Karim BELABAS on Wed, 16 Apr 2003 19:46:23 +0200 (MEST)


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Re: Elliptic Curves 

On Mon, 7 Apr 2003, Paul Duncan wrote:
> I am using PARI-2.1.4 and am working with elliptic curves. According
> to the PARI 2.1.4 manual (section 3.5), the 'roots' member function
> applied to the output of ellinit gives the 'roots of the associated
> Weierstrass equation'.  Am I correct in believing that the associated
> Weierstrass equation referred to here is g(x) = 0 where
>   (y - ax - b)^2 = g(x)
> is obtained by completing the square on the left hand side of the
> general Weierstrass model for the elliptic curve?

Quite correct.

Cheers,

    Karim.
-- 
Karim Belabas                     Tel: (+33) (0)1 69 15 57 48
Dép. de Mathématiques, Bât. 425   Fax: (+33) (0)1 69 15 60 19
Université Paris-Sud              http://www.math.u-psud.fr/~belabas/
F-91405 Orsay (France)            http://www.parigp-home.de/  [PARI/GP]