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arXiv · 1511.04869

The CM class number one problem for curves of genus $2$

Pinar Kilicer·Marco Streng
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Abstract

The CM class number one problem for elliptic curves asked to find all elliptic curves defined over the rationals with non-trivial endomorphism ring. For genus-2 curves it is the problem of determining all CM curves of genus $2$ defined over the reflex field. We solve the problem by showing that the list given in Bouyer and Streng [LMS J. Comput. Math., 18(1):507{538, 2015] is complete.

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Pinar Kilicer, Marco Streng. 2015-11-16. The CM class number one problem for curves of genus $2$. https://arxiv.org/abs/1511.04869

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