curve #3318

y² + xy = x³ − x² − 3999x + 98343

a-invariants: [1, -1, 0, -3999, 98343]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/6ℤ
conductor (N): 1170
discriminant (Δ): 1140750
Faltings height: 0.5645
naive height: 36.4951
primes of bad reduction: 2, 3, 5, 13
regulator: 2.683624853472045407371643724068477971489
submitted by: David Renshaw
submitted at: 2026-09-26 20:56:56 UTC
last updated: 2026-09-26 20:56:56 UTC

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

(67, 324)

Commentary

Cremona 1170b2 = LMFDB 1170.c2: https://www.lmfdb.org/EllipticCurve/Q/1170/c/2 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 1170, minimal discriminant 1140750, torsion ℤ/6ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:56:56 UTC · history