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arXiv · 1404.0399

On the distribution of Atkin and Elkies primes for reductions of elliptic curves on average

Igor E. Shparlinski·Andrew V. Sutherland
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Abstract

For an elliptic curve E/Q without complex multiplication we study the distribution of Atkin and Elkies primes l, on average, over all good reductions of E modulo primes p. We show that, under the Generalised Riemann Hypothesis, for almost all primes p there are enough small Elkies primes l to ensure that the Schoof-Elkies-Atkin point-counting algorithm runs in (log p)^(4+o(1)) expected time.

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Igor E. Shparlinski, Andrew V. Sutherland. 2014-04-01. On the distribution of Atkin and Elkies primes for reductions of elliptic curves on average. https://doi.org/10.1112/s1461157015000017

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