Form class groups for extended ring class fields (Q1634411)

Let \(L\) be an extended ring class field of an imaginary quadratic field \(K\) other than \(Q(\sqrt{-1})\) and \(Q(\sqrt{-3})\). The authors show that there is a form class group induced from a congruence subgroup which describes the Galois group of \(L\) over \(K\) in a concrete way. They also construct a primitive generator of \(L\) over \(K\) as a real algebraic integer which can be applied to certain quadratic Diophantine equations