The modified Szpiro conjecture is described in Wikipedia and here and here.

The modified Szpiro conjecture states that: given $\varepsilon > 0$, there exists a constant $C(\varepsilon)$ such that for any elliptic curve $E$ defined over $\mathbb{Q}$ with invariants $c4, c6$ and conductor $f$, we have

$$\max\{ \vert c_4 \vert^3, \vert c_6\vert^2\} \leq C(\varepsilon )\cdot f^{6+\varepsilon } $$

The original Szpiro conjecture requires minimal model, while the modified one appears to doesn't require minimal model.

Does the modified Szpiro conjecture require minimal model?

Does the modified Szpiro conjecture allow $a_1 \ne 0$ and/or $a_3 \ne 0$?

Reference for it and other names?