Even lattices of rank 4 and determinant 5

Complete list here (see the main page for format details).

• 1 isometry class, mass 1/240.
• 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): Exceptional vectors in rank 5 unimodular lattices (unique orbit). Norm 5/6 vectors in duals of rank 5 even lattices of determinant 6. Norm 5/14 vectors in duals of rank 5 even lattices of determinant 14. Embeddings of \({\rm A}_4\) in rank 8 even unimodular lattices.
• Extra information: Lattice \(\#1\) is the \({\rm A}_4\) lattice.