Let's say you were given a genus one algebraic curve by the equation $y^2 = (x-a)(x-b)(x-c)$ and you wanted to parametrize it. We could go ahead and convert it to Weierstrass form: $y^2 = 4t^3 - g_2t - g_3$ and as long as the coefficients $g_2$ and $g_3$ satisfy a certain condition, by uniformization, there exists a lattice $\Lambda \subset \mathbb{C}$ for which $t = \wp_\Lambda(z)$ and $y = \wp'_{\Lambda}(z)$ does the required parametrization. In other words, $\wp$ and $\wp'$ generate the field of elliptic functions.
Now my question pertains to genus two curves namely, $$y^2 = \prod_{i=1}^{6}(x-a_i)$$ and whether an analogous procedure exists for their parametrization. What kind of meromorphic functions would get the job done? References are appreciated.