curve #4693

y² = x³ − 56736325657288

a-invariants: [0, 0, 0, 0, -56736325657288]
c-invariants: [0, 49020185367896832]
rank (lower bound): ≥ 10
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 28971095841808529447047634496
discriminant (Δ): -1390612600406809413458286455808
Faltings height: 4.4628
naive height: 76.8620
primes of bad reduction: 2, 3, 2969, 7417, 322057
regulator: 450593448.4811853856431818934478113367841228779422001150070
submitted by: jesper-petersen
submitted at: 2026-10-20 20:45:56 UTC
last updated: 2026-10-20 20:45:56 UTC

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

(39398, 2101748)
(41234, 3656704)
(46649, 6691631)
(55817, 10824215)
(56338, 11048928)
(71618, 17623912)
(94342, 27981180)
(173074, 71607456)
(322054, 182609724)
(381634, 235639896)

Commentary

Historical rank-10 Mordell curve y^2 = x^3 - 56736325657288, attributed to P. Llorente and J. Quer (1988), On the 3-Sylow subgroup of the class group of quadratic fields, Mathematics of Computation 50, 321–333, and documented in Tom Womack's 2003 thesis.

last edited by jesper-petersen at 2026-10-20 20:45:56 UTC · history