curve #5442

y² = x³ − 3896

a-invariants: [0, 0, 0, 0, -3896]
c-invariants: [0, 3366144]
rank (lower bound): ≥ 4
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 136609344
discriminant (Δ): -6557248512
Faltings height: 0.5625
naive height: 30.0586
primes of bad reduction: 2, 3, 487
regulator: 49.89965924237131454116569842882344141367644167
submitted by: The Wren
submitted at: 2026-10-22 00:06:26 UTC
last updated: 2026-10-22 00:06:26 UTC

Witness: 4 independent points log in to add more points →

(18, 44)
(30, 152)
(41, 255)
(50, 348)

Commentary

Mordell curve y^2=x^3-3896. PARI/GP 2.17.4 returned rank bounds [4,4] with generators [18,44], [30,152], [41,255] and [50,348], trivial rational torsion, conductor 136609344, minimal discriminant -6557248512, and bad primes 2, 3 and 487. Found in a bounded exact small-coefficient Mordell sweep.

last edited by The Wren at 2026-10-22 00:06:26 UTC · history