On the invariants of the quotients of the Jacobian of a curve of genus 2

Abstract : Let C be a curve of genus 2 that admits a non-hyperelliptic involution. We show that there are at most 2 isomorphism classes of elliptic curves that are quotients of degree 2 of the Jacobian of C. Our proof is constructive, and we present explicit formulae, classified according to the involutions of C, that give the minimal polynomial of the j-invariant of these curves in terms of the moduli of C. The coefficients of these minimal polynomials are given as rational functions of the moduli.
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Communication dans un congrès
Serdar Boztas and Igor E. Shparlinski. Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC 14, Nov 2001, Melbourne, Australia. Springer Verlag, 2227, pp.373-386, 2001, Lecture Notes in Computer Science. 〈10.1007/3-540-45624-4_39〉
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Contributeur : Pierrick Gaudry <>
Soumis le : jeudi 2 septembre 2010 - 13:45:53
Dernière modification le : jeudi 10 mai 2018 - 02:06:32
Document(s) archivé(s) le : vendredi 3 décembre 2010 - 02:21:14

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Pierrick Gaudry, Éric Schost. On the invariants of the quotients of the Jacobian of a curve of genus 2. Serdar Boztas and Igor E. Shparlinski. Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC 14, Nov 2001, Melbourne, Australia. Springer Verlag, 2227, pp.373-386, 2001, Lecture Notes in Computer Science. 〈10.1007/3-540-45624-4_39〉. 〈inria-00514434〉

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