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$X_1(N)$ is the modular curve $X_H$ for $H\le \GL_2(\widehat\Z)$ the inverse image of $\begin{pmatrix} 1 & * \\ 0 & * \end{pmatrix} < \GL_2(\Z/N\Z)$. As a moduli space it parameterizes pairs $(E,P)$, where $E$ is an elliptic curve over $k$, and $P \in E[N](k)$ is a point of exact order $N$.

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  • Review status: beta
  • Last edited by John Voight on 2023-11-26 23:05:58
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