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Canadian Number Theory Association X Meeting (CNTA X)
July 13-18, 2008
University of Waterloo
Waterloo, Ontario, Canada

Organizers
Kevin Hare (Waterloo, Wentang Kuo (Waterloo), Yu-Ru Liu (Waterloo), David McKinnon (Waterloo), Michael Rubinstein (Waterloo), Cam Stewart (Waterloo)

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On divisors of the number of points on an elliptic curve mod p
by
Amir Akbary
University of Lethbridge

For a CM elliptic curve E defined over the rationals, we study the density of primes p for which the number of points on the reduction mod p of E has a divisor in a given (short) interval.

As an application, we investigate that for a free subgroup of the Mordell-Weil group of E, how the order of the reduction of this subgroup mod p varies as p goes to infinity. We discuss some results regarding the lower bound on the size of the reduced subgroup.

Date received: April 16, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawl-23.