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.
© 1996-9 Eric W. Weisstein
1999-05-25