“…Then, in §2.2, we study orbits of SL n /µ 2 on pairs of n-ary quadratic forms (A, B) for fixed A. In §2.3, we define the ring R f associated to a binary n-ic form f , and in §2.4, we recall a parametrization from [38] of square roots of the ideal class of the inverse different of R f in terms of orbits of the aforementioned representations. We conclude in §2.5 by describing the image of the parametrization discussed in §2.4.…”