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4 documents, page 1 of 1

Computing isogenies between Abelian Varieties

Lubicz , David; Robert , Damien (2012)
Projects: EC | ANTICS (278537)
We describe an efficient algorithm for the computation of separable isogenies between abelian varieties represented in the coordinate system given by algebraic theta functions. Let $A$ be an abelian variety of dimension $g$ defined over a field of odd characteristic. Our algorithm decomposes in two principal steps. First, given a theta null point for $A$ and a subgroup $K$ isotropic for the Weil pairing, we explain how to compute the theta null point corresponding to the quotient abelian vari...

Computing modular Galois representations

Mascot, Nicolas (2012)
Projects: EC | ANTICS (278537)
International audience; We compute modular Galois representations associated with a newform $f$, and study the related problem of computing the coefficients of $f$ modulo a small prime $\ell$. To this end, we design a practical variant of the complex approximations method presented in the book edited by B. Edixhoven and J.-M. Couveignes. Its efficiency stems from several new ingredients. For instance, we use fast exponentiation in the modular jacobian instead of analytic continuation, which g...

Haberland's formula and numerical computation of Petersson scalar products

Cohen , Henri (2012)
Projects: EC | ANTICS (278537)
International audience; We study several methods for the numerical computation of Petersson scalar products, and in particular we prove a generalization of Haberland's formula to any subgroup of finite index G of Gamma = PSL_2 (Z), which gives a fast method to compute these scalar products when a Hecke eigenbasis is not necessarily available.

Improved CRT Algorithm for Class Polynomials in Genus $2$

Lauter , Kristin; Robert , Damien (2012)
Projects: EC | ANTICS (278537)
International audience; We present a generalization to genus~2 of the probabilistic algorithm of Sutherland for computing Hilbert class polynomials. The improvement over the Br{ö}ker-Gruenewald-Lauter algorithm for the genus~2 case is that we do not need to find a curve in the isogeny class whose endomorphism ring is the maximal order; rather, we present a probabilistic algorithm for ''going up'' to a maximal curve (a curve with maximal endomorphism ring), once we find any curve in the right ...
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