curve #906

y² + xy + y = x³ − x² − 213x − 1257

a-invariants: [1, -1, 1, -213, -1257]
rank (lower bound): ≥ 0
torsion subgroup: trivial
conductor (N): 26
discriminant (Δ): -125497034
Faltings height: 0.2898
naive height: 27.8786
primes of bad reduction: 2, 13
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 14:58:15 UTC
last updated: 2026-09-23 14:58:15 UTC

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Commentary

Cremona 26b2 = LMFDB 26.b1: https://www.lmfdb.org/EllipticCurve/Q/26/b/1 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 26, minimal discriminant -125497034, trivial torsion.

last edited by David Renshaw at 2026-09-23 14:58:15 UTC · history