Determination of the modular Jacobian varieties $J_1(M,MN)$ with the Mordell-Weil rank zero

Koji Matsuda

doi:10.1007/s40993-023-00430-4

paper

Determination of the modular Jacobian varieties $J_{1} (M, M N)$ with the Mordell-Weil rank zero

arXiv:2111.08215 · doi:10.1007/s40993-023-00430-4

Abstract

In this paper, we determine all modular Jacobian varieties $J_{1} (M, M N)$ over the number field $Q (ζ_{M})$ with the Mordell-Weil rank zero following the method of Derickx, Etropolski, van Hoeij, Morrow, and Zureick-Brown.

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Sporadic Cubic Torsion

Determination of the modular Jacobian varieties J1​(M,MN) with the Mordell-Weil rank zero

Abstract

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Determination of the modular Jacobian varieties $J_{1} (M, M N)$ with the Mordell-Weil rank zero