Rational functions with two critical points of maximum multiplicity

In this paper, we consider the functions on algebraic curves whose divisors have the form $nA-nC$. Combinatorial-topological and algebraic descriptions are introduced for exploring such functions. All Belyi functions with such divisor are described. The case of curves of genus 1 is considered in more detail. The number of Belyi functions with divisor $nA-nC$ is explicitly calculated. For general functions of this type on a curve of genus 1, we consider the space of the parameters and a method of its calculation that uses the Padé approximation.