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We give another solution to the class number one problem by showing thatimaginary quadratic fields $\Q(\sqrt{-d})$ with class number $h(-d)=1$correspond to integral points on a genus two curve $\mscrK_3$. In fact one canfind all rational points on $\mscrK_3$. The curve $\mscrK_3$ arises naturallyvia certain coverings of curves:\ $\mscrK_3\rg\mscrK_6$,\$\mscrK_1\rg\mscrK_2$\ with $\mscrK_2\colon y^2=2x(x^3-1)$ denoting the Heegnercurve, also in connection with the so-called Heegner-Stark covering$\mscrK_1\rg\mscrK_s$.

A Genus Two Curve Related to the Class Number One Problem