Date of Award
Master of Science (MS)
Calkin , Neil
Brown , James
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.
Hedetniemi, Jason, "Champion Primes For Elliptic Curves" (2012). All Theses. 1339.