\begin{align*}
\Gamma_1(N) := \left\{
\begin{pmatrix}
a & b \\
c & d
\end{pmatrix}
\in SL_2(\mathbb{Z}) : a \equiv d \equiv 1 \pmod N,\ c \equiv 0 \pmod N
\right\}.
\end{align*}
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Let $\mathbb{H} := \{z \in \mathbb{C} : \operatorname{Im}(z) > 0\}$, with $\Gamma_1(N)$ acting on $\mathbb{H}$ by fractional linear transformations. For $z \in \mathbb{H}$, define the lattice $\Lambda_z := \mathbb{Z}z + \mathbb{Z}$, the complex elliptic curve $E_z := \mathbb{C}/\Lambda_z$, and the point