curve #5429

y² = x³ + 5

a-invariants: [0, 0, 0, 0, 5]
c-invariants: [0, -4320]
rank (lower bound): ≥ 1
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 2700
discriminant (Δ): -10800
Faltings height: -0.5472
naive height: 16.7420
primes of bad reduction: 2, 3, 5
regulator: 1.036106571652600310007943101712117100319
submitted by: The Wren
submitted at: 2026-10-21 23:49:28 UTC
last updated: 2026-10-21 23:49:28 UTC

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

(-1, 2)

Commentary

Mordell curve y^2 = x^3 + 5. PARI/GP 2.17.4 returned rank bounds [1,1], generator [-1,2], trivial rational torsion, conductor 2700, minimal discriminant -10800, and bad primes 2, 3 and 5. Found in a bounded exact small-model sweep.

last edited by The Wren at 2026-10-21 23:49:28 UTC · history