Basepoint problem

[jvoight]

> SetVerbose("EndoFind", 2);
> SetVerbose("EndoCheck", 2);
> _<x> := PolynomialRing(Rationals());
> f := x^5 - 3*x^4 + 5*x^3 + 27*x^2 + 18*x;
> X := HyperellipticCurve(f);
> CertifiedEndomorphismAlgebra(X : Geometric := true);

Curve after transformation to standard form:
Hyperelliptic Curve defined by y^2 = x^5 - 3*x^4 + 5*x^3 + 27*x^2 + 18*x over 
Rational Field

Calculating period matrix...
done calculating period matrix.

Finding geometric homomorphisms...
done finding geometric homomorphisms.

Calculating period matrix...
using stored period matrix.

Finding number field defined by endomorphisms...

Number field extended. Current field:
Number Field with defining polynomial x^12 - 2*x^11 + 2*x^10 - 18*x^9 - 27*x^8 -
    40*x^7 + 296*x^6 + 296*x^5 + 164*x^4 + 992*x^3 + 1152*x^2 - 768*x + 256 over
the Rational Field
done finding number field defined by endomorphisms:
Number Field with defining polynomial x^12 - 2*x^11 + 2*x^10 - 18*x^9 - 27*x^8 -
    40*x^7 + 296*x^6 + 296*x^5 + 164*x^4 + 992*x^3 + 1152*x^2 - 768*x + 256 over
the Rational Field

Chosen base point on X:
(1 : 0 : 0)
Chosen base point on Y:
(1 : 0 : 0)

Chosen base point on X:
(1 : 0 : 0)
Chosen base point on Y:
(1 : 0 : 0)

CertifiedEndomorphismAlgebra(
    X: Hyperelliptic Curve defined by y^2 = x^5 - 3*x^4 + 5*x^3 + 2...
)
Correspondence(
    X: Hyperelliptic Curve defined by y^2 = x^5 - 3*x^4 + 5*x^3 + 2...,
    Y: X,
    mor: [* [1/372869376*(257893*$.1^11 - 652057*$.1^10 + 845092*$.1^...
)
CantorFromMatrixAmbientSplit(
    X: Hyperelliptic Curve defined by y^2 = x^5 - 3*x^4 + 5*x^3 + 2...,
    P0: (1 : 0 : 0),
    Y: X,
    Q0: (1 : 0 : 0),
    M: [1/372869376*(257893*$.1^11 - 652057*$.1^10 + 845092*$.1^9 -...
)
InitializeCurve(
    X: X,
    P0: (1 : 0 : 0)
)
In file "/Users/jvoight/Dropbox/github/CHIMP/endomorphisms/endomorphisms/magma/\
puiseux/Initialize.m", line 195, column 21:
>> if AssertNonWP then assert not IsWeierstrassPlace(Place(X ! P0)); end if;
                       ^
Runtime error in assert: Assertion failed

Fixed by running beforehand

> SmallBasePoint(X : NW := true);
[* (1 : 4*$.1 : 1),
    Mapping from: Rational Field to Number Field with defining polynomial t^2 - 
        3 over the Rational Field
    Composition of Mapping from: Rational Field to Number Field with defining 
    polynomial t^2 - 192 over the Rational Field and
    Mapping from: Number Field with defining polynomial t^2 - 192 over the 
    Rational Field to Number Field with defining polynomial t^2 - 3 over the 
    Rational Field
*]

[edgarcosta]

Thank you @jvoight

Keep reporting these