curve #5688

y² + y = x³ − 362700107282

a-invariants: [0, 0, 1, 0, -362700107282]
c-invariants: [0, 313372892691432]
rank (lower bound): ≥ 9
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 1159799814269129764275867
discriminant (Δ): -56830190899187358449517483
Faltings height: 3.6207
naive height: 66.7568
primes of bad reduction: 3, 7, 29608172023
regulator: 8922047144022.7683330619150771572893244156127833274182967
submitted by: jesper-petersen
submitted at: 2026-10-24 10:08:40 UTC
last updated: 2026-10-24 10:08:40 UTC

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

(483636777122/229441, -336340348094383917/109902239)
(12703848788/1138489, -1230863547255554/1214767763)
(28943751861024449/214341220900, 4923798220664418533651957/99233555040073000)
(1437271378031966/7239457225, 54487652579623818033361/615969217989125)
(9417266421996724/1299839411025, 196499968307023409328493/1481953411706657625)
(124080970019870033/2576127721024, 43636686556264796095983961/4134767428330592768)
(56241270159838121/7337001516100, 5885797926053279560842169/19873662636644909000)
(5888632668785799836/32942262016225, -14289199834279319623376889541/189073265821293955375)
(46930466403581040806/129396198810025, -321499761923765702942223690454/1471913463532742831125)

Commentary

Mordell curve constructed using the Bruin–Nasserden rational parametrization of the Burkhardt quartic, with parameters (u,v,w)=(-1/2,1,1/4), specialized at t=71/465.

last edited by jesper-petersen at 2026-10-24 10:08:41 UTC · history