|sage disagrees with magma for the genus of a curve over number field||Georgi Guninski||9/30/12 1:25 AM|
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)
Is this a bug in sage or magma?
5.3 and 4.3 on linux x86_64
|Re: sage disagrees with magma for the genus of a curve over number field||luisfe||10/1/12 6:23 AM|
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)
The problem seems to be in singular.
sage: I = Ideal(p)
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.
|Re: sage disagrees with magma for the genus of a curve over number field||Georgi Guninski||10/1/12 6:47 AM|
magma found parametrization too, so the problem is in sage/singular.
(probably you mean "genus zero", not one).