
P2<X,Y,Z>:=ProjectiveSpace(Rationals(),2);
C:=Curve(P2,X^2+Y^2);
Qp:=pAdicField(2);
IsEmpty(C(Qp));
IsEmpty(C(Qp):Smooth);
_<x>:=ext<Rationals()|>;
C:=HyperellipticCurve(3*(x^2+x+1));
bl,pt:=IsEmpty(C(Qp));
C:=HyperellipticCurve(3*(x^2+1));
IsEmpty(C(Qp));


// Bug fixed May 2013
R<x,w,z> := ProjectiveSpace(Rationals(),2);
f := x^6 - 4*x^5*z - 2*x^3*w^2*z - 10*x^4*z^2 - 12*x^2*w^2*z^2 + w^4*z^2 +
56*x^3*z^3 + 14*x*w^2*z^3 + 301*x^2*z^4 + 48*w^2*z^4 + 724*x*z^5 + 660*z^6;
C := Curve(R,f);
assert IsLocallySolvable(C,2 : Smooth := true);

