In the Deligne-Rapoport paper entitled "Les schemas de modules de courbes elliptiques" the following is written (I translated in english):

Let $E$ be an elliptic curve with $\Gamma(N)$-level structure defined over $\mathbb{C}((T))$. Let $E'$ be the minimal model of $E$ over $\mathbb{C}[[T]]$. It may happen that $E'$ has bad reduction (i.e. when one reduces modulo $T$). So let $A$ be the neron model of $E'$ over the d.v.r. $\mathbb{C}[[T]]$. Then it seems that the special fiber of $A$ (i.e. when $T=0$) is always isomorphic to $\mathbb{C}^{\times}\times\mathbb{Z}/kN$ for some suitable integer $k$.

**Q: How come this $N$ shows up in the special fiber of $A$ ?**

This is a little bit strange since in the definition of a Neron model no such $N$ appears.