On the Frequency of Finitely Anomalous Elliptic Curves

On the Frequency of Finitely Anomalous Elliptic Curves

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...

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Main Author: Ridgdill, Penny Catherine
Format: Others
Published: ScholarWorks@UMass Amherst 2010
Subjects:
Anomalous Primes
Elliptic Curve Cryptography
Elliptic Curves
Galois Representations
Number Theory
Mathematics
Statistics and Probability
Online Access:https://scholarworks.umass.edu/open_access_dissertations/238
https://scholarworks.umass.edu/cgi/viewcontent.cgi?article=1218&context=open_access_dissertations
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spelling ndltd-UMASS-oai-scholarworks.umass.edu-open_access_dissertations-12182020-12-02T14:39:15Z On the Frequency of Finitely Anomalous Elliptic Curves Ridgdill, Penny Catherine 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. 2010-05-01T07:00:00Z text application/pdf https://scholarworks.umass.edu/open_access_dissertations/238 https://scholarworks.umass.edu/cgi/viewcontent.cgi?article=1218&context=open_access_dissertations Open Access Dissertations ScholarWorks@UMass Amherst Anomalous Primes Elliptic Curve Cryptography Elliptic Curves Galois Representations Number Theory Mathematics Statistics and Probability
collection NDLTD
format Others
sources NDLTD
topic Anomalous Primes
Elliptic Curve Cryptography
Elliptic Curves
Galois Representations
Number Theory
Mathematics
Statistics and Probability
spellingShingle Anomalous Primes
Elliptic Curve Cryptography
Elliptic Curves
Galois Representations
Number Theory
Mathematics
Statistics and Probability
Ridgdill, Penny Catherine
On the Frequency of Finitely Anomalous Elliptic Curves
description 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.
author Ridgdill, Penny Catherine
author_facet Ridgdill, Penny Catherine
author_sort Ridgdill, Penny Catherine
title On the Frequency of Finitely Anomalous Elliptic Curves
title_short On the Frequency of Finitely Anomalous Elliptic Curves
title_full On the Frequency of Finitely Anomalous Elliptic Curves
title_fullStr On the Frequency of Finitely Anomalous Elliptic Curves
title_full_unstemmed On the Frequency of Finitely Anomalous Elliptic Curves
title_sort on the frequency of finitely anomalous elliptic curves
publisher ScholarWorks@UMass Amherst
publishDate 2010
url https://scholarworks.umass.edu/open_access_dissertations/238
https://scholarworks.umass.edu/cgi/viewcontent.cgi?article=1218&context=open_access_dissertations
work_keys_str_mv AT ridgdillpennycatherine onthefrequencyoffinitelyanomalousellipticcurves
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