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On the distribution of Atkin and Elkies primes for reductions of elliptic curves on average
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.Comment: 20 pages, to appear in LMS J. Comput. Mat
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