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Genus two curves covering elliptic curves: a computational approach

2005
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Computational Aspects of Algebraic Curves
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A genus 2 curve C has an elliptic subcover if there exists a degree n maximal covering ψ : C → E to an elliptic curve E. Degree n elliptic subcovers occur in pairs (E, E ). The Jacobian J C of C is isogenous of degree n 2 to the product E × E . We say that J C is (n, n)-split. The locus of C, denoted by Ln, is an algebraic subvariety of the moduli space M 2 . The space L 2 was studied in Shaska/Völklein [32] and Gaudry/Schost [10]. The space L 3 was studied in [26] were an algebraic description

doi:10.1142/9789812701640_0013
fatcat:rnilovvsv5effext2ztkmu7q3i