curve #5687

y² + y = x³ − 18510891211455

a-invariants: [0, 0, 1, 0, -18510891211455]
c-invariants: [0, 15993410006696904]
rank (lower bound): ≥ 10
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 49342045455693029099176026849
discriminant (Δ): -148026136367079087297528080547
Faltings height: 4.2761
naive height: 74.6219
primes of bad reduction: 3, 74043564845819
regulator: 14629793993.47736351366208574277951913953243886638252214524
submitted by: jesper-petersen
submitted at: 2026-10-24 09:06:33 UTC
last updated: 2026-10-24 09:06:33 UTC

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

(26463, 144543)
(44273, 8262478)
(189915, 82651604)
(6721145/4, 17424649457/8)
(48546443, 338248688923)
(773021/25, 415565681/125)
(1170941/25, 1147278386/125)
(4170205/9, 8515216558/27)
(12811419/289, 40693507611/4913)
(1549158553/16641, 60270309279782/2146689)

Commentary

Mordell curve obtained from a rationally parametrized Burkhardt-quartic family using (u,v,w) = (1,-2,5/2), specialized at t = -14/143. PARI/GP 2.17.4 returned matching rank bounds [10,10].

last edited by jesper-petersen at 2026-10-24 09:06:34 UTC · history