(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
*X*_{0}(*p*^{3}) 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 **F***p* 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.