Study of an Isogeny Class
نویسنده
چکیده
This is a translation of: Etude d’une class d’isogénie, in Variétiés de Shimura et Fonctions L (Ed. L. Breen and J.P. Labesse), Publications Mathématiques de l’Université Paris 7 (1979), 73-81. It is available at www.jmilne.org/math/.
منابع مشابه
Groups of Points on Abelian Varieties over Finite Fields
Fix an isogeny class of abelian varieties with commutative endomorphism algebra over a finite field. This isogeny class is determined by a Weil polynomial fA without multiple roots. We give a classification of groups of k-rational points on varieties from this class in terms of Newton polygons of fA(1− t).
متن کاملOn isogeny classes of Edwards curves over finite fields
We count the number of isogeny classes of Edwards curves over finite fields, answering a question recently posed by Rezaeian and Shparlinski. We also show that each isogeny class contains a complete Edwards curve, and that an Edwards curve is isogenous to an original Edwards curve over IFq if and only if its group order is divisible by 8 if q ≡ −1 (mod 4), and 16 if q ≡ 1 (mod 4). Furthermore, ...
متن کاملDescent by 3-isogeny and 3-rank of quadratic fields
In this paper families of elliptic curves admitting a rational isogeny of degree 3 are studied. It is known that the 3-torsion in the class group of the field defined by the points in the kernel of such an isogeny is related to the rank of the elliptic curve. Families in which almost all the curves have rank at least 3 are constructed. In some cases this provides lower bounds for the number of ...
متن کاملIsogeny Class and Frobenius Root Statistics for Abelian Varieties over Finite Fields
Let I(g, q, N) be the number of isogeny classes of g-dimensional abelian varieties over a finite field Fq having a fixed number N of Fq-rational points. We describe the asymptotic (for q →∞) distribution of I(g, q, N) over possible values of N . We also prove an analogue of the Sato—Tate conjecture for isogeny classes of g-dimensional abelian varieties. 2000 Math. Subj. Class. Primary: 11G25, 1...
متن کاملGroups of Rational Points on Abelian Varieties over Finite Fields
Fix an isogeny class of abelian varieties with commutative endomorphism algebra over a finite field. This isogeny class is determined by a Weil polynomial fA without multiple roots. We give a classification of groups of rational points on varieties from this class in terms of Newton polygons of fA(1− t).
متن کامل