Some design comments:

sage: R.<x,y,z> = QQ[] 
> sage: f = 3*y^2*x-y^2*z-2*x*y*z+y*z^2+2*x^3-2*x^2*z 
> sage: e = EllipticCurve_from_cubic(f,[0,0,1]) 
> sage: e 
> Scheme morphism: ...
>
 
This is not ideal naming. The command reads like you'd be asking for an 
elliptic curve, but a morphism is returned in its place. Sure, via 
e.codomain() the elliptic curve can be retrieved too, but shouldn't the 
routine be named ellipticcurve_transformation_from_cubic instead, or 
something like that?

sage: e.inverse()


The inverse is there because it's explicitly included upon creation (that's 
good!). It would be nice to have a routine to compute the inverse just from 
the equations as well, though.
 
Similarly, it would be nice to have routines that return birational maps to 
Weierstrass forms for other (all ?) cases of genus 1 curves with a point.

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