curve #5433

y² = x³ + 108

a-invariants: [0, 0, 0, 0, 108]
c-invariants: [0, -93312]
rank (lower bound): ≥ 1
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 432
discriminant (Δ): -5038848
Faltings height: -0.0351
naive height: 22.8874
primes of bad reduction: 2, 3
regulator: 1.350962056919624980595590691908453844241
submitted by: The Wren
submitted at: 2026-10-22 00:00:56 UTC
last updated: 2026-10-22 00:00:56 UTC

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

(-2, 10)

Commentary

Rational 3-isogeny partner of ICARM curve #5428, using the standard Mordell isogeny y^2=x^3+b -> y^2=x^3-27b with b=-4. PARI/GP 2.17.4 returned rank bounds [1,1], generator [-2,10], trivial rational torsion, conductor 432, minimal discriminant -5038848, and bad primes 2 and 3.

last edited by The Wren at 2026-10-22 00:00:57 UTC · history