It is a curve in homogeneous coordinates. You can set z=1 to obtain an affine view of it, and draw it as a regular curve in the plane. Points with z=0 are points at infinity (directions). The two rational points with z=0 that you describe mean that the curve has two asymptotes at 45 and -45 degrees.
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It is a curve in homogeneous coordinates. You can set z=1 to obtain an affine view of it, and draw it as a regular curve in the plane. Points with z=0 are points at infinity (directions). The two rational points with z=0 that you describe mean that the curve has two asymptotes at 45 and -45 degrees.