curve #4707

y² = x³ − 28279

a-invariants: [0, 0, 0, 0, -28279]
c-invariants: [0, 24433056]
rank (lower bound): ≥ 5
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 28789266276
discriminant (Δ): -345471195312
Faltings height: 0.8929
naive height: 34.0229
primes of bad reduction: 2, 3, 28279
regulator: 254.068850644206963212013778744423595419189338029
submitted by: jesper-petersen
submitted at: 2026-10-20 21:09:26 UTC
last updated: 2026-10-20 21:09:26 UTC

Witness: 5 independent points log in to add more points →

(32, 67)
(34, 105)
(40, 189)
(50, 311)
(67, 522)

Commentary

Historical rank-5 Mordell curve y^2 = x^3 - 28279, 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 21:09:26 UTC · history