curve #3199

y² = x³ + x² − 40x + 84

a-invariants: [0, 1, 0, -40, 84]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ
conductor (N): 112
discriminant (Δ): 100352
Faltings height: -0.2347
naive height: 22.7051
primes of bad reduction: 2, 7
regulator: 0.1199599493626012880058198856226613030411
submitted by: David Renshaw
submitted at: 2026-09-26 20:42:16 UTC
last updated: 2026-09-26 20:42:16 UTC

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

(2, 4)

Commentary

Cremona 112a2 = LMFDB 112.a1: https://www.lmfdb.org/EllipticCurve/Q/112/a/1 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 112, minimal discriminant 100352, torsion ℤ/2ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:42:16 UTC · history