  We give an effective proof of Faltings' theorem for curves mapping to Hilbert
modular stacks over odd-degree totally real fields. We do this by giving an
effective proof of the Shafarevich conjecture for abelian varieties of
$\mathrm{GL}_2$-type over an odd-degree totally real field. We deduce for
example an effective height bound for $K$-points on the curves $C_a : x^6 +
4y^3 = a^2$ ($a\in K^\times$) when $K$ is odd-degree totally real. (Over
$\overline{\mathbb{Q}}$ all hyperbolic hyperelliptic curves admit an \'{e}tale
cover dominating $C_1$.)
