About: Genus of a quadratic form

In mathematics, the genus is a classification of quadratic forms and lattices over the ring of integers. An integral quadratic form is a quadratic form on Zn, or equivalently a free Z-module of finite rank. Two such forms are in the same genus if they are equivalent over the local rings Zp for each prime p and also equivalent over R. The Smith–Minkowski–Siegel mass formula gives the weight or mass of the quadratic forms in a genus, the count of equivalence classes weighted by the reciprocals of the orders of their automorphism groups.