文摘
We obtain a conditional, under the Generalized Riemann Hypothesis, lower bound on the number of distinct elliptic curves E over a prime finite field \(\mathbb{F}_p\) of p elements, such that the discriminant D(E) of the quadratic number field containing the endomorphism ring of E over \(\mathbb{F}_p\) is small. For almost all primes we also obtain a similar unconditional bound. These lower bounds complement an upper bound of F. Luca and I.E. Shparlinski (2007).