Bielliptic intermediate modular curves

Daeyeol Jeon; Chang Heon Kim; Andreas Schweizer

doi:10.1016/j.jpaa.2019.05.007

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arXiv · 1709.00510

Bielliptic intermediate modular curves

Daeyeol Jeon·Chang Heon Kim·Andreas Schweizer

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Abstract

We determine which of the modular curves $X_\Delta(N)$, that is, curves lying between $X_0(N)$ and $X_1(N)$, are bielliptic. Somewhat surprisingly, we find that one of these curves has exceptional automorphisms. Finally we find all $X_\Delta(N)$ that have infinitely many quadratic points over $\mathbb{Q}$.

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Daeyeol Jeon, Chang Heon Kim, Andreas Schweizer. 2017-09-02. Bielliptic intermediate modular curves. https://doi.org/10.1016/j.jpaa.2019.05.007

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