The modified Szpiro conjecture is described in 
[Wikipedia](https://en.wikipedia.org/wiki/Szpiro_conjecture)
and [here](http://modular.math.washington.edu/mcs/archive/Fall2001/notes/12-10-01/12-10-01/node2.html) and [here](http://www.encyclopediaofmath.org/index.php/Szpiro%27s_conjecture).

>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?