Covers of Elliptic Curves with Unique, Totally Ramified Branch Points
  A well-known and difficult problem in computational number theory and algebraic geometry is to write down equations for branched covers of algebraic curves with specified monodromy type. In this article, we present a technique for computing such covers in the case of totally ramified covers of elliptic curves branched at one point. 
Simon Rubinstein-Salzedo
math.AG