On the average exponent of CM Elliptic Curves Modulo p

Sungjin Kim

doi:10.1016/j.ffa.2014.07.003

paper

On the average exponent of CM Elliptic Curves Modulo p

arXiv:1207.6652 · doi:10.1016/j.ffa.2014.07.003

Abstract

Let $E$ be an elliptic curve defined over $\Q$ and with complex multiplication by $\mO_K$, the ring of integers in an imaginary quadratic field $K$ . It is known that $E(\F_p)$ has a structure E(\F_p)\simeq \Z/d_p\Z \oplus \Z/e_p\Z. with $d_{p} ∣ e_{p}$ . We give an asymptotic formula for the average order of $e_{p}$ , with improved error term, and upper bound estimate for the average of $d_{p}$ .

7 pages, improvement in Theorem 2, conductor dependence

References in corpus (2)

Cited by in corpus (1)

The average of the first invariant factor for reductions of CM elliptic curves mod $p$