curve #4704

y² = x³ − 174

a-invariants: [0, 0, 0, 0, -174]
c-invariants: [0, 150336]
rank (lower bound): ≥ 3
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 13079232
discriminant (Δ): -13079232
Faltings height: 0.0444
naive height: 23.8413
primes of bad reduction: 2, 3, 29
regulator: 46.105698573234592609330665386680381254988284
submitted by: jesper-petersen
submitted at: 2026-10-20 21:07:33 UTC
last updated: 2026-10-20 21:07:33 UTC

Witness: 3 independent points log in to add more points →

(7, 13)
(799, 22585)
(5215, 376601)

Commentary

Historical rank-3 Mordell curve y^2 = x^3 - 174, documented by Gebel, Pethő and Zimmer (1998), "On Mordell's Equation", and in Tom Womack's Mordell curve table.

last edited by jesper-petersen at 2026-10-20 21:07:34 UTC · history