Radical Parametrization of Algebraic Curves by Adjoint Curves
  We present algorithms for parametrizing by radicals an irreducible curve, not necessarily plane, when the genus is less o equal to 4 and they are defined over an algebraically closed field of characteristic zero. In addition, we also present an algorithm for parametrizing by radicals any irreducible plane curve of degree $d$ having at least a point of multiplicity $d-r$, with $1\leq r \leq 4$ and, as a consequence, every irreducible plane curve of degree $d \leq 5$ and every irreducible singular plane curve of degree 6. 
J. Rafael Sendra and David Sevilla