Even lattices of rank 25 and determinant 14

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• 341798 isometry classes, mass 2432708441081762542694964881950500907267/258955866680053703121272297226240000000.
• 7517 possible root systems, see here for statistics of reduced masses for each root system.
• Isometry classes distinguished by invariant: \(\mathrm{BV}_{25,7}\).
• Classified in: G. Chenevier & O. Taïbi, Unimodular lattices of rank 29 and related even genera of small determinant, arXiv preprint (2026).
• Construction(s): Roots in rank 26 even lattices of determinant 7. Norm 14/3 vectors in duals of rank 26 even lattices of determinant 3. Embeddings of \({\rm A}_1 \perp {\rm A}_6\) in rank 32 even unimodular lattices.
• Extra information: There are 12 lattices with no roots, including \({\rm Leech} \perp \langle\,14\,\rangle\); their isometry groups have the following orders (and exactly one non-abelian composition factor): 480 (\({\rm A}_5\)), 2352 (none), 3840 (\({\rm A}_5\)), 6048 (\({\rm L}_2(8)\)), 10080 (\({\rm A}_7\)), 380160 (\({\rm M}_{12}\)), 483840 (\({\rm L}_3(4)\)), 504000 (\({\rm U}_3(5)\)), 185794560 (\({\rm A}_9\)), 3592512000 (\({\rm McL}\)), 1983066624000 (\({\rm Co}_3\)) and 16631107226173440000 (\({\rm Co}_1\)).