curve #4705

y² = x³ + 2089

a-invariants: [0, 0, 0, 0, 2089]
c-invariants: [0, -1804896]
rank (lower bound): ≥ 4
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 157101156
discriminant (Δ): -1885213872
Faltings height: 0.4587
naive height: 28.8120
primes of bad reduction: 2, 3, 2089
regulator: 17.56533942659183585179155577222651737140015582
submitted by: jesper-petersen
submitted at: 2026-10-20 21:08:06 UTC
last updated: 2026-10-20 21:08:06 UTC

Witness: 4 independent points log in to add more points →

(-12, 19)
(-10, 33)
(-4, 45)
(3, 46)

Commentary

Historical rank-4 Mordell curve y^2 = x^3 + 2089, 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 21:08:07 UTC · history