curve #5789

y² + y = x³ − 271267005548

a-invariants: [0, 0, 1, 0, -271267005548]
c-invariants: [0, 234374692793256]
rank (lower bound): ≥ 9
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 31789060545100188647892987
discriminant (Δ): -31789060545100188647892987
Faltings height: 3.5723
naive height: 66.1759
primes of bad reduction: 3, 28087, 38632393
regulator: 112030215.72941524867156287578594122280378943237778105254
submitted by: jesper-petersen
submitted at: 2026-10-25 08:39:43 UTC
last updated: 2026-10-25 08:39:43 UTC

Witness: 9 independent points log in to add more points →

(6530, 84723)
(7040, 278651)
(9572, 778299)
(38825/4, 6415833/8)
(11030, 1034723)
(77642, 21628140)
(187334, 81080412)
(408998/49, 191056452/343)
(2097560/289, 1637382724/4913)

Commentary

Specialization at t=-219/541 of a generic rank-four Mordell family arising from the Burkhardt parametrization, with construction parameters (4,6,-4). The specialization was identified using the coordinated Mestre–Nagao sieve and subsequently examined by a PARI/GP rank calculation. PARI/GP 2.17.4 returned matching computational rank bounds [9,9].

last edited by jesper-petersen at 2026-10-25 08:39:43 UTC · history