sage disagrees with magma for the genus of a curve over number field

[Georgi Guninski]

For this curve over a number field sage claims genus 10 and magma
claims genus 0.

I am pretty sure the curve has infinitely many rationals points.

sage: pr.<Z>=QQ[];K.<v>=NumberField(Z**2-5);Kp.<x,y>=K[];p=y^10 + (1/2*v - 1/2)*x^3*y^5 + (-3/2*v + 3/2)*x*y^5 + (-1/2*v + 3/2);C=Curve(p);C
Affine Curve over Number Field in v with defining polynomial Z^2 - 5 defined by y^10 + (1/2*v - 1/2)*x^3*y^5 + (-3/2*v + 3/2)*x*y^5 + (-1/2*v + 3/2)
sage: C.genus()
10

Is this a bug in sage or magma?

5.3 and 4.3 on linux x86_64

[luisfe]

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.

[Georgi Guninski]

Thank you.

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