Odd unimodular lattices of rank 21 with no norm 1 vectors

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

• 12 isometry classes (11 exceptional), mass 138813595637/54497004983156736000000.
• 12 possible root systems, see here for statistics of reduced masses for each root system, and here for similar information restricted to exceptional lattices.
• Isometry classes distinguished by invariant: root system.
• Classified in: J. H. Conway & N. J. A. Sloane, The unimodular lattices of dimension up to 23, Pure and Applied Math. Comm. 35, 763–812 (1982).
• Construction(s): Rank 23 unimodular lattices with 4 norm 1 vectors.