Even lattices of rank 25 and determinant 10

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• 38749 isometry classes, mass 42909517952590896925519951603660928971/258955866680053703121272297226240000000.
• 4648 possible root systems, see here for statistics of reduced masses for each root system.
• Isometry classes distinguished by invariant: \(\mathrm{BV}_{25,5}\).
• Classified in: G. Chenevier & O. Taïbi, Unimodular lattices of rank 29 and related even genera of small determinant, arXiv preprint (2026).
• Construction(s): Norm 10 characteristic vectors in rank 26 unimodular lattices.
• Extra information: There are 5 lattices with no roots, including \({\rm Leech} \perp \langle\,10\,\rangle\); their isometry groups have the following orders (and exactly one non-abelian composition factor): 60000 (\({\rm A}_5\)), 380160 (\({\rm M}_{12}\)), 177408000 (\({\rm HS}\)), 1983066624000 (\({\rm Co}_3\)) and 16631107226173440000 (\({\rm Co}_1\)).