713232)
(4595955, 12387942157)
(13316485, 49170902007)
(13407135, 49662170617)
(29141385, 157492342507)
(129989769/16, 1558018169221/64)

Commentary

Bruin–Nasserden rational parametrization of the Burkhardt quartic with parameters (u,v,w)=(5/4,1/4,15/8), specialized at t=-51/572. PARI/GP 2.17.4 returned rank bounds [11,11].

last edited by jesper-petersen at 2026-10-31 08:48:28 UTC · history