I often heard that each smooth cubic surface contains even $27$ straight lines, such as this statement. So I use the Mathematica plot the equation with this code:$$\begin{align}1 + 54 x y z - &9 (x + y + z) + 126 (x y + x z + y z) - 9 (x^2 + y^2 + z^2) - \\&189 (x^2 y + x y^2 + x^2 z + y^2 z + x z^2 + y z^2) + 81 (x^3 + y^3 + z^3)=0\end{align}$$
But when I solve a cubic equation, like $x^3 + 3 y^3 + z^3-2 x^2 + 5 x y - x + 7=0$ Now I only just find $3$ lines:
Is this surface not smooth? Or is the theorem wrong? Or am I getting it wrong? How to understand this phenomenon?