  Every quadratic form represents 0; therefore, if we take any number of
quadratic forms and ask which integers are simultaneously represented by all
members of the collection, we are guaranteed a nonempty set. But when is that
set more than just the "trivial" 0? We address this question in the case of
integral, positive- definite, reduced, binary quadratic forms. For forms of the
same discriminant, we can use the structure of the underlying class group. If,
however, the forms have different discriminants, we must apply class field
theory.
