curve #3160

y² = x³ − 1596x + 23920

a-invariants: [0, 0, 0, -1596, 23920]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 6336
discriminant (Δ): 13006946304
Faltings height: 0.7186
naive height: 33.7394
primes of bad reduction: 2, 3, 11
regulator: 1.77345600924051887400126084837012768331573
submitted by: David Renshaw
submitted at: 2026-09-26 20:40:10 UTC
last updated: 2026-09-26 20:40:10 UTC

Witness: 2 independent points log in to add more points →

(2, 144)
(18, 32)

Commentary

Cremona 6336ck2 = LMFDB 6336.o3: https://www.lmfdb.org/EllipticCurve/Q/6336/o/3 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 6336, minimal discriminant 13006946304, torsion ℤ/2ℤ × ℤ/2ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:40:10 UTC · history