Even lattices of rank 5 and determinant 6

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• 1 isometry class, mass 1/1440.
• 1 possible root systems, see here for statistics of reduced masses for each root system.
• Classified in: J. H. Conway & N. J. A. Sloane, Low dimensional lattices I. Quadratic Forms of Small Determinant, Proc. Roy. Soc. London Ser. A 418, 17–41 (1988).
• Construction(s): Roots in rank 6 even lattices of determinant 3. Norm 6/7 vectors in duals of rank 6 even lattices of determinant 7 (unique orbit). Exceptional vectors in rank 6 unimodular lattices.
• Extra information: Lattice \(\#1\) is the \({\rm A}_5\) lattice.