Even lattices of rank 7 and determinant 14

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• 2 isometry classes, mass 43/725760.
• 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 14 vectors in rank 8 even unimodular lattices. Norm 7/2 vectors in duals of rank 8 even lattices of residue \({\rm qres}\, {\rm A}_1 \perp -{\rm qres} {\rm A}_1\) (a mod 2 vector of norm 2 mod 4 in a rank 8 even unimodular lattice).
• Extra information: Lattice \(\#1\) is the \({\rm A}_1\perp {\rm A}_6\) root lattice.