In this work we use elementary methods to discuss the question of the minimal number of points with bad reduction over $\pl$ for elliptic curves $E/k(T)$ which are non-constant, respectively have non-constant $j$-invariant.
Johannes Sprang. "Minimal number of points with bad reduction for elliptic curves overP1." Rocky Mountain J. Math. 43 (6) 2017 - 2032, 2013. https://doi.org/10.1216/RMJ-2013-43-6-2017