## There’s no 4-branched Belyi’s theorem — right?

Much discussion on Math Overflow has not resolved the following should-be-easy question:

Give an example of a curve in ${\mathcal{M}}_g$ defined over $\bar{Q}$ which is not a family of 4-branched covers of P^1.

Surely there is one!  But then again, you’d probably say “surely there’s a curve over $\bar{Q}$ which isn’t a 3-branched cover of P^1.”  But there isn’t — that’s Belyi’s theorem.