curve #3264

y² + y = x³ − 559908x + 161258688

a-invariants: [0, 0, 1, -559908, 161258688]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/3ℤ
conductor (N): 74655
discriminant (Δ): -373275
Faltings height: 1.5325
naive height: 51.3202
primes of bad reduction: 3, 5, 7, 79
regulator: 35.4130544805723035226181467763774330621745
submitted by: David Renshaw
submitted at: 2026-09-26 20:48:12 UTC
last updated: 2026-09-26 20:48:12 UTC

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

(666, 9152)
(17281/36, 380107/216)

Commentary

Cremona 74655j1 = LMFDB 74655.f1: https://www.lmfdb.org/EllipticCurve/Q/74655/f/1 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 74655, minimal discriminant -373275, torsion ℤ/3ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:48:12 UTC · history