From: jbuddenh@artsci.wustl.edu (Jim Buddenhagen)
Newsgroups: sci.math.research
Subject: Re: elliptic curves
Date: 3 Aug 1995 12:01:42 GMT

Ohn Christian (chohn@vub.ac.be) wrote:
: Let

: a x^3 + b y^3 + c z^3 + d x^2 y + e x^2 z + f y^2 x + g y^2 z + h z^2 x
:   + i z^2 y + k x y z = 0

: be an cubic curve in P^2(C).

: 1) Can one express a "discriminant" D explicitely in the ten
: coefficients a,b,c,d,e,f,g,h,i,k such that the curve is elliptic
: iff D is not zero?

: 2) If so, can one express explicitely the j-invariant of that elliptic
: curve in terms of a,b,c,d,e,f,g,h,i,k?

: For both questions, I mean: *without* reducing the equation of the curve
: first.
       
For computationally oriented elliptic curve questions take a look at
Ian Connell's Elliptic Curve Handbook, chapters 1 and 2 of which are
available (postscript and dvi) by anon ftp at math.mcgill.ca (132.206.150.3)
in directory ftp/pub/ECH1.  I also recommend Ian Connell's Arith of Plane
Ellip. Curves Maple package (APECS).

Although your specific question may not be addressed there is lots of closely
related material.   Please post a summary (or email) if you get useful
answers.
--
Jim Buddenhagen (jb1556@daditz.sbc.com)