TY - JOUR

T1 - On primitive points of elliptic curves with complex multiplication

AU - Chen, Yen Mei J.

AU - Yu, Jing

N1 - Funding Information:
Research partially supported by National Science Council, Republic of China. ∗Corresponding author. Department of Mathematics, National Central University, Taoyuan, Taiwan, ROC. E-mail addresses: [email protected] (Y.-M.J. Chen), [email protected] (J. Yu).

PY - 2005/9

Y1 - 2005/9

N2 - 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.

AB - 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.

KW - Complex multiplication

KW - Density

KW - Elliptic curves

KW - Primitive points

UR - http://www.scopus.com/inward/record.url?scp=23844492787&partnerID=8YFLogxK

U2 - 10.1016/j.jnt.2005.02.005

DO - 10.1016/j.jnt.2005.02.005

M3 - 期刊論文

AN - SCOPUS:23844492787

SN - 0022-314X

VL - 114

SP - 66

EP - 87

JO - Journal of Number Theory

JF - Journal of Number Theory

IS - 1

ER -