"Source: Text/Geometry/CrvHyp.text";
"Line: 4196";
"Date: Fri Sep 26 09:12:34 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/CrvHyp.text, line: 4196
// Example: H137E28 ()
print "Example: H137E28";
ei := GetEchoInput();
SetEchoInput(true);
_<x> := PolynomialRing(Rationals());
for a := 1 to 50 do 
   if a mod 3 eq 1 then
      Ca :=  HyperellipticCurve( 3*(x^6-x^2+a) ); 
      assert IsDeficient(Ca,3);  
         // (This causes a failure if our assertion is wrong.)
      if not HasSquareSha(Jacobian(Ca)) then print Ca; end if;
   end if;
end for;
C7 :=  HyperellipticCurve( 3*(x^6-x^2+7) );
J := Jacobian(C7);
#TwoTorsionSubgroup(J);
assert $1 eq 1;
#TwoSelmerGroup(J);
assert $1 eq 2;
RankBound(J);
assert $1 eq 0;
SetEchoInput(ei);
