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Computational Aspects of Algebraic Curves
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  and Gaudry/Schost . The space L 3 was studied in  were an algebraic descriptiondoi:10.1142/9789812701640_0013 fatcat:rnilovvsv5effext2ztkmu7q3i