✦ LIBER ✦

On primitive points of elliptic curves with complex multiplication

✍ Scribed by Yen-Mei J. Chen; Jing Yu

Publisher: Elsevier Science
Year: 2005
Tongue: English
Weight: 297 KB
Volume: 114
Category: Article
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2005.02.005

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✦ Synopsis

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 M E,P the set of rational primes such that splits in k, E has good reduction at , and P is a primitive point modulo . Under the generalized Riemann hypothesis, we can determine the positivity of the density of the set M E,P explicitly.

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