"Source: Text/Geometry/CrvHyp.text";
"Line: 4143";
"Date: Thu Aug 18 16:02:10 2022";
"Main: Thu May 25 10:02:38 2023";
// original file: Text/Geometry/CrvHyp.text, line: 4143
// Example: H134E28 ()
print "Example: H134E28";
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);
