Journal of the Mathematical Society of Japan

Non-elliptic Shimura curves of genus one

Josep GONZÁLEZ and Victor ROTGER

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Abstract

We present explicit models for non-elliptic genus one Shimura curves X 0 ( D , N ) with Γ 0 ( N ) -level structure arising from an indefinite quaternion algebra of reduced discriminant D , and Atkin-Lehner quotients of them. In addition, we discuss and extend Jordan's work [10, Ch. III] on points with complex multiplication on Shimura curves.

Article information

Source
J. Math. Soc. Japan, Volume 58, Number 4 (2006), 927-948.

Dates
First available in Project Euclid: 21 May 2007

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1179759530

Digital Object Identifier
doi:10.2969/jmsj/1179759530

Mathematical Reviews number (MathSciNet)
MR2276174

Zentralblatt MATH identifier
1123.11019

Subjects
Primary: 11G18: Arithmetic aspects of modular and Shimura varieties [See also 14G35]
Secondary: 14G35: Modular and Shimura varieties [See also 11F41, 11F46, 11G18]

Keywords
Shimura curve curve of genus one elliptic curve complex multiplication points

Citation

GONZÁLEZ, Josep; ROTGER, Victor. Non-elliptic Shimura curves of genus one. J. Math. Soc. Japan 58 (2006), no. 4, 927--948. doi:10.2969/jmsj/1179759530. https://projecteuclid.org/euclid.jmsj/1179759530


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