curve #4703

y² = x³ + 113

a-invariants: [0, 0, 0, 0, 113]
c-invariants: [0, -97632]
rank (lower bound): ≥ 3
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 1379052
discriminant (Δ): -5516208
Faltings height: -0.0275
naive height: 22.9779
primes of bad reduction: 2, 3, 113
regulator: 4.8869090595792227617397871254573393831665086
submitted by: jesper-petersen
submitted at: 2026-10-20 21:06:49 UTC
last updated: 2026-10-20 21:06:49 UTC

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

(-4, 7)
(2, 11)
(8, 25)

Commentary

Historical rank-3 Mordell curve y^2 = x^3 + 113, documented by Gebel, Pethő and Zimmer (1998), "On Mordell's Equation", Compositio Mathematica 110, 335–367, and in Tom Womack's Mordell curve table.

last edited by jesper-petersen at 2026-10-20 21:06:49 UTC · history