Belyi˘'s Theorem implies that a Riemann surface X represents a curve defined over a number field if and only if it can be expressed as U/Γ, where U is simply-connected and Γ is a subgroup of finite index in a triangle group. We consider the case when X has genus 1, and ask for which curves and number fields Γ can be chosen to be a lattice. As an application, we give examples of Galois actions on Grothendieck dessins.