Champion Primes For Elliptic Curves

Author

Jason Hedetniemi, Clemson UniversityFollow

Date of Award

5-2012

Document Type

Thesis

Degree Name

Master of Science (MS)

Legacy Department

Mathematical Science

Committee Chair/Advisor

James, Kevin

Committee Member

Calkin , Neil

Committee Member

Brown , James

Abstract

Let E_a,b be the elliptic curve y2 = x3 + ax + b over F_p. A well known result of Hasse states that over F_p
(p+1) - 2p½ ≤ #E_a,b ≤ (p+1)+2p½
If #E_a,b = (p+1) + floor(2p½) over F_p and E_a,b is nonsingular, then we call p a champion prime for E_a,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.

Recommended Citation

Hedetniemi, Jason, "Champion Primes For Elliptic Curves" (2012). All Theses. 1339.
https://tigerprints.clemson.edu/all_theses/1339