$A$ is a $10 \times 10$ nilpotent matrix of order $4$ ($A^4=0$) over $\mathbb C$ with $\operatorname{rank} (A)=6$.
Find all possible Jordan Canonical forms
The nullity of $A$ is $4$ so there are $4$ blocks. the rank is $6$ so the rank of the JCF matrix is also $6$. The minimal polynomial is $\lambda^4$ so there are $4$ blocks.
The options I figured are: $$\operatorname{diag}(J_{4}(0),J_{4}(0),J_1(0),J_1(0)),\\\operatorname{diag}(J_4(0),J_3(0),J_2(0),J_1(0)),\\\operatorname{diag}(J_4(0),J_2(0),J_2(0),J_2(0))$$
Is there anything i'm missing when it comes to analyzing the possible Jordan forms for nilpotent matrices?