Saddle or Minimum?

A toy two-parameter loss surface is

$L(x,y) = x^3 + y^3 - 3xy$

Find every critical point of $L$, then classify each one with the second-derivative test

$D = L_{xx}L_{yy} - (L_{xy})^2$

where $D < 0$ means a saddle point, and $D > 0$ means a local minimum or maximum depending on the sign of $L_{xx}$.

Which description of this landscape is correct?