Paul Duncan on Mon, 07 Apr 2003 18:05:22 +0100

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Elliptic Curves


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?

Thank you in advance for your help.