Explicit models of genus 2 curves with split CM

Details Explicit models of genus 2 curves with split CM Explicit models of genus 2 curves with split CM

2006-12-21

arxiv.org/abs/math/0612666v1

Mathematics

Number Theory

Scientific paper

We outline a general algorithm for computing an explicit model over a number
field of any curve of genus 2 whose (unpolarized) Jacobian is isomorphic to the
product of two elliptic curves with CM by the same order in an imaginary
quadratic field. We give the details and some examples for the case where the
order has prime discriminant and class number one

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