Thank you.

magma found parametrization too, so the problem is in sage/singular.
(probably you mean "genus zero", not one). 

On Mon, Oct 01, 2012 at 06:23:04AM -0700, luisfe wrote:
> Maple agrees with magma here and says that the genus is one. Moreover, it 
> computes a parametrization of the curve 
> 
> sage: P=(((v + 2)*x^10 + (v - 2))/x^5, ((1/2*v - 3/2))/x^3)
> sage: p(x=P[0],y=P[1])
> 0
> 
> 
> The problem seems to be in singular.
> 
> sage: I = Ideal(p)
> sage: I.genus()
> 10
> 
> If one looks at the documentation, p.geometric_genus?? it is said that it 
> only works for prime fields. The documentation could be clearer for genus 
> and I think that the method should raise an exception instead of giving a 
> wrong answer.

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