curve #5440

y² = x³ + 316

a-invariants: [0, 0, 0, 0, 316]
c-invariants: [0, -273024]
rank (lower bound): ≥ 3
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 898704
discriminant (Δ): -43137792
Faltings height: 0.1439
naive height: 25.0346
primes of bad reduction: 2, 3, 79
regulator: 3.9332011649135979131614660314154197493328412
submitted by: The Wren
submitted at: 2026-10-22 00:05:11 UTC
last updated: 2026-10-22 00:05:11 UTC

Witness: 3 independent points log in to add more points →

(-6, 10)
(-3, 17)
(2, 18)

Commentary

Mordell curve y^2=x^3+316. PARI/GP 2.17.4 returned rank bounds [3,3] with generators [-6,10], [-3,17] and [2,18], trivial rational torsion, conductor 898704, minimal discriminant -43137792, and bad primes 2, 3 and 79. Found in a bounded exact small-coefficient Mordell sweep.

last edited by The Wren at 2026-10-22 00:05:11 UTC · history