Author(s)： Shinnya Okumura

J. Math-for-Ind. 5B (2013) 111-128.

• File： JMI2013B-4.pdf (511KB)

Abstract
We present a conjecture refining those of Koblitz and Zywina on the primality and divisibility of the number of $\mathbb{F}_{p}$-valued points of elliptic curves when $p$ varies satisfying a congruence condition. We give also numerical data which support our conjecture.

Keyword(s).　 elliptic curves modulo $p$, Galois representations, Koblitz's conjecture, Zywina's conjecture