Algebraic points on the hyperelliptic curves y^2 = x^5 + n^2

Authors

  • Moustapha Camara Mathematics and Applications Laboratory U.F.R of Sciences and Technologie, University Assane Seck of Ziguinchor
  • Moussa Fall Mathematics and Applications Laboratory U.F.R of Sciences and Technologie, University Assane Seck of Ziguinchor
  • Oumar Sall Mathematics and Applications Laboratory U.F.R of Sciences and Technologie, University Assane Seck of Ziguinchor

Keywords:

Hyperelliptic curves, rational points, 2-descent, Mordell-Weil groups

Abstract

We give an algebraic description of the set of algebraic points of degree at most d over Q on hyperelliptic curves y2=x5+n2.

References

Carmen Anthony Bruni. Twisted Extensions of Fermat’s Last Theorem. PhD diss. The University of British Columbia (Canada), 2015.
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Faltings, Gerd. "Endlichkeitsätze für abelsch Varietäten über Zahlkörpen." Invent. Math. , 73 no. 3 (1983): 349-366.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Moussa, Fall. "Parametrization of Algebraic Points of Low Degrees on the Schaeffer Curve." J. Math. Sci. Model., 4 no. 2 (2021): 51-55.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Griffiths, Phillip Augustus. Introduction to algebraic curves. Vol. 76 of Translations of mathematical monographs. Providence, RI: American Mathematical Society, 1989.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Mulholland, J. T. Elliptic curves with rational 2-torsion and related ternary Diophantine equations. PhD diss. The University of British Columbia (Canada), 2006.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Hindry, Marc, and Joseph Hillel Silverman. Diophantine geometry, an introduction. Vol. 201 of Graduade Texts in Mathematics. New York: Springer-Verlag, 2000.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Sall, Oumar, and Moussa Fall, and Chérif Mamina Coly. "Points algbriques de degré donné sur la courbe d’équation affine y2 = x5 +1." International Journal of Development Research 6 no. 11 (2016): 10295-10300.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Schaefer, Edward Frank. "Computing a Selmer group of a Jacobian using functions on the curve." Math. Ann. 310, no. 3 (1998): 447-471.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Stoll, Michael. "On the arithmetic of the curves y2 = xl+A; and their Jacobians." J. Reine Angew. Math. 501 (1998): 171-189.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Stoll, Michael. "On the arithmetic of the curves y2 = xl+A. II." J. Number Theory 93, no. 2 (2002): 183-206.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Stoll, Michael, and Tonghai Yang. "On the L-function of the curves y2 = x5 +A." J. London Math. Soc. (2) 68, no. 2 (2003): 273-287.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Stoll, Michael. "Implementing 2-descent for Jacobians of hyperelliptic curves." Acta Arith. 98, no. 3 (2001): 245-277.
##plugins.generic.googleScholarLinks.settings.viewInGS##

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Published

2023-04-29

How to Cite

Camara, M., Fall, M., & Sall, O. (2023). Algebraic points on the hyperelliptic curves y^2 = x^5 + n^2. Annales Universitatis Paedagogicae Cracoviensis Studia Mathematica, 22, 21–31. Retrieved from https://studmath.uken.krakow.pl/article/view/10274

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