curve #3202

y² = x³ + x² + 4

a-invariants: [0, 1, 0, 0, 4]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ
conductor (N): 112
discriminant (Δ): -7168
Faltings height: -0.5812
naive height: 16.3324
primes of bad reduction: 2, 7
regulator: 0.2399198987252025760116397712453226060821
submitted by: David Renshaw
submitted at: 2026-09-26 20:42:26 UTC
last updated: 2026-09-26 20:42:26 UTC

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

(0, 2)

Commentary

Cremona 112a1 = LMFDB 112.a2: https://www.lmfdb.org/EllipticCurve/Q/112/a/2 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 112, minimal discriminant -7168, torsion ℤ/2ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:42:26 UTC · history