Bielliptic intermediate modular curves

Daeyeol Jeon; Chang Heon Kim; Andreas Schweizer

doi:10.1016/j.jpaa.2019.05.007

Bielliptic intermediate modular curves

Number Theory 2019-08-19 v2 Algebraic Geometry

Authors: 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 $\mathbb{Q}$ .

Keywords

elliptic curves algebraic curves curves

Cite

@article{arxiv.1709.00510,
  title  = {Bielliptic intermediate modular curves},
  author = {Daeyeol Jeon and Chang Heon Kim and Andreas Schweizer},
  journal= {arXiv preprint arXiv:1709.00510},
  year   = {2019}
}

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35 pages, published version, improved exposition, added many details

Bielliptic intermediate modular curves

Abstract

Keywords

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