curve #3248

y² + y = x³ − 6924x + 221760

a-invariants: [0, 0, 1, -6924, 221760]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/3ℤ
conductor (N): 171
discriminant (Δ): -13851
Faltings height: 0.5827
naive height: 38.1418
primes of bad reduction: 3, 19
regulator: 2.033701819431253908761036383969322555591
submitted by: David Renshaw
submitted at: 2026-09-26 20:45:34 UTC
last updated: 2026-09-26 20:45:34 UTC

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

(62, 175)

Commentary

Cremona 171b3 = LMFDB 171.b1: https://www.lmfdb.org/EllipticCurve/Q/171/b/1 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 171, minimal discriminant -13851, torsion ℤ/3ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:45:34 UTC · history