  Let $\mathfrak p$ be any point in the moduli space of genus-two curves
$\mathcal M_2$ and $K$ its field of moduli. We provide a universal equation of
a genus-two curve $\mathcal C_{\alpha, \beta}$ defined over $K(\alpha, \beta)$,
corresponding to $\mathfrak p$, where $\alpha $ and $\beta$ satisfy a quadratic
$\alpha^2+ b \beta^2= c$ such that $b$ and $c$ are given in terms of ratios of
Siegel modular forms. The curve $\mathcal C_{\alpha, \beta}$ is defined over
the field of moduli $K$ if and only if the quadratic has a $K$-rational point
$(\alpha, \beta)$. We discover some interesting symmetries of the Weierstrass
equation of $\mathcal C_{\alpha, \beta}$. This extends previous work of Mestre
and others.
