curve #5721

y² = x³ − 387465402692

a-invariants: [0, 0, 0, 0, -387465402692]
c-invariants: [0, 334770107925888]
rank (lower bound): ≥ 9
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 4053494833648390462865328
discriminant (Δ): -64855917338374247405845248
Faltings height: 3.6317
naive height: 66.8889
primes of bad reduction: 2, 3, 96866350673
regulator: 43805023.522748652939187651909228742528607948879896222633
submitted by: jesper-petersen
submitted at: 2026-10-24 16:42:28 UTC
last updated: 2026-10-24 16:42:28 UTC

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

(7317, 65389)
(7677, 254929)
(7842, 307886)
(11922, 1143266)
(30546, 5302238)
(55866, 13189802)
(68466, 17904002)
(65938/9, 2055302/27)
(136138/9, 47335598/27)

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) = (7,-2,10), with specialization t = -59/76. PARI/GP 2.17.4 returned matching rank bounds [9,9] and nine rational points.

last edited by jesper-petersen at 2026-10-24 16:42:28 UTC · history