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?