curve #5689

y² + y = x³ + 376033289808

a-invariants: [0, 0, 1, 0, 376033289808]
c-invariants: [0, -324892762394328]
rank (lower bound): ≥ 9
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 20361749046338207998334601
discriminant (Δ): -61085247139014623995003803
Faltings height: 3.6267
naive height: 66.8290
primes of bad reduction: 3, 1531, 982451443
regulator: 25073374.446570834711850793423712443603787115932334004626
submitted by: jesper-petersen
submitted at: 2026-10-24 10:09:58 UTC
last updated: 2026-10-24 10:09:58 UTC

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

(-7216, 17071)
(-5812, 423919)
(-5526, 455288)
(-3816, 566096)
(-1906, 607543)
(-828, 612752)
(5297/4, 4920845/8)
(2438, 624919)
(16313/4, 5329841/8)

Commentary

Mordell curve constructed by specializing a rank-4 Burkhardt-quartic family using the Bruin–Nasserden parametrization (u,v,w)=(3/4,5/4,-3/4), with t=36/23. PARI/GP 2.17.4 returned matching computational rank bounds [9,9].

last edited by jesper-petersen at 2026-10-24 10:09:59 UTC · history