Optimal affine reparametrization of rational curves

Let K be a characteristic zero field, let ϕ(t) be a birational parametrization ϕ(t) of a K-definable curve C with coefficients in an algebraic extension K(α) over K. We propose an algorithm to solve the optimization problem of computing the affine reparametrization t→at+b such that ϕ(at+b) has coefficients over an extension of K with algebraic degree as small as possible.