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Prime Divisors of the Number of Rational Points on Elliptic Curves with Complex Multiplication

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2005-ecturan-cm.pdf (117.41 KB)

Date

2005

Authors

Liu, Yu-Ru

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Wiley

Abstract

Let E/Q be an elliptic curve. For a prime p of good reduction, let E(Fp) be the set of rational points defined over the finite field Fp. Denote by ω(#E(Fp)) the number of distinct prime divisors of #E(Fp). For an elliptic curve with complex multiplication, the normal order of ω(#E(Fp)) is shown to be log log p. The normal order of the number of distinct prime factors of the exponent of E(Fp) is also studied. 2000 Mathematics Subject Classification 11N37, 11G20.

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This is the peer reviewed version of the following article: Liu, Y.-R. (2005). Prime divisors of the number of rational points on elliptic curves with complex multiplication. Bulletin of the London Mathematical Society, 37(5), 658–664, which has been published in final form at https://doi.org/10.1112/s0024609305004558. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.

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https://doi.org/10.1112/S0024609305004558
 http://hdl.handle.net/10012/20012

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Waterloo Research