Bill Allombert on Wed, 05 Apr 2017 17:08:24 +0200 |
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Re: your mail |
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.