Quote:
Originally Posted by akruppa
This is pushing my understanding of elliptic curves... but would a point not on E(p) be on the twist curve? Then it would be clear why you're getting group structure again.
Alex

Are you sure about this?
In the example with:
p=19;
a=14;b=10;
There is a point of order 13.
The twisted curve has order 23 and the original curve has order 17.