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. 



Neron models of elliptic curves with level N structure?
Roughly speaking, the N-torsion defined over the base injects into the Neron model (in characteristic 0), so the special fiber of the Neron model needs to have a subgroup isomorphic to Z/NZ x Z/NZ, since by assumption there is full level N structure. The special fiber (since there's bad reduction) has the form C^\* x F, where F is a finite cycle group. So F contains an N-torsion element, which means F = Z/kN.


