We determine the stable models of the modular curves for primes . An essential ingredient is the close relationship between the deformation theories of elliptic curves and formal groups, which was established in the Woods Hole notes of 1964. This enables us to apply results of Hopkins and Gross in our analysis of the supersingular locus.
"Stable reduction of $X_0(p^3)$." Algebra Number Theory 4 (4) 357 - 431, 2010. https://doi.org/10.2140/ant.2010.4.357