On Rademacher's conjecture: congruence subgroups of genus zero of the modular group

Defining equations of modular curves

“…Moreover, generalizing the above result, we successfully determined Hauptmoduls for all genus 0 congruence subgroups of SL 2 (Z) (up to conjugation) in Chua et al [2]. In this note we will make use of the above functions to construct modular functions that parameterize modular curves.…”

“…From Property (2) in Proposition 2 we see that there are essentially only five distinct E g . In order to fulfill the conditions in Proposition 3 we follow the notation of Fine [6], and set W k = E 4k /E 2k .…”