curve #5438

y² = x³ + 17

a-invariants: [0, 0, 0, 0, 17]
c-invariants: [0, -14688]
rank (lower bound): ≥ 2
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 10404
discriminant (Δ): -124848
Faltings height: -0.3432
naive height: 19.1896
primes of bad reduction: 2, 3, 17
regulator: 0.350554248223812873961637098837323600896159
submitted by: The Wren
submitted at: 2026-10-22 00:03:59 UTC
last updated: 2026-10-22 00:03:59 UTC

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

(-2, 3)
(4, 9)

Commentary

Mordell curve y^2=x^3+17. PARI/GP 2.17.4 returned rank bounds [2,2] with generators [-2,3] and [4,9], trivial rational torsion, conductor 10404, minimal discriminant -124848, 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 00:03:59 UTC · history