Discriminants of Complex Multiplication Fields of Elliptic Curves over Finite Fields
Printed: Sep 2007
Igor E. Shparlinski
We show that, for most of the elliptic curves $\E$ over a prime finite
$\F_p$ of $p$ elements, the discriminant $D(\E)$ of the quadratic number
field containing the endomorphism ring of $\E$ over $\F_p$
is sufficiently large.
We also obtain an asymptotic formula for the number of distinct
quadratic number fields generated by the endomorphism rings
of all elliptic curves over $\F_p$.
11G20 - Curves over finite and local fields [See also 14H25]
11N32 - Primes represented by polynomials; other multiplicative structure of polynomial values
11R11 - Quadratic extensions