I tried to convert
2*x*y^2 + 2*a5*t*x*y - x^2 + (2*a4 - 8*t^3)*x - 1,
where a4, a5, and t are some complex parameters (which I would like to
keep as undetermined parameters), to Weierstrass normal form using
Nagell's algorithm and was not quite successful since some steps near
the end do not finish in a reasonable time (i.e. a few minutes). It is
possible that I have done some mistakes, since I didn't really tested
my code yet, but Jacob Lewis told me that this algorithm isn't very
fast anyway.

As far as I can tell, Sage can do this conversion using MAGMA, but
only over rational field. Can anyone recommend an efficient way of
doing such a conversion with symbolic coefficients? Or, perhaps, it is
already done and I just cannot find the proper function?

Thank you!
Andrey
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