ASKSAGE: Sage Q&A Forum - Latest question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Tue, 28 May 2013 05:16:57 -0500elliptic curves in quartic and standard formhttp://ask.sagemath.org/question/8766/elliptic-curves-in-quartic-and-standard-form/ y^2 = a*x^4+b*x^3+c*x^2+d*x+e
is birationally equivalent to an elliptic curve in standard Weierstrass form `y^2=cubic(x)`.
How to I get sage to exhibit/find the birational transformation that accomplishes that?
[I am specifically interested in knowing all about this class of curves:
`8*D*y^2 = (x-2)*(x-1)*(x+1)*(x+2)`
for integer D. I am pretty new to both SAGE and elliptic curves.]Warren D SmithSat, 03 Mar 2012 04:29:02 -0600http://ask.sagemath.org/question/8766/Birational Transformationhttp://ask.sagemath.org/question/10161/birational-transformation/How do I apply a birational transformation x --> 1/x, then clear the denominators. Is there a way I could do that in SAGE?
x, y = QQ['x,y'].gens()
C = Curve(x^2+y^2)
# the code I'm looking for here
$x^2 + y^2 \mapsto 1/x^2 + y^2 \mapsto 1/x^2 + x^2y^2/x^2 \mapsto 1 + x^2y^2$guissmoTue, 28 May 2013 05:16:57 -0500http://ask.sagemath.org/question/10161/How to check two curves on birational equivalence?http://ask.sagemath.org/question/8443/how-to-check-two-curves-on-birational-equivalence/I have two curves, for example hyperelliptic:
y^2 = x^6 + 14*x^4 + 5*x^3 + 14*x^2 + 18
y^2 = x^6 + 14*x^4 + 5*x^3 + 14*x^2 + 5*x + 1
How to check them on birational equivalence (is able one curve be birationally transformed to another?) via Sage?petRUShkaSat, 05 Nov 2011 03:06:30 -0500http://ask.sagemath.org/question/8443/