"Source: Text/Geometry/CrvCon.text";
"Line: 361";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/CrvCon.text, line: 361
// Example: H130E3 ()
print "Example: H130E3";
ei := GetEchoInput();
SetEchoInput(true);
P2<x,y,z> := ProjectiveSpace(Rationals(), 2);
C0 := Curve(P2, x^2 - 54321*x*y + y^2 - 97531*z^2);
IsNonsingular(C0);
assert $1;
bool, C1 := IsConic(C0);
bool;
assert $1;
C1;
HasRationalPoint(C1);
RationalPoint(C1);
P1<u,v> := ProjectiveSpace(Rationals(), 1);
phi := Parametrization(C1, Curve(P1));
phi;
time RationalPoints(C1 : Bound := 100000);
phi(P1![0, 1]);
phi(P1![1, 1]);
phi(P1![1, 0]);
SetEchoInput(ei);
