I am trying to classify the equilibrium point of this system
x' = $-2xy$
y' = $-3x^2 -y^2 + 4$
When I find the equilibrium points, I get $$(0,0) , (0,-2), (\frac{-2}{\sqrt3},0), (\frac{2}{\sqrt3},0)$$
The Jacobian matrix gives $$ \begin{bmatrix} -2y & -2x \\ -6x & -2y \\ \end{bmatrix} $$
So for equilibrium point (0,0), I get $$ \begin{bmatrix} 0 & 0 \\ 0 & 0 \\ \end{bmatrix} $$
Can I conclude that the system is nonhyperbolic at this point? Or there a classification for this?