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Action of Modular Correspondences around CM Points

  • Jean-Marc Couveignes
  • Thierry Henocq
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2369)

Abstract

We study the action of modular correspondences in the p-adic neighborhood of CM points. We deduce and prove two stable and efficient p-adic analytic methods for computing singular values of modular functions. On the way we prove a non trivial lower bound for the density of smooth numbers in imaginary quadratic rings and show that the canonical lift of an elliptic curve over \( \mathbb{F}_q \) can be computed in probabilistic time ≪ exp((log q)1/2+ε) under GRH. We also extend the notion of canonical lift to supersingular elliptic curves and show how to compute it in that case.

Keywords

Elliptic Curve Elliptic Curf Isomorphism Class Modular Function Endomorphism Ring 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Jean-Marc Couveignes
    • 1
  • Thierry Henocq
    • 1
  1. 1.Groupe de Recherche en Informatique et Mathématiques du MirailUniversité de Toulouse IIToulouseFrance

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