Intersection numbers of curves on Hilbert modular surfaces

Friedrich Hirzebruch

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Intersection Numbers of Curves on Hilbert Modular Surfaces and Modular Forms of Nebentypus.

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Bielliptic modular curves X₁(N)

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Modular parametrizations of certain elliptic curves

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Kaneko and Sakai (2013) recently observed that certain elliptic curves whose associated newforms (by the modularity theorem) are given by the eta-quotients can be characterized by a particular differential equation involving modular forms and Ramanujan-Serre differential operator. In this paper, we study certain properties of the modular parametrization associated to the elliptic curves over ℚ, and as a consequence we generalize and explain some of their findings. ...

A Siegel modular 3-fold that is a Picard modular 3-fold

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The Fixed Points of the Symmetrie Hilbert Modular Group of a Real Quadratic Field with Arbitrary Discriminant.

Wilfried Hausmann (1982)

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Bielliptic and hyperelliptic modular curves X(N) and the group Aut(X(N))

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We determine all modular curves X(N) (with N ≥ 7) that are hyperelliptic or bielliptic. We also give a proof that the automorphism group of X(N) is PSL₂(ℤ/Nℤ), whence it coincides with the normalizer of Γ(N) in PSL₂(ℝ) modulo ±Γ(N).