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Curves of genus 2 with real multiplication by a square root of 5

Abstract:

Our aim in this work is to produce equations for curves of genus 2 whose Jacobians have real multiplication (RM) by $\mathbb{Q}(\sqrt{5})$, and to examine the conjecture that any abelian surface with RM by $\mathbb{Q}(\sqrt{5})$ is isogenous to a simple factor of the Jacobian of a modular curve $X_0(N)$ for some $N$. To this end, we review previous work in this area, and are able to use a criterion due to Humbert in the last century to produce a family of curves of genus 2 with RM by $\mathb...

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Publication date:
1998
URN:
uuid:7dca2555-b555-4849-9640-3770ecbe3f94
Local pid:
oai:eprints.maths.ox.ac.uk:32

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