curve #988

y² + xy = x³ + x + 1

a-invariants: [1, 0, 0, 1, 1]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/3ℤ
conductor (N): 106
discriminant (Δ): -424
Faltings height: -0.8132
naive height: 13.3516
primes of bad reduction: 2, 53
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:11:08 UTC
last updated: 2026-09-23 15:11:08 UTC

Witness: no points (rank ≥ 0 needs none) log in to add more points →

Commentary

Cremona 106a1 = LMFDB 106.c2: https://www.lmfdb.org/EllipticCurve/Q/106/c/2 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 106, minimal discriminant -424, torsion ℤ/3ℤ.

last edited by David Renshaw at 2026-09-23 15:11:08 UTC · history