In this paper, the integral binary quadratic forms for which the set of represented values is closed under k-fold products, for even positive integers k, will be characterized. This property will be seen to distinguish the elements of odd order in the form class group of a fixed discriminant. Further, it will be shown that this closure under k-fold products can always be expressed by a k-linear mapping from (Z2)k to Z2. In the case k = 2, this resolves a conjecture of Aicardi and Timorin.
Earnest, A. G. and Fitzgerald, Robert W. "Multiplicative Properties of Integral Binary Quadratic Forms." (Jan 2008).