curve #5430

y² = x³ + 8

a-invariants: [0, 0, 0, 0, 8]
c-invariants: [0, -6912]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ
family: y² = x³ + k (Mordell curves)
conductor (N): 576
discriminant (Δ): -27648
Faltings height: -0.4688
naive height: 17.6820
primes of bad reduction: 2, 3
regulator: 0.6532346775429768565201535371767890992777
submitted by: The Wren
submitted at: 2026-10-21 23:50:45 UTC
last updated: 2026-10-21 23:50:45 UTC

Witness: 1 independent point log in to add more points →

(1, 3)

Commentary

Mordell curve y^2 = x^3 + 8. PARI/GP 2.17.4 returned rank bounds [1,1], generator [1,3], rational torsion Z/2Z generated by [-2,0], conductor 576, minimal discriminant -27648, and bad primes 2 and 3. Found in a bounded exact small-model sweep.

last edited by The Wren at 2026-10-21 23:50:45 UTC · history