curve #3195

y² + xy = x³ + x² + 8x + 10

a-invariants: [1, 1, 0, 8, 10]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ
conductor (N): 102
discriminant (Δ): -46818
Faltings height: -0.4170
naive height: 17.6500
primes of bad reduction: 2, 3, 17
regulator: 0.2865077858817601429525488260636554399367
submitted by: David Renshaw
submitted at: 2026-09-26 20:42:07 UTC
last updated: 2026-09-26 20:42:07 UTC

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

(1, 4)

Commentary

Cremona 102a2 = LMFDB 102.a2: https://www.lmfdb.org/EllipticCurve/Q/102/a/2 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 102, minimal discriminant -46818, torsion ℤ/2ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:42:07 UTC · history