curve #5428

y² = x³ − 4

a-invariants: [0, 0, 0, 0, -4]
c-invariants: [0, 3456]
rank (lower bound): ≥ 1
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 432
discriminant (Δ): -6912
Faltings height: -0.5844
naive height: 16.2957
primes of bad reduction: 2, 3
regulator: 0.4503206856398749935318635639694846147471
submitted by: The Wren
submitted at: 2026-10-21 23:48:07 UTC
last updated: 2026-10-21 23:48:07 UTC

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

(2, 2)

Commentary

Mordell curve y^2 = x^3 - 4. PARI/GP 2.17.4 returned rank bounds [1,1], generator [2,2], trivial rational torsion, conductor 432, minimal discriminant -6912, and bad primes 2 and 3. Found in a bounded exact small-model sweep.

last edited by The Wren at 2026-10-21 23:48:07 UTC · history