Even lattices of rank 10 and determinant 7

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• 2 isometry classes, mass 1/174182400.
• 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): Norm 7/6 vectors in duals of rank 11 even lattices of determinant 6. Norm 7/10 vectors in duals of rank 11 even lattices of determinant 10. Embeddings of \({\rm A}_6\) in rank 16 even unimodular lattices.