curve #3231

y² = x³ − 46x + 120

a-invariants: [0, 0, 0, -46, 120]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ
conductor (N): 4352
discriminant (Δ): 8704
Faltings height: -0.3145
naive height: 23.0995
primes of bad reduction: 2, 17
regulator: 1.88143684322227386875464464983028979652256
submitted by: David Renshaw
submitted at: 2026-09-26 20:43:46 UTC
last updated: 2026-09-26 20:43:46 UTC

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

(2, 6)
(12, 36)

Commentary

Cremona 4352h1 = LMFDB 4352.a2: https://www.lmfdb.org/EllipticCurve/Q/4352/a/2 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 4352, minimal discriminant 8704, torsion ℤ/2ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:43:46 UTC · history