Robert Coleman and Ken McMurdy with an appendix by Everett W. Howe: Stable reduction of X0(p3), Algebra Number Theory 4 (2010) 357–431, MR 2011k:14022.

(An official version is available online, and McMurdy has posted a preprint version.)

In this paper, Coleman and McMurdy determine stable models of the modular curves X0(p3) for primes p≥13. I provide an appendix that gives a simple proof of the fact that for every prime p≥13 there is a supersingular elliptic curve over Fp with j-invariant different from 0 and from 1728.

The appendix is really just a posting that I made to the NMBRTHRY listserv in 1997. Kevin Buzzard asked for a simple proof for the statement about supersingular curves given above. I answered. Then, in 2005, Coleman and McMurdy asked if they could use my argument in their forthcoming paper. Of course I said yes, and they inserted my NMBRTHRY post as an appendix to their paper.