On the frequency of finitely anomalous elliptic curves.

摘要

Given an elliptic curve E over Q , we can then consider E over the finite field Fp. If Np is the number of points on the curve over Fp, then we define ap(E) = p + 1 - Np. We say primes p for which ap( E) = 1 are anomalous. In this paper, we search for curves E so that this happens for only a finite number of primes. We call such curves finitely anomalous. This thesis deals with the frequency of their occurrence and finds several examples.