Odd unimodular lattices of rank 26 with no norm 1 vectors

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• 1901 isometry classes (97 exceptional), mass 15661211867944570315962162816169/34253421518525622105988399104000000.
• 1086 possible root systems, see here for statistics of reduced masses for each root system, and here for similar information restricted to exceptional lattices.
• Isometry classes distinguished by invariant: BV.
• Classified in: G. Chenevier, Unimodular hunting, Algebraic Geometry 12 (6), 769–812 (2025). The lattices with root systems \(n\,{\bf A}_1\) with \(n \geq 0\) were found by Bacher and Venkov in Réseaux entiers unimodulaires sans racine en dimension 27 et 28, Enseign. Math. 37 212–267 (2001). Masses root system by root system first computed by King in A mass formula for unimodular lattices with no roots, Math. Comp. 72 (242), 839–863 (2003).
• Construction(s): Determined by Chenevier as cyclic neighbors of the standard lattice \({\rm I}_{26}\).
• Extra information: Lattice \(\#1882\) is unique lattice with no root (Borcherds); its isometry group is \({\rm O}_5(5) : \mathbb{Z}/4\).