# 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.]