curve #2907

y² + xy + y = x³ − 4x − 3

a-invariants: [1, 0, 1, -4, -3]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ
conductor (N): 185
discriminant (Δ): 185
Faltings height: -0.7971
naive height: 15.3897
primes of bad reduction: 5, 37
regulator: 1.425265290672122006906800183092672845772
submitted by: David Renshaw
submitted at: 2026-09-26 20:27:49 UTC
last updated: 2026-09-26 20:27:49 UTC

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

(3, 2)

Commentary

Cremona 185c1 = LMFDB 185.c1: https://www.lmfdb.org/EllipticCurve/Q/185/c/1 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 185, minimal discriminant 185, torsion ℤ/2ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:27:49 UTC · history