On primitive points of elliptic curves with complex multiplication
Journal
Journal of Number Theory
Journal Volume
114
Journal Issue
1
Pages
66-87
Date Issued
2005
Author(s)
Abstract
Let E be an elliptic curve defined over ℚ and P ∈ E(ℚ) a rational point of infinite order. Suppose that E has complex multiplication by an order in the imaginary quadratic field k. Denote by ME,P the set of rational primes ℓ such that ℓ splits in k, E has good reduction at ℓ, and P is a primitive point modulo ℓ. Under the generalized Riemann hypothesis, we can determine the positivity of the density of the set ME,P explicitly. © 2005 Elsevier Inc. All rights reserved.
Type
journal article