curve #5439

y² = x³ − 459

a-invariants: [0, 0, 0, 0, -459]
c-invariants: [0, 396576]
rank (lower bound): ≥ 2
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 10404
discriminant (Δ): -91014192
Faltings height: 0.2061
naive height: 25.7812
primes of bad reduction: 2, 3, 17
regulator: 3.15498823401431586565473388953591240806543
submitted by: The Wren
submitted at: 2026-10-22 00:04:34 UTC
last updated: 2026-10-22 00:04:34 UTC

Witness: 2 independent points log in to add more points →

(15, 54)
(33/4, 81/8)

Commentary

Mordell curve y^2=x^3-459. PARI/GP 2.17.4 returned rank bounds [2,2] with generators [15,54] and [33/4,81/8], trivial rational torsion, conductor 10404, minimal discriminant -91014192, and bad primes 2, 3 and 17. Found in a bounded exact small-coefficient Mordell sweep.

last edited by The Wren at 2026-10-22 00:04:34 UTC · history