curve #3322

y² + xy = x³ − 14146x − 168060

a-invariants: [1, 0, 0, -14146, -168060]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/6ℤ
conductor (N): 174230
discriminant (Δ): 169137661313600
Faltings height: 1.4212
naive height: 40.2852
primes of bad reduction: 2, 5, 7, 19, 131
regulator: 4.68306307866784586001383654308472038031659
submitted by: David Renshaw
submitted at: 2026-09-26 20:57:35 UTC
last updated: 2026-09-26 20:57:35 UTC

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

(128, 286)
(-26, 440)

Commentary

Cremona 174230d1 = LMFDB 174230.u3: https://www.lmfdb.org/EllipticCurve/Q/174230/u/3 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 174230, minimal discriminant 169137661313600, torsion ℤ/6ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:57:35 UTC · history