On the arithmetic of certain modular curves

Daeyeol Jeon; Chang Heon Kim

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Displaying similar documents to “On the arithmetic of certain modular curves”

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

Francesc Bars, Aristides Kontogeorgis, Xavier Xarles (2013)

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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).

Equations of hyperelliptic modular curves

Josep Gonzalez Rovira (1991)

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We compute, in a unified way, the equations of all hyperelliptic modular curves. The main tool is provided by a class of modular functions introduced by Newman in 1957. The method uses the action of the hyperelliptic involution on the cusps.

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Modular parametrizations of certain elliptic curves

Matija Kazalicki, Koji Tasaka (2014)

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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. ...