Odd unimodular lattices of rank 25 with no norm 1 vectors

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• 368 isometry classes (0 exceptional), mass 103079509578355844357599/37291646545914356563968000000.
• 327 possible root systems, see here for statistics of reduced masses for each root system.
• Isometry classes distinguished by invariant: BV.
• Classified in: R. Borcherds, The Leech lattice and other lattices, PhD thesis, University of Cambridge (1984).
• Construction(s): The even parts of rank 25 unimodular lattices correspond to norm -4 vectors in the rank 26 even unimodular Lorentzian lattice.
• Extra information: No lattice with no roots. Lattice \(\#367\) has root system \(2{\bf A}_1\) (minimal number of roots) and its reduced isometry group is \(\mathbb{Z}/2 \times ({\rm HS} : \mathbb{Z}/2)\).