 Level-two modular curve

The quotient $\mathbb{H}/\Gamma (2)$ is a genus-zero Riemann surface with three cusps and no elliptic Möbius transformations, hence is biholomorphic to $\mathbb{C}\setminus \{0,1\}$. The integer level-two principal congruence subgroup has projective index six; reduction modulo two gives three cusp classes.