curve #5683

y² + y = x³ + 36409141674515

a-invariants: [0, 0, 1, 0, 36409141674515]
c-invariants: [0, -31457498406781176]
rank (lower bound): ≥ 10
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 261851969871589756596804441
discriminant (Δ): -572670258109166797677211312467
Faltings height: 4.3889
naive height: 75.9748
primes of bad reduction: 3, 568163, 9493661
regulator: 135318171075.7055350497176271402641493918417284104902454005
submitted by: jesper-petersen
submitted at: 2026-10-24 09:02:26 UTC
last updated: 2026-10-24 09:02:26 UTC

Witness: 10 independent points log in to add more points →

(9249/4, 48280181/8)
(-16959042327/538756, 903339615173729/395446904)
(-240624723/27889, 27854144033729/4657463)
(-50673695/5184, 2223102284207/373248)
(-43511/100, 6033991487/1000)
(102205545/256, 1033560470965/4096)
(225609585/16384, 13100096481143/2097152)
(481730145/3364, 10638526131283/195112)
(134978343/5041, 2668934529743/357911)
(746805651/121, 20408516032262/1331)

Commentary

Mordell curve obtained by specializing a rationally parametrized Burkhardt-quartic rank-4 family at (u,v,w) = (1/2,-1,2/3), t = -22/71. PARI/GP 2.17.4 returned matching rank bounds [10,10].

last edited by jesper-petersen at 2026-10-24 09:02:26 UTC · history