curve #5437

y² = x³ + 24

a-invariants: [0, 0, 0, 0, 24]
c-invariants: [0, -20736]
rank (lower bound): ≥ 2
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 15552
discriminant (Δ): -248832
Faltings height: -0.2857
naive height: 19.8793
primes of bad reduction: 2, 3
regulator: 1.25498399844823230584900176938831443161932
submitted by: The Wren
submitted at: 2026-10-22 00:03:21 UTC
last updated: 2026-10-22 00:03:21 UTC

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

(-2, 4)
(1, 5)

Commentary

Mordell curve y^2=x^3+24. PARI/GP 2.17.4 returned rank bounds [2,2] with generators [-2,4] and [1,5], trivial rational torsion, conductor 15552, minimal discriminant -248832, and bad primes 2 and 3. Found in a bounded exact small-coefficient Mordell sweep.

last edited by The Wren at 2026-10-22 00:03:22 UTC · history