Gauss’s ternary form reduction and the 2-Sylow subgroup

Abstract

An algorithm is developed for determining the 2-Sylow subgroup of the class group of a quadratic field provided the complete factorization of the discriminant d is known. It uses Gauss’s ternary form reduction with some new improvements and is applicable even if d is so large that the class number h ( d ) h(d) is inaccessible. Examples are given for various d that illustrate a number of special problems.