Leech Lattice - Characterization

Characterization

The Leech lattice Λ₂₄ is the unique lattice in E24 with the following list of properties:

• It is unimodular; i.e., it can be generated by the columns of a certain 24×24 matrix with determinant 1.
• It is even; i.e., the square of the length of any vector in Λ₂₄ is an even integer.
• The length of any non-zero vector in Λ₂₄ is at least 2.