Even lattices of rank 23 and determinant 14

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• 5535 isometry classes, mass 15981689794652429741270154317/21479988410446669380845568000000.
• 2251 possible root systems, see here for statistics of reduced masses for each root system.
• Isometry classes distinguished by invariant: \(\mathrm{BV}_{23,7}\).
• Classified in: G. Chenevier & O. Taïbi, Unimodular lattices of rank 29 and related even genera of small determinant, arXiv preprint (2026).
• Construction(s): Norm 14 vectors in Niemeier lattices. Norm 7/2 vectors in duals of rank 24 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 Niemeier lattice).