On Saturday, May 24, 2014 9:18:29 AM UTC-7, Volker Braun wrote:
>
> Its a 4:1 map so you can't invert it...
>

I would find that surprising. For a general plane cubic, there are good 
recipes for getting a 9:1 map to a Weierstrass model in general and a 1:1 
map when a rational point is specified. A 4:1 map is rather unnatural to 
get in that situation. You'd expect that from a y^2=quartic in x model.

Indeed, the map returned is invertible, the inverse being:

[   -12*x*z - 4*y*z,  32*x*z,  x^2 - 28*x*z - 4*y*z]


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