curve #903

y² + xy + y = x³ − 5x − 8

a-invariants: [1, 0, 1, -5, -8]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/3ℤ
conductor (N): 26
discriminant (Δ): -17576
Faltings height: -0.4949
naive height: 17.5190
primes of bad reduction: 2, 13
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 14:58:14 UTC
last updated: 2026-09-23 14:58:14 UTC

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

Commentary

Cremona 26a1 = LMFDB 26.a2: https://www.lmfdb.org/EllipticCurve/Q/26/a/2 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 26, minimal discriminant -17576, torsion ℤ/3ℤ.

last edited by David Renshaw at 2026-09-23 14:58:14 UTC · history