Let b ≥ 2 be an integer and let E/ q be a fixed elliptic curve. In this paper, we estimate the number of primes p ≤ x such that the number of points nE(p) on the reduction of E modulo p is a base b prime or pseudoprime. In particular, we improve previously known bounds which applied only to prime values of nE(p).
|Number of pages||10|
|Journal||Mathematical Proceedings of the Cambridge Philosophical Society|
|Publication status||Published - May 2009|
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Corrigendum can be found in Mathematical Proceedings of the Cambridge Philosophical Society, Volume 152(3), 571, http://dx.doi.org/10.1017/S0305004111000399.