"Source: Text/Geometry/CrvHyp.text";
"Line: 2257";
"Date: Fri Sep 26 09:12:34 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/CrvHyp.text, line: 2257
// Example: H137E13 ()
print "Example: H137E13";
ei := GetEchoInput();
SetEchoInput(true);
_<x> := PolynomialRing(Rationals());
C := HyperellipticCurve(x^6-3*x-1);
C;
J := Jacobian(C);
J;
ptsC := Points(C : Bound := 100);  
ptsC;
ptsJ := [ ptsC[i] - ptsC[1] : i in [2,3,4] ];
ptsJ;
pt1 := elt< J | [1,x^3], 2 >;
pt1 eq ptsJ[1]; 
assert $1;
pt1 := J! [1,x^3];
pt1; pt1 eq J!0;
SetEchoInput(ei);
