Fast algorithms for computing isogenies between elliptic curves
  We survey algorithms for computing isogenies between elliptic curves defined over a field of characteristic either 0 or a large prime. We introduce a new algorithm that computes an isogeny of degree $\ell$ ($\ell$ different from the characteristic) in time quasi-linear with respect to $\ell$. This is based in particular on fast algorithms for power series expansion of the Weierstrass $\wp$-function and related functions. 
Alin Bostan (INRIA Rocquencourt), Bruno Salvy (INRIA Rocquencourt),   Francois Morain (LIX, INRIA Futurs), Eric Schost (LIX)