On the Invariants of the Quotients of the Jacobian of a Curve of Genus 2

  • P. Gaudry
  • É. Schost
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2227)

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • P. Gaudry
    • 1
  • É. Schost
    • 2
  1. 1.LIXÉcole polytechniquePalaiseauFrance
  2. 2.Laboratoire GAGE, UMS MEDICISÉcole polytechniquePalaiseauFrance

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