Even lattices of rank 19 and determinant 14

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• 119 isometry classes, mass 4312205800066019/528678313605023662080000.
• 111 possible root systems, see here for statistics of reduced masses for each root system.
• Isometry classes distinguished by invariant: \(\mathrm{BV}_{19,7}\).
• Classified in: G. Chenevier & O. Taïbi, Unimodular lattices of rank 29 and related even genera of small determinant, arXiv preprint (2026).
• Construction(s): Norm 14/5 vectors in duals of rank 20 even lattices of determinant 5.