We give the set of algebraic points of degree at most 3 over  on the affine curve  studied by Tsuzuki and Yamauchi in [3].

degree of algebraic point, curve, linear system, Mordell-Weil group, Jacobian.

Received: February 1, 2024; Revised: February 12, 2024; Accepted: March 29, 2024; Published: April 29, 2024

How to cite this article: El Hadji SOW, Points of low degrees on the Tsuzuki-Yamauchi smooth curve, JP Journal of Geometry and Topology 30(1) (2024), 63-67. https://doi.org/10.17654/0972415X24004

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References:

[1] P. A. Griffiths, Introduction to algebraic curves, Translations of Mathematical Monographs, American Mathematical Society, Providence, Volume 76, 1989.
[2] El Hadji SOW, Moussa FALL and Oumar SALL, Algebraic points on the genus 2 curve Journal of Contemporary Applied Mathematics 14(1) (2024), 28-32.
[3] N. Tsuzuki and T. Yamauchi, Automorphy of mod 2 Galois representations associated to the quintic Dwork family and reciprocity of some quintic trinomials, arXiv:2008.09852v4 [math.NT] 28 Sep 2022.