Proceedings of the Japan Academy, Series A, Mathematical Sciences

Trigonal modular curves $X_0^*(N)$

Yuji Hasegawa and Mahoro Shimura

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For a positive integer $N$, let $X_0^*(N)$ denote the quotient curve of $X_0(N)$ by the Atkin-Lehmer involutions. In this paper, we determine the trigonality of $X_0^*(N)$ for all $N$. It turns out that there are seven values of $N$ for which $X_0^*(N)$ is a non-trivial trigonal curve.

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Proc. Japan Acad. Ser. A Math. Sci., Volume 76, Number 6 (2000), 83-86.

First available in Project Euclid: 23 May 2006

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Zentralblatt MATH identifier

Primary: 11F11: Holomorphic modular forms of integral weight
Secondary: 11F03: Modular and automorphic functions 11G30: Curves of arbitrary genus or genus = 1 over global fields [See also 14H25] 14E20: Coverings [See also 14H30] 14H25: Arithmetic ground fields [See also 11Dxx, 11G05, 14Gxx]

Modular curve trigonal curve Atkin-Lehmer involution


Hasegawa, Yuji; Shimura, Mahoro. Trigonal modular curves $X_0^*(N)$. Proc. Japan Acad. Ser. A Math. Sci. 76 (2000), no. 6, 83--86. doi:10.3792/pjaa.76.83.

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