Even lattices of rank 7 and determinant 2

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• 1 isometry class, mass 1/2903040.
• 1 possible root systems, see here for statistics of reduced masses for each root system.
• Classified in: M. Kneser, Klassenzahlen definiter quadratischer Formen, Archiv der Math. 8, 241–250 (1957).
• Construction(s): Roots in rank 8 even unimodular lattices. Norm 2/5 vectors in dual of rank 8 even lattices of determinant 5.
• Extra information: Lattice \(\#1\) is the \({\rm E}_7\) lattice.