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Journal Articles Research in Number Theory Year : 2023

The CM class number one problem for curves of genus 2

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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hal-01248630 , version 1 (29-12-2015)

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Pınar Kılıçer, Marco Streng. The CM class number one problem for curves of genus 2. Research in Number Theory, 2023, 9 (1), pp.article 15. ⟨10.1007/s40993-022-00417-7⟩. ⟨hal-01248630⟩
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