curve #5598

y² = x³ − 20947933269332

a-invariants: [0, 0, 0, 0, -20947933269332]
c-invariants: [0, 18099014344702848]
rank (lower bound): ≥ 10
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 3949343174307478086465536016
discriminant (Δ): -189568472366758948150345728768
Faltings height: 4.2968
naive height: 74.8693
primes of bad reduction: 2, 3, 5236983317333
regulator: 18342546109615.65683387439567548264854263931253920740870147
submitted by: jesper-petersen
submitted at: 2026-10-23 21:42:20 UTC
last updated: 2026-10-23 21:42:20 UTC

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

(5239342070822/189805729, 762919148738035170/2614953528433)
(24131170879901/506475025, 106444167631847948601/11398220437625)
(6294756484694/102111025, 15070513912641274878/1031831907625)
(2261053401544117/1084845969, 107514175068384261042635/35731571680953)
(7280290607582/58415449, -19537116129339905250/446469276707)
(8308306162694/158130625, -22151186657298121122/1988492609375)
(72165787191557/2601714049, -83203000012591313715/132705628497343)
(334715133567422/6228839929, 5695355690528390471970/491598733716467)
(1787345175452273/295633636, 75563597838469074401655/5083124737384)
(3192668884060937/104379394084, -93385783595099599022565/33722685881870552)

Commentary

The rational 3-isogenous partner of our accepted rank-10 Mordell curve obtained from the Burkhardt quartic with parameters (u,v,w) = (-1,-4,5), specialized at t = 247/229.

last edited by jesper-petersen at 2026-10-23 21:42:21 UTC · history