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arXiv · 0802.1886

Abelian Varieties with Prescribed Embedding Degree

David Freeman·Peter Stevenhagen·Marco Streng
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Abstract

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 $A$.

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David Freeman, Peter Stevenhagen, Marco Streng. 2008-02-13. Abelian Varieties with Prescribed Embedding Degree. https://arxiv.org/abs/0802.1886

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