Even lattices of rank 21 and determinant 10

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• 210 isometry classes, mass 708161255758676994349/27121197487937713864704000000.
• 199 possible root systems, see here for statistics of reduced masses for each root system.
• Isometry classes distinguished by invariant: \(\mathrm{BV}_{21,5}\).
• Classified in: G. Chenevier & O. Taïbi, Unimodular lattices of rank 29 and related even genera of small determinant, arXiv preprint (2026).
• Construction(s): Norm 10/3 vectors in duals of rank 22 even lattices of determinant 3. Norm 10/7 vectors in duals of rank 22 even lattices of determinant 7.