Even lattices of rank 23 and determinant 6

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• 290 isometry classes, mass 65862519711199575367246519/988079466880546791518896128000000.
• 274 possible root systems, see here for statistics of reduced masses for each root system.
• Isometry classes distinguished by invariant: \(\mathrm{BV}_{23,3}\).
• Classified in: G. Chenevier & O. Taïbi, Unimodular lattices of rank 29 and related even genera of small determinant, arXiv preprint (2026).
• Construction(s): Norm 6 vectors in Niemeier lattices. Norm 3/2 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).
• Extra information: Lattice \(\#271\) is the unique lattice with no root; its isometry group is \(\mathbb{Z}/2 \times {\rm Co}_3\).