Even lattices of rank 6 and determinant 3

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• 1 isometry class, mass 1/103680.
• 1 possible root systems, see here for statistics of reduced masses for each root system.
• Classified in: M. Kneser, Klassenzahlen definiter quadratischer Formen, Archiv der Math. 8, 241–250 (1957).
• Construction(s): Norm 3/2 vectors in duals of rank 7 even lattices of determinant 2. Embeddings of \({\rm A}_2\) in rank 8 even unimodular lattices.
• Extra information: Lattice \(\#1\) is the \({\rm E}_6\) lattice.