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) sage: C.genus() 10 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 curveĀ 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. |

Re: sage disagrees with magma for the genus of a curve over number field | Georgi Guninski | 10/1/12 6:47 AM | Thank you.
magma found parametrization too, so the problem is in sage/singular. (probably you mean "genus zero", not one). |