The authors proved that there are only finite pairs \((D,f)\), where \(D\) is the discriminant of an imaginary quadratic number field and \(f\) the conductor of the corresponding ring class field \(\text{mod }f\) , \(K_f\) over \(K\), so that the order of the Heegner points on \(E(K_f)\) of an modular elliptic curve \(E\) defined over \(\mathbb Q\) is finite.