|Bill Allombert on Wed, 09 Nov 2011 18:33:43 +0100|
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|Re: defining elliptic curves over a finite field|
On Wed, Nov 09, 2011 at 04:51:50PM +0000, McLaughlin, James (MATH) wrote: > 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],) > 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]? You need to give coefficients in F_5. Try ec=ellinit([0,0,0,1,1]*Mod(1,5)) Cheers, Bill.