%0 Journal Article
%T Abelian Varieties with Prescribed Embedding Degree
%A David Freeman
%A Peter Stevenhagen
%A Marco Streng
%J Mathematics
%D 2008
%I arXiv
%X We present an algorithm that, on input of a CM-field $K$, an integer $k\ge1$, and a prime $r \equiv 1 \bmod k$, constructs a $q$-Weil number $\pi \in \O_K$ corresponding to an ordinary, simple abelian variety $A$ over the field $\F$ of $q$ elements that has an $\F$-rational point of order $r$ and embedding degree $k$ with respect to $r$. We then discuss how CM-methods over $K$ can be used to explicitly construct $A$.
%U http://arxiv.org/abs/0802.1886v1