Twisted cubic
= Twisted cubic
{wiki}
The twisted cubic is the image of
$$
[s:t]\mapsto[s^3:s^2t:st^2:t^3]
$$
in $\mathbb P^3$. Its ideal is generated by the three $2\times2$ minors of
$$
\begin{pmatrix}x_0&x_1&x_2\\x_1&x_2&x_3\end{pmatrix},
$$
and it has degree three.