denotes the elliptic Group modulo whose elements are and together with the pairs of
Integers with satisfying

(1) 
with and Integers such that

(2) 
Given , define

(3) 
The Order of is given by

(4) 
where is the Legendre Symbol, although this Formula quickly becomes impractical. However, it
has been proven that

(5) 
Furthermore, for a Prime and Integer in the above interval, there exists and such that

(6) 
and the orders of elliptic Groups mod are nearly uniformly distributed in the interval.
© 19969 Eric W. Weisstein
19990525