curve #3189

y² + xy + y = x³ − x² − 17x + 30

a-invariants: [1, -1, 1, -17, 30]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ
conductor (N): 99
discriminant (Δ): 3267
Faltings height: -0.4887
naive height: 20.0576
primes of bad reduction: 3, 11
regulator: 0.1512856922807474995880715174057811938860
submitted by: David Renshaw
submitted at: 2026-09-26 20:41:48 UTC
last updated: 2026-09-26 20:41:48 UTC

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

(0, 5)

Commentary

Cremona 99a2 = LMFDB 99.a1: https://www.lmfdb.org/EllipticCurve/Q/99/a/1 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 99, minimal discriminant 3267, torsion ℤ/2ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:41:48 UTC · history