"Source: Text/Geometry/CrvHyp.text";
"Line: 4963";
"Date: Fri Sep 26 09:12:34 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/CrvHyp.text, line: 4963
// Example: H137E35 ()
print "Example: H137E35";
ei := GetEchoInput();
SetEchoInput(true);
_<x> := PolynomialRing(Rationals());
C := HyperellipticCurve(x^6+x^2+2);
ptsC := Points(C : Bound:=1000); ptsC;
J := Jacobian(C);
RankBound(J);
assert $1 eq 1;
PJ1 := J! [ ptsC[3], ptsC[1] ]; 
Order(PJ1);
assert $1 eq 8;
PJ2 := J! [ ptsC[5], ptsC[1] ]; 
Order(PJ2);
assert $1 eq 0;
all_pts := Chabauty(PJ2); all_pts;
okay := all_pts eq Chabauty(12*PJ2);
assert okay; // Check that it is okay
BadPrimes(C);
Chabauty(PJ2, 3);
SetEchoInput(ei);
