Minimal resolution of Atkin-Lehner quotients of X0(N)

Let X-0(N) be the classic modular curve of level N over Z. Let W-M be the Atkin-Lehner involution of X-0(N) associated to a divisor M with (M, N/M) = 1. In this paper an explicit description is given for the minimal resolution over Z[1/6] of the Atkin-Lehner quotient X-0(N)/W-M. As an application a new proof of Deuring's formula on the number of supersingular j-invariants in F-p is given. In certain cases it is also shown that the action of Hecke operators on the component group of the Jacobian of the Atkin-Lehner quotient is Eisenstein. (C) 2009 Elsevier Inc. All rights reserved.