ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Mon, 28 Sep 2015 12:53:15 +0200Compute $j$-invariant of elliptic curve in non-Weierstrass form with arbitrary coefficientshttps://ask.sagemath.org/question/29632/compute-j-invariant-of-elliptic-curve-in-non-weierstrass-form-with-arbitrary-coefficients/ One can compute the $j$-invariant of an elliptic curve not in Weierstrass form in Sage via the following (where the curve $ x+x^2+y-x^2y-xy^2+x^2y^2=0 $ -- not in Weierstrass form -- is used as an example):
x,y = polygen(QQ,'x,y')
E = Jacobian(x+x^2+y-x^2*y-x*y^2+x^2*y^2)
E.j_invariant()
If we include numerical coefficients of the various terms, this still works. However, I would like Sage to compute the j-invariant of such curves in non-Weierstrass form with arbitrary coefficients, e.g. $ax+bx^2+cy-dx^2y-exy^2+fx^2y^2$. Is this possible? I tried including the line:
var('a,b,c,d,e,f')
But got an error. Can anyone help? Thanks!
JamesReadMon, 28 Sep 2015 12:53:15 +0200https://ask.sagemath.org/question/29632/Finding Cremona label for Tunnell's y^2-x^3-n^2xhttps://ask.sagemath.org/question/9122/finding-cremona-label-for-tunnells-y2-x3-n2x/When I enter
E = EllipticCurve([-n^2,0]); E;E.label()
Sage gives an error that I have an unsupported operand type. I assume the problem is that I have not defined the variable 'n', which is a square free integer, but how does one do this? Any help would be greatly appreciated!!memory13Mon, 02 Jul 2012 11:20:30 +0200https://ask.sagemath.org/question/9122/