Date of Award
Master of Science (MS)
Dr. Kevin James, Committee Chair
Dr. William Bridges
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.
Hahn, Alan R., "Some data collection and analysis of the distribution of Champion Primes for non-CM Elliptic Curves" (2018). All Theses. 2939.