Singularitie of type j10

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Why the condition $4a^3 + 27\neq0$ in the familie of unimodal singularities $J_{10}$ given by $f_a(x,y)= x^3 + a x^2 y^2 + y^6$. Do I need this condition to prove that this family is 6-$\mathcal{R}$-determined?