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2012-03-03 11:29:02 +0100 asked a question 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.]