curve #5793

y² + y = x³ − 27433179236798

a-invariants: [0, 0, 1, 0, -27433179236798]
c-invariants: [0, 23702266860593256]
rank (lower bound): ≥ 10
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 641251020813674852592574641
discriminant (Δ): -325114267552533150264435342987
Faltings height: 4.3417
naive height: 75.4087
primes of bad reduction: 3, 13, 649306017439
regulator: 149968378.4841974263958217707706619135745739626072362161375
submitted by: jesper-petersen
submitted at: 2026-10-25 10:31:19 UTC
last updated: 2026-10-25 10:31:19 UTC

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

(30160, 33598)
(122993/4, 10238445/8)
(37972, 5226625)
(41470, 6624598)
(49192, 9571009)
(53210, 11100473)
(55900, 12134401)
(66872, 16480574)
(82784, 23235777)
(2269033/64, 2119126325/512)

Commentary

Specialization t = -975/928 of a generic rank-four Mordell family derived from the Burkhardt parametrization with construction parameters (-9, 8, -2). The specialization was identified in a coordinated multi-family search using a 328-prime Mestre–Nagao sieve. PARI/GP 2.17.4 returned matching computational rank bounds [10,10].

last edited by jesper-petersen at 2026-10-25 10:31:20 UTC · history