  Certain identities of Ramanujan may be succinctly expressed in terms of the
rational function w_N(g) = w_N(f) - 1/w_N(f) on the modular curve X_0(N), where
f is a certain modular unit on the Nebentypus cover X_\chi(N) introduced by Ogg
and Ligozat for N prime congruent to 1 (mod 4) and w_N is the Fricke
involution. These correspond to levels N = 5, 13, where the genus of X_0(N) is
zero. In this paper we produce some analogs of these identities for each w_N(g)
such that X_0(N) has genus 1, 2, and also for each h = g + w_N(g) such that the
Atkin-Lehner quotient X_0+(N) has genus 1, 2. We also found that if n is the
degree of the field of definition F of the non-trivial zeros of the latter,
then the degree of the normal closure of F over Q is the n-th solution of
Singmaster's Problem.
