Some data collection and analysis of the distribution of Champion Primes for non-CM Elliptic Curves

Author

Alan R. Hahn, Clemson UniversityFollow

Date of Award

8-2018

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematical Sciences

Committee Member

Dr. Kevin James, Committee Chair

Committee Member

Dr. William Bridges

Committee Member

Dr. Hui Xue

Abstract

For a fixed non-singular elliptic curve E given by y² + axy + cy = x³ + bx² + dx + e, the frequency of extremal primes for E up to a given X value is of interest, where an extremal prime p is a prime for which the order of E defined over F_p is a maximum or minimum with respect to Hasse’s Theorem. For CM elliptic curves this distribution is known to not be curve dependent, and in this paper some preliminary work on determining the distribution of such primes for the non -CM case is presented.

Recommended Citation

Hahn, Alan R., "Some data collection and analysis of the distribution of Champion Primes for non-CM Elliptic Curves" (2018). All Theses. 2939.
https://tigerprints.clemson.edu/all_theses/2939