We determine a parametrization of algebraic points of degree at most 2 over  on the curve C given by the affine equation  This note treats a special case of quotients of Fermat curves  with  Theses curves are described by Sall in [4] who extended the works of Gross and Rohrlich in [2].

degree of algebraic points, rational points, algebraic extensions.

Received: March 19, 2023; Accepted: April 21, 2023; Published: April 26, 2023

How to cite this article: El Hadji SOW and Moussa Fall, Algebraic points of low degree on the affine curve , Universal Journal of Mathematics and Mathematical Sciences 19(1) (2023), 49-59. http://dx.doi.org/10.17654/2277141723016

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:

[1] D. Faddeev, On the divisor class groups of some algebraic curves, Dokl. Akad. Nauk SSSR 136 (1961), 296-298. English translation: Soviet Math. Dokl. 2(1) (1961), 67-69.
[2] B. Gross and D. Rohrlich, Some results on the Mordell-Weil group of the Jacobian of the Fermat curve, Invent. Math. 44 (1978), 201-224.
[3] P. A. Griffiths, Introduction to algebraic curves, Translations of Mathematical Monographs, Vol. 76, American Mathematical Society, Providence, 1989.
[4] O. Sall, Points algébriques sur certains quotients de courbes de Fermat, C. R. Acad. Sci. Paris Ser. I 336 (2003), 117-120.
[5] P. Tzermias, Torsion parts of Mordell-Weil groups of Fermat Jacobians, Internat. Math. Res. Notices 7 (1998), 359-369.