Re: your mail

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On Wed, Apr 05, 2017 at 07:12:36PM +0430, Benyamin Gholami wrote:
> is it possible to transform arbitrary curve in weierstrass form to a
> quartic so that the coefficients becomes smaller? the inverse is possible:
> , I.Connell's "elliptic curve handbook". but i announced that the descent
> method for sage and mwrank use this trick to decrease the coeffs. in brief,
> i just want to put the curve in the form witth smaller coeffs
> thaks

The curve 
y^2 = x^3+a*x+b
is isomorphic to
y^2 = b*x^4+a*x^3+x

(via (x->1/x, y->y/x^2))
then you can use the fonction redquartic in Denis Simon ellQ.gp script
to reduce the quartic.

Cheers,
Bill.