The AGM-X0(N) Heegner Point Lifting Algorithm and Elliptic Curve Point Counting

  • David R. Kohel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2894)


We describe an algorithm, AGM-X 0(N), for point counting on elliptic curves of small characteristic p using p-adic lifts of their invariants associated to modular curves X 0(N). The algorithm generalizes the contruction of Satoh [10], SST [11], and Mestre [9]. We describe this method and give details of its implementation for characteristics 2, 3, 5, 7, and 13.


Elliptic curve cryptography modular curves point counting 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • David R. Kohel
    • 1
  1. 1.School of Mathematics and StatisticsUniversity of SydneyAustralia

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