curve #5787

y² + y = x³ − 36389806175815

a-invariants: [0, 0, 1, 0, -36389806175815]
c-invariants: [0, 31440792535903944]
rank (lower bound): ≥ 9
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 141467779688813072909649
discriminant (Δ): -572062173197773818148340969187
Faltings height: 4.3888
naive height: 75.9738
primes of bad reduction: 3, 43, 2689, 1084297
regulator: 160444540.18062893491809986016064303890268696870624849909
submitted by: jesper-petersen
submitted at: 2026-10-25 08:38:04 UTC
last updated: 2026-10-25 08:38:04 UTC

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

(33205, 470210)
(39775, 5151335)
(246691, 122377892)
(851925, 786301789)
(948709/25, 534128802/125)
(4551249/100, 7608163693/1000)
(3413125/9, 6303523303/27)
(4640259/25, 9967220348/125)
(6445749/25, 16347395057/125)

Commentary

Specialization at t=-234/95 of a generic rank-four Mordell family generated from the Burkhardt parametrization, using construction parameters (-9,-1,0). The specialization was selected by the common 328-prime Mestre–Nagao sieve in a coordinated search across multiple Burkhardt families and the rank-five quadratic base-change family. PARI/GP 2.17.4 returned matching computational rank bounds [9,9].

last edited by jesper-petersen at 2026-10-25 08:38:25 UTC · history