We determine the set of algebraic points of any given degree of a family of curves C_r given by the affine equation These curves are described by Jdrzȩjak in [3], who showed that the Mordell-Weill group is finite when r = 13, 17 [20], and found the generators of the torsion group of this family of curves.

Mordell-Weil group, degree of algebraic points, linear system.

Received: August 23, 2023; Accepted: October 31, 2023; Published: December 5, 2023

How to cite this article: Mohamadou Mor Diogou Diallo, Cherif Mamina Coly and Oumar Sall, Algebraic points of the family of superelliptic curves of TOMASZ JDRZȨJAK for a given degree, JP Journal of Geometry and Topology 29(2) (2023), 167-172. http://dx.doi.org/10.17654/0972415X23008

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References:
[1] P. A. Griffiths, Introduction to algebraic curves, Translation Mathematical Monographs, American Mathematical Society, Providence 76 (1989), 225.
[2] M. Fall, M. M. D. Diallo and C. M. Coly, Algebraic points of any given degree on the affine curves Journal of Contemporary Applied Mathematics 13(1) (2023).
[3] T. Jdrzȩjak, On two twists of the Fermat cubic Journal of Number Theory 142 (2014), 402-425.
[4] T. Jdrzȩjak, Characterisation of the torsion of the Jacobians of two families of hyperelliptic curves, Acta. Arithmetica 161(3) (2013), 201-218.