Date of Award

5-2012

Document Type

Thesis

Degree Name

Master of Science (MS)

Legacy Department

Mathematical Science

Advisor

James, Kevin

Committee Member

Calkin , Neil

Committee Member

Brown , James

Abstract

Let Ea,b be the elliptic curve y2 = x3 + ax + b over Fp. A well known result of Hasse states that over Fp
(p+1) - 2p½ ≤ #Ea,b ≤ (p+1)+2p½
If #Ea,b = (p+1) + floor(2p½) over Fp and Ea,b is nonsingular, then we call p a champion prime for Ea,b. We will discuss methods for finding champion primes for elliptic curves. In addition, we will show that the set of elliptic curves which have a champion prime has density one.

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