Change of variables?

[jvoight]

prec := 100;
QQ := RationalsExtra(prec);
R<X,Z,T> := PolynomialRing(QQ,3);
G := X^6 - 297/58*X^5*Z + 33/29*X^5*T - 2745/29*X^4*Z^2 - 1989/58*X^4*Z*T + 
        3825/116*X^4*T^2 - 21969/58*X^3*Z^3 - 9369/29*X^3*Z^2*T + 
        58527/232*X^3*Z*T^2 + 1031/116*X^3*T^3 - 19071/29*X^2*Z^4 - 
        27540/29*X^2*Z^3*T + 37359/116*X^2*Z^2*T^2 + 131355/232*X^2*Z*T^3 - 
        43689/232*X^2*T^4 - 14958/29*X*Z^5 - 66195/58*X*Z^4*T - 
        44307/232*X*Z^3*T^2 + 213993/232*X*Z^2*T^3 + 117351/464*X*Z*T^4 - 
        29007/116*X*T^5 - 4212/29*Z^6 - 13851/29*Z^5*T - 39591/116*Z^4*T^2 + 
        33111/116*Z^3*T^3 + 86031/232*Z^2*T^4 - 18*Z*T^5 - 2566/29*T^6;
G := Evaluate(G,[X+Z,Z-T,T]);
C := Curve(Proj(R), G);   
HeuristicEndomorphismDescription(C);

gives error

> HeuristicEndomorphismDescription(C);

HeuristicEndomorphismDescription(
    X: Curve over Rational Field defined by X^6 + 51/58*X^5*Z + 363...
)
HeuristicEndomorphismAlgebra(
    X: Curve over Rational Field defined by X^6 + 51/58*X^5*Z + 363...
)
GeometricEndomorphismRepresentation(
    X: Curve over Rational Field defined by X^6 + 51/58*X^5*Z + 363...
)
PeriodMatrix(
    X: Curve over Rational Field defined by X^6 + 51/58*X^5*Z + 363...
)
PeriodMatrixRetry(
    f: $.1^6 + 51/58*$.1^5*$.2 + 363/58*$.1^5 - 6105/58*$.1^4*$.2^2...,
    g: 4,
    CC: Complex field of precision 110
)
TransformForm(
    f: $.1^6 + 51/58*$.1^5*$.2 + 363/58*$.1^5*$.3 - 6105/58*$.1^4*$...,
    T: [ 2 -1  1  1] [ 2  0  0  1] [ 1 -2  2  0] [-1  0  1  0]
)
In file "/Users/jvoi0135/Dropbox/github/CHIMP/endomorphisms/endomorphisms/magma\
/heuristic/Periods.m", line 31, column 48:
>>     return Evaluate(f, Eltseq(ChangeRing(T, R) * vars));
                                                  ^
Runtime error: Arguments have incompatible degrees

Sorry I don't have time to debug this right now...

[jvoight]

It might just be that the plane curve is singular? But I still think the error is too soon, the Riemann surface code, for example, just needs any cover of the projective line...

[edgarcosta]

This is the same bug as https://github.com/edgarcosta/endomorphisms/issues/76

[jvoight]

Ah, good catch--I checked but saw "number fields" in the title, so assumed that was something else. Closing this one, and will change the title and tag the other one.