We show that, for most of the elliptic curves E over a prime finite field double script F signp of p elements, the discriminant D(E) of the quadratic number field containing the endomorphism ring of E over double script F signp 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 double script F signp.
|Number of pages||9|
|Journal||Canadian Mathematical Bulletin|
|Publication status||Published - Sep 2007|