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arXiv · 1106.1884

Abelian surfaces admitting an (l,l)-endomorphism

Reinier Broker·Kristin Lauter·Marco Streng
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Abstract

We give a classification of all principally polarized abelian surfaces that admit an $(l,l)$-isogeny to themselves, and show how to compute all the abelian surfaces that occur. We make the classification explicit in the simplest case $l=2$. As part of our classification, we also show how to find all principally polarized abelian surfaces with multiplication by a given imaginary quadratic order.

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Reinier Broker, Kristin Lauter, Marco Streng. 2013-02-12. Abelian surfaces admitting an (l,l)-endomorphism. https://arxiv.org/abs/1106.1884

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