  We propose an algorithm that calculates isogenies between elliptic curves
defined over an extension $K$ of $\mathbb{Q}_2$. It consists in efficiently
solving with a logarithmic loss of $2$-adic precision the first order
differential equation satisfied by the isogeny.
  We give some applications, especially computing over finite fields of
characteristic 2 isogenies of elliptic curves and irreducible polynomials, both
in quasi-linear time in the degree.
