I was reading de Weger's paper on bounding the cardinality of the Tate-Shafarevich group and in lemma 1 (pg 111), he claims that for any $n \in \mathbb{N}$, we have that $ c(n) << N^{((log \; 3 / 3)(1+\epsilon))/ log \; log \; n)}. $ where $c(n)$ is the product of the exponents of the prime decomposition of $n$.
This is confusing however as in page 108, he defines $N$ as the conductor of an elliptic curve over $\mathbb{Q}$, and he doesn't seem to redefine it anywhere else.
Following his proof I computed that $ c(n) < n^\delta exp\left(-\dfrac{log \; 3}{3}+\delta \; log \; n\right) $ where $ \delta = \dfrac{\frac{log \; 3}{3}(1 + \frac{\epsilon}{2})}{log \; log \; n}. $
So my question is if this is indeed a typo or is there some connection here between $c(n)$ and $N$ that I am indeed missing here?
Also it is indeed a typo and if $ c(n) < n^\delta exp\left(-\dfrac{log \; 3}{3}+\delta \; log \; n\right) $ then how does the result follow for $n$ sufficiently large?