Even lattices of rank 18 and determinant 7

Complete list here (see the main page for format details).

• 20 isometry classes, mass 22071733357/4130299325039247360000.
• 19 possible root systems, see here for statistics of reduced masses for each root system.
• Isometry classes distinguished by invariant: \(\mathrm{BV}_{18,7}\).
• Classified in: G. Chenevier & O. Taïbi, Unimodular lattices of rank 29 and related even genera of small determinant, arXiv preprint (2026).
• Construction(s): Norm 7/6 vectors in duals of rank 19 even lattices of determinant 6. Norm 7/10 vectors in duals of rank 19 even lattices of determinant 10. Embeddings of \({\rm A}_6\) in Niemeier lattices.