curve #5685

y² + y = x³ + 2834809937478

a-invariants: [0, 0, 1, 0, 2834809937478]
c-invariants: [0, -2449275785981208]
rank (lower bound): ≥ 10
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 3471615668862189939154704363
discriminant (Δ): -3471615668862189939154704363
Faltings height: 3.9634
naive height: 70.8691
primes of bad reduction: 3, 11339239749913
regulator: 3437963860.394181498218329940061243305690811980794341900427
submitted by: jesper-petersen
submitted at: 2026-10-24 09:03:57 UTC
last updated: 2026-10-24 09:03:57 UTC

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

(-13938, 356517)
(-9696, 1386818)
(-1662, 1682325)
(2034, 1686186)
(8457/4, 13491945/8)
(21648, 3602754)
(-114158/9, 24059575/27)
(-62246/225, 5682428758/3375)
(603636/25, 514047241/125)
(37636558/9, 230895174439/27)

Commentary

Mordell curve obtained from the rational Burkhardt-quartic parametrization (u,v,w) = (2/5,3/5,6/5), specialized at t = -64/23. PARI/GP 2.17.4 returned matching rank bounds [10,10].

last edited by jesper-petersen at 2026-10-24 09:03:58 UTC · history