#### Date of Award

5-2010

#### Document Type

Open Access Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Degree Program

Mathematics

#### First Advisor

Tom Weston

#### Second Advisor

Farshid Hajir

#### Third Advisor

Siman Wong

#### Subject Categories

Mathematics | Statistics and Probability

#### Abstract

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.

#### Recommended Citation

Ridgdill, Penny Catherine, "On the Frequency of Finitely Anomalous Elliptic Curves" (2010). *Open Access Dissertations*. 238.

https://scholarworks.umass.edu/open_access_dissertations/238