  In this work, we determine all Lattes maps which are Belyi morphisms. It
turns out that in the generic case, i.e. when the automorphism group is
$\ZZ/2\ZZ$, the corresponding family of Lattes maps are Belyi morphisms if and
only if the isogeny is multiplication by two. This family form a continuous
family of Belyi maps. Elliptic curves with complex multiplication also
determine a family over $\ZZ$ of Belyi morphisms. We give the explicit formulas
for the first few Belyi morphisms when the curve has complex multiplication by
3rd root of unity.
