curve #5847

y² + y = x³ + 189943711588

a-invariants: [0, 0, 1, 0, 189943711588]
c-invariants: [0, -164111366812248]
rank (lower bound): ≥ 9
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 5195320354356522816605481
discriminant (Δ): -15585961063069568449816443
Faltings height: 3.5129
naive height: 65.4631
primes of bad reduction: 3, 983, 12473, 61967
regulator: 19253765.641875476226867841026164315310708758826659255291
submitted by: jesper-petersen
submitted at: 2026-10-25 11:09:13 UTC
last updated: 2026-10-25 11:09:13 UTC

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

(-5372, 186859)
(-4582, 306179)
(-3716, 372331)
(-3518, 382627)
(-2362, 420435)
(3944, 501291)
(11134, 1253068)
(148937/4, 57583945/8)
(-586631/196, 1108288847/2744)

Commentary

Specialization at t = 22/827 of a generic rank-four Mordell family constructed through the Burkhardt parametrization with parameters (-6, 8, -10). The specialization was identified using a 328-prime Mestre–Nagao sieve with an improved multistage candidate-retention algorithm. Its score was approximately 47.039518. PARI/GP 2.17.4 returned matching computational rank bounds [9,9].

last edited by jesper-petersen at 2026-10-25 11:09:13 UTC · history