On the Classification of Integral Quadratic Forms

Abstract

This chapter gives an account of the classification of integral quadratic forms. It is particularly designed for readers who wish to be able to do explicit calculations. Novel features include an elementary system of rational invariants (defined without using the Hilbert norm residue symbol), an improved notation for the genus of a form, an efficient way to compute the number of spinor genera in a genus, and some conditions which imply that there is only one class in a genus. We give tables of the binary forms with − 100 ⩽ det ⩽ 50, the indecomposable ternary forms with |det| ⩽ 50, the genera of forms with |det| ⩽ 11, the genera of p-elementary forms for all p, and the positive definite forms with determinant 2 up to dimension 18 and determinant 3 up to dimension 17.