curve #3170

y² + xy = x³ − x² − 123993x + 16705885

a-invariants: [1, -1, 0, -123993, 16705885]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 185562
discriminant (Δ): 1885427356994064
Faltings height: 1.7540
naive height: 46.7975
primes of bad reduction: 2, 3, 13, 61
regulator: 5.9571288026243407459883380351495428391701294
submitted by: David Renshaw
submitted at: 2026-09-26 20:40:40 UTC
last updated: 2026-09-26 20:40:40 UTC

Witness: 3 independent points log in to add more points →

(62, 3011)
(270, 1555)
(231, 476)

Commentary

Cremona 185562ba2 = LMFDB 185562.d3: https://www.lmfdb.org/EllipticCurve/Q/185562/d/3 Mordell–Weil rank exactly 3 (Cremona's tables). Conductor 185562, minimal discriminant 1885427356994064, torsion ℤ/2ℤ × ℤ/2ℤ. The witnesses are the generators from Cremona's tables.

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