curve #5720

y² + y = x³ − 7289852825841228

a-invariants: [0, 0, 1, 0, -7289852825841228]
c-invariants: [0, 6298432841526820776]
rank (lower bound): ≥ 11
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 22957324224087744117498003103023867
discriminant (Δ): -22957324224087744117498003103023867
Faltings height: 5.2721
naive height: 86.5737
primes of bad reduction: 3, 29159411303364911
regulator: 44004088563.0655763234782343253905343097247684614627841639231
submitted by: jesper-petersen
submitted at: 2026-10-24 16:40:39 UTC
last updated: 2026-10-24 16:40:39 UTC

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

(794553/4, 187249095/8)
(225630, 64782108)
(251430, 92762108)
(258330, 99747891)
(1168113/4, 1061755885/8)
(328092, 167413860)
(545100, 393291108)
(3415929/16, 3162241683/64)
(5065497/16, 10005881571/64)
(13653630/49, 41081477669/343)
(65685873/64, 530565268105/512)

Commentary

Constructed by specializing a rank-four Mordell family arising from the rational parametrization of the Burkhardt quartic. The construction parameters are (u,v,w) = (-2,-9,10), with specialization t = -69/79. PARI/GP 2.17.4 returned matching rank bounds [11,11] and eleven rational points.

last edited by jesper-petersen at 2026-10-24 16:40:39 UTC · history