Even lattices of rank 24 and determinant 5

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• 352 isometry classes, mass 1711620950810249655231709777/3952317867522187166075584512000000.
• 323 possible root systems, see here for statistics of reduced masses for each root system.
• Isometry classes distinguished by invariant: \(\mathrm{BV}_{24,5}\).
• Classified in: G. Chenevier & O. Taïbi, Unimodular lattices of rank 29 and related even genera of small determinant, arXiv preprint (2026).
• Construction(s): Norm 5/2 vectors in duals of rank 25 even lattices of determinant 2.
• Extra information: There are no lattices with no roots.