Even lattices of rank 16 and determinant 1

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• 2 isometry classes, mass 691/277667181515243520000.
• 2 possible root systems, see here for statistics of reduced masses for each root system.
• Isometry classes distinguished by invariant: root system.
• Classified in: E. Witt, Eine Identität zwischen Modulformen zweiten Grades, Abh. Math. Seminar Univ. Hamburg. 14, 323–337 (1941).
• Extra information: Lattices \(\#1\) and \(\#2\) have same theta series in genus 1, 2 and 3 (Witt, Igusa).