y^2 = ax^4+bx^3+cx^2+dx+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?
Warren D Smith warren.wds AT gmail.com
Revision history [back]
 | 1 | initial version |
elliptic curves in quartic and standard form
| | 2 | No.2 Revision |
elliptic curves in quartic and standard form
y^2=cubic(x).
How to I get sage to exhibit/find the birational transformation that accomplishes that? Warren D Smith warren.wds AT gmail.com
| | 3 | No.3 Revision |
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: 8Dy^2 = (x-2)(x-1)(x+1)*(x+2) for integer D. I am pretty new to both SAGE and elliptic curves.]
| | 4 | eq formatting |
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:
8Dy^2 8*D*y^2 = (x-2)(x-1)(x+1)*(x+2)
(x-2)*(x-1)*(x+1)*(x+2) for integer D. I am pretty new to both SAGE and elliptic curves.]
| | 5 | retagged |
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.]
