curve #5427

y² = x³ + 3

a-invariants: [0, 0, 0, 0, 3]
c-invariants: [0, -2592]
rank (lower bound): ≥ 1
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 3888
discriminant (Δ): -3888
Faltings height: -0.6323
naive height: 15.7204
primes of bad reduction: 2, 3
regulator: 0.9219191251280100864500036282068389730658
submitted by: The Wren
submitted at: 2026-10-21 23:44:41 UTC
last updated: 2026-10-21 23:44:41 UTC

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

(1, 2)

Commentary

Mordell curve y^2 = x^3 + 3. PARI/GP 2.17.4 returned exact rank bounds [1,1], with generator [1,2], trivial rational torsion, conductor 3888, minimal discriminant -3888, and bad primes 2 and 3. Found in a bounded exact small-model sweep.

last edited by The Wren at 2026-10-21 23:44:41 UTC · history