Even lattices of rank 17 and determinant 2

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• 4 isometry classes, mass 2499347/9440684171518279680000.
• 4 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): Norm 2/3 vectors in dual of rank 18 even lattices of determinant 3 (unique orbit). Norm 2/7 vectors in dual of rank 18 even lattices of determinant 7. Embeddings of \({\rm E}_7\) in Niemeier lattices.