Premium
Prime Divisors of the Number of Rational Points on Elliptic Curves with Complex Multiplication
Author(s) -
Liu YuRu
Publication year - 2005
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609305004558
Subject(s) - mathematics , multiplication (music) , prime (order theory) , complex multiplication , elliptic curve , pure mathematics , arithmetic , algebra over a field , combinatorics
Let E/Q be an elliptic curve. For a prime p of good reduction, let E (F p ) be the set of rational points defined over the finite field F p . Denote by ω(# E (F p )) the number of distinct prime divisors of # E (F p ). For an elliptic curve with complex multiplication, the normal order of ω(# E (F p )) is shown to be log log p . The normal order of the number of distinct prime factors of the exponent of E (F p ) is also studied. 2000 Mathematics Subject Classification 11N37, 11G20.