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ALGEBRAIC POINTS OF THE FAMILY OF SUPERELLIPTIC CURVES OF TOMASZ JDRZEJAK FOR A GIVEN DEGREE
Keywords:
Mordell-Weil group, degree of algebraic points, linear system.DOI:
https://doi.org/10.17654/0972415X23008Abstract
We determine the set of algebraic points of any given degree of a family of curves $\mathcal{C}_r$ given by the affine equation $y^2=x^5+(16 r)^5$. These curves are described by Jdrzejak 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.
Received: August 23, 2023
Accepted: October 31, 2023
References
P. A. Griffiths, Introduction to algebraic curves, Translation Mathematical Monographs, American Mathematical Society, Providence 76 (1989), 225.
M. Fall, M. M. D. Diallo and C. M. Coly, Algebraic points of any given degree on the affine curves $y^2=x(x+2 p)(x+4 p)left(x^2-8 p^2right)$. Journal of Contemporary Applied Mathematics 13(1) (2023).
T. Jdrzejak, On two twists of the Fermat cubic $x^3+y^3=2$, Journal of Number Theory 142 (2014), 402-425.
T. Jdrzejak, Characterisation of the torsion of the Jacobians of two families of hyperelliptic curves, Acta. Arithmetica 161(3) (2013), 201-218.
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