Calculating Root Numbers of Elliptic curves over Q.
Cohomologie des courbes elliptiques
Combinatoire des arbres planaires et arithmétique des courbes hyperelliptiques
Le but de cet article est de proposer une nouvelle méthode pour des études dans le cadre de la théorie des “dessins d’enfants” de A. Grothendieck de certaines questions concernant l’action du groupe de Galois absolu sur l’ensemble des arbres planaires.On définit l’application qui associe à chaque arbre planaire à arêtes, une courbe hyperelliptique avec un point de -division. Cette construction permet d’établir un lien entre la théorie de la torsion des courbes hyperelliptiques et celle des “dessins...
Combinatorial aspects of elliptic curves.
Companion forms and Kodaira-Spencer theory.
Complete systems of addition laws on Abelian varieties.
Complex Hyperbolic Surfaces of Abelian Type
2000 Mathematics Subject Classification: 11G15, 11G18, 14H52, 14J25, 32L07.We call a complex (quasiprojective) surface of hyperbolic type, iff – after removing finitely many points and/or curves – the universal cover is the complex two-dimensional unit ball. We characterize abelian surfaces which have a birational transform of hyperbolic type by the existence of a reduced divisor with only elliptic curve components and maximal singularity rate (equal to 4). We discover a Picard modular surface of...
Computation of the Selmer groups of certain parametrized elliptic curves
Computing integral points on Mordell's elliptic curves.
Concernant la relation de distribution satisfaite par la fonction ...associé à un réseau complexe.
Congruences entre séries d'Eisenstein, dans le cas supersingulier.
Congruences for Special Values of L-functions of Elliptic Curves with Complex Multiplication.
Constructive and non-constructive methods of proofs of irrationality and transcendency and algebraic independence of periods of abelian varieties
Correction and remarks concerning quasifunctions on elliptic curves.
Correction to the paper "Explicit form of the modular equation".
Counting points of small height on elliptic curves
Counting points on elliptic curves over finite fields
We describe three algorithms to count the number of points on an elliptic curve over a finite field. The first one is very practical when the finite field is not too large ; it is based on Shanks's baby-step-giant-step strategy. The second algorithm is very efficient when the endomorphism ring of the curve is known. It exploits the natural lattice structure of this ring. The third algorithm is based on calculations with the torsion points of the elliptic curve [18]. This deterministic polynomial...
Courbes de Weil et courbes super-singulières.
Courbes de Weil semi-stables de discriminant une puissance m-ième.
Courbes Elliptiques et 2 - Extensions Abeliennes