Even lattices of rank 24 and determinant 1

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

• 24 isometry classes, mass 1027637932586061520960267/129477933340026851560636148613120000000.
• 24 possible root systems, see here for statistics of reduced masses for each root system.
• Isometry classes distinguished by invariant: root system.
• Classified in: H.-V. Niemeier, Definite quadratische Formen der Dimension 24 und Diskriminante 1, J. Number Theory 5, 142–178 (1973). A few lattices previously found by Witt (1941).
• Extra information: Lattice \(\#24\) is the Leech lattice (Leech, 1965), with no root, and isometry group Conway's \({\rm Co}_0\). The root systems of \(\#1\) to \(\#23\) are the 23 rank 24 equi-Coxeter ADE root systems.