I am trying to solve the following problem:
Find an elliptic curve over F101 with 103 points.
I know all of the equations when needing to find alpha, and beta and all that when I am given two points P and Q on an already given Elliptic Curve, however dont know how to go about finding a specific Elliptic Curve with a certain amount of points.
Using a theorem: I know that if P is a prime (101 is prime) and N (103) is an integer satisfying
|N-(p+1)|≤ 2√p
This holds so I know there exists an elliptic Curve E mod p with exactly N points. I just dont know how to find this specific curve E
Thanks