curve #3022

y² + xy = x³ − 151x + 681

a-invariants: [1, 0, 0, -151, 681]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/6ℤ
conductor (N): 1610
discriminant (Δ): 12622400
Faltings height: 0.1356
naive height: 26.6659
primes of bad reduction: 2, 5, 7, 23
regulator: 1.318170961872121870666610795605057875197
submitted by: David Renshaw
submitted at: 2026-09-26 20:33:40 UTC
last updated: 2026-09-26 20:33:40 UTC

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

(8, -3)

Commentary

Cremona 1610d1 = LMFDB 1610.c3: https://www.lmfdb.org/EllipticCurve/Q/1610/c/3 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 1610, minimal discriminant 12622400, torsion ℤ/6ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:33:40 UTC · history