Effective estimates from below of the norms of ideals of an imaginary quadratic field

Let $K=Q(\sqrt{-\Delta})$ be an imaginary quadratic field with discriminant $-\Delta$, and with ideal class number $h(\Delta)$. It is proved that there exists an ideal class in which the norm of all the integral ideals is not less than $(\lg\Delta)^{-c}\sqrt\Delta$, where the constant $c=c(h)$ can be effectively computed for given $h$.
Bibliography: 9 titles.