On complex quadratic fields wth class-number two

Let $d < 0$ be the discriminant of a complex quadratic field of class-number $h(d)$. In a previous paper the author has effectively shown how to find all d with $h(d) = 2$. In this paper, it is proved that, if $h(d) = 2$, then $\vert d\vert\; \leqslant 427$.