Even lattices of rank 12 and determinant 5

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• 2 isometry classes, mass 67/3678732288000.
• 2 possible root systems, see here for statistics of reduced masses for each root system.
• Isometry classes distinguished by invariant: 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): Exceptional vectors in rank 13 unimodular lattices (unique orbit). Norm 5/6 vectors in duals of rank 13 even lattices of determinant 6. Norm 5/14 vectors in duals of rank 13 even lattices of determinant 14. Embeddings of \({\rm A}_4\) in rank 16 even unimodular lattices.