The CM class number one problem for curves of genus 2

Pınar Kılıçer 1, 2 Marco Streng 2
1 LFANT - Lithe and fast algorithmic number theory
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
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–Streng [3, Tables 1a, 1b, 2b, and 2c] is complete.
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Submitted on : Tuesday, December 29, 2015 - 12:49:54 PM
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Pınar Kılıçer, Marco Streng. The CM class number one problem for curves of genus 2. 2015. ⟨hal-01248630⟩

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