Torsion Points on Modular Curves

Authors

  • Hasan Sankari Tishreen University
  • Mustafa Bojakli Tishreen University

Abstract

Let  be a quadratic field. Let  be modular curves and  be Jacobian curves of modular curves defined over . In this paper, we investigate torsion points on modular curves  and the Mordell-Weil group of the Jacobian curves . Let  be one of the primes 17,19,23,29,31. We prove that the Mordell-Weil group of the Jacobian curves  over  is finite and the modular curves  have no -points of order . Whereas in case , we find the Jacobian curves  has a finite Mordell-Weil group over  where  is an imaginary quadratic field and conclude that the modular curves  has no -points of order .

 

Author Biographies

Hasan Sankari, Tishreen University

Professor – Department of Mathematics – Faculty of Science

Mustafa Bojakli, Tishreen University

PhD student – Department of Mathematics – Faculty of Science

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Published

2021-03-30

How to Cite

1.
سنكري ح, بوجقلي م. Torsion Points on Modular Curves. TUJ-BA [Internet]. 2021Mar.30 [cited 2024Apr.27];43(1). Available from: https://journal.tishreen.edu.sy/index.php/bassnc/article/view/10464

Issue

Vol. 43 No. 1 (2021): Tishreen University Journal for Research and Scientific Studies - Basic Sciences Series

Section

Articles

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