1. In you checking make sure that you have the correct polynomial satisfied 
by the field generator f:

sage: F.<f> = GF(11^2,'f')
sage: f.minpoly()
x^2 + 7*x + 2

2. You can define your curve more simply by

sage: ff2 = EllipticCurve(F,[0,1])

3. The code which computes the generators and group structure uses random 
points on the curve so will not give the same generators in different 
situations (I wrote that code!).  I get

sage: ff2.gens()
[(9 : 9 : 1), (3*f + 9 : 5*f + 1 : 1)]

I would be very surprised if you got points which did not satisfy the curve 
equation since Sage will refuse to construct points on the curve unless 
they do.  You can check manually, of course:

sage: (3*f+9)^3 + 1 == (5*f+1)^2
True
sage: (F(9))^3 + 1 == (F(9))^2
True

John Cremona

On Wednesday, October 1, 2014 8:16:57 AM UTC+1, Padmanabhan Tr wrote:
>
> I am working with Elliptic curve in extended field.  I tried to get points 
> / order in the group.  I have copied a small code set & results from 
> notebook. The points obtained are not in the EC; I have checked it using a 
> Python program I coded for this.  Is it a bug / wrong use of codes by me?
>
> F.<f> = GF(11^2,'f')
> ff2 = EllipticCurve([0+f*0,1+f*0])
> ff2
> Elliptic Curve defined by y^2 = x^3 + 1 over Finite Field in f of size
> 11^2
> fg =ff2.gens()
> fg
> [(8*f : 6*f + 6 : 1), (5*f + 8 : 3*f + 6 : 1)]
>

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