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Conference Papers Year : 2001

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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Dates and versions

inria-00514434 , version 1 (02-09-2010)

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Pierrick Gaudry, Éric Schost. On the invariants of the quotients of the Jacobian of a curve of genus 2. Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC 14, Nov 2001, Melbourne, Australia. pp.373-386, ⟨10.1007/3-540-45624-4_39⟩. ⟨inria-00514434⟩
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