Date of Award


Document Type


Degree Name

Master of Science (MS)


Mathematical Sciences

Committee Member

Dr. Kevin James, Committee Chair

Committee Member

Dr. William Bridges

Committee Member

Dr. Hui Xue


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 Fp 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.