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Yu-Ru Liu, Prime Divisors of the Number of Rational Points on Elliptic Curves with Complex Multiplication, Bulletin of the London Mathematical Society, Volume 37, Issue 5, October 2005, Pages 658–664, https://doi.org/10.1112/S0024609305004558
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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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