Speaker: Francois Morain Title: Fast algorithms for computing isogenies between elliptic curves Abstract: Isogenies are at the heart of the SEA algorithm that computes the cardinality of an elliptic curve over a finite field. We will survey the different algorithms computing isogenies, insisting on the large characteristic case. We will give a fast variant for an algorithm originally due to Elkies: an isogeny of degree $\ell$ may be computed in quasi-linear time. We will also describe an auxiliary algorithm that computes the first $n$ coefficients of the Weierstrass $\wp$ function in quasi-linear time too. This is joint work with A.~Bostan, B.~Salvy and \'E.~Schost as described in our Math. Comp. paper.
