Showing $E_4(z)$ and $E_6(z)$ are algebraically independent over $\mathbb{C}$

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Let

$E_4(z)= - \frac{B_4}{8}+ \sum_{n=1}^\infty \sigma_3(n) q^n$

and

$E_6(z)= - \frac{B_6}{12}+ \sum_{n=1}^\infty \sigma_5(n) q^n$

How does one show they are algebraically independant over $\mathbb{C}$ ?