defining elliptic curves over a finite field

["McLaughlin, James (MATH)" <jmclaughlin@wcupa.edu>]

How do I get pari to define an elliptic curve over a finite field F_p (say F_5)?

The instructions for ellinit have nothing to say about this. The manual several talks about curves being defined over a prime field F_p, but does not actually say how to do it.

 

Example: y^2=x^3+x+1

I do            ec=ellinit([0,0,0,1,1])

If I do  ellad(ec,[0,1],[01])

the output is [1/4,-9/8] (so the arithmetic appears to be over Q).

 

How can I define the curve so the output treats the curve as being over F_5 and outputs [4,2]?

 

Thanks,

 

Jimmy Mc Laughlin