Displaying similar documents to “Equations of hyperelliptic modular curves”

Arithmetic of the modular function j 1 , 4

Chang Heon Kim, Ja Kyung Koo (1998)

Acta Arithmetica

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We find a generator j 1 , 4 of the function field on the modular curve X₁(4) by means of classical theta functions θ₂ and θ₃, and estimate the normalized generator N ( j 1 , 4 ) which becomes the Thompson series of type 4C. With these modular functions we investigate some number theoretic properties.

Modular parametrizations of certain elliptic curves

Matija Kazalicki, Koji Tasaka (2014)

Acta Arithmetica

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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. ...

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

Francesc Bars, Aristides Kontogeorgis, Xavier Xarles (2013)

Acta Arithmetica

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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).

An integrality criterion for elliptic modular forms

Andrea Mori (1990)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Let f be an elliptic modular form level of N. We present a criterion for the integrality of f at primes not dividing N. The result is in terms of the values at CM points of the forms obtained applying to f the iterates of the Maaß differential operators.