Journal of the Ramanujan Mathematical Society

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On ℚ-Simple Factors of Jacobian Varieties of Quotient Modular Curves


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1 Department of Mathematics, Graduate School of Science, Hiroshima University, Higashi-Hiroshima 739-8526, Japan
     

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Let N be a positive integer and W(N) be the group generated by Atkin-Lehner involutions with respect to Γ0(N). Let J*0(N) be the Jacobian variety of the quotient modular curve X*0(N)= X0(N)/W(N). This paper gives a complete list of levels N such that all ℚ-simple factors of J*0(N) are completely decomposable over ℚ.
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  • On ℚ-Simple Factors of Jacobian Varieties of Quotient Modular Curves

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Authors

Takuya Yamauchi
Department of Mathematics, Graduate School of Science, Hiroshima University, Higashi-Hiroshima 739-8526, Japan

Abstract


Let N be a positive integer and W(N) be the group generated by Atkin-Lehner involutions with respect to Γ0(N). Let J*0(N) be the Jacobian variety of the quotient modular curve X*0(N)= X0(N)/W(N). This paper gives a complete list of levels N such that all ℚ-simple factors of J*0(N) are completely decomposable over ℚ.