PARAMETRIZATION OF ALGEBRAIC POINTS OF LOW DEGREES ON THE AFFINE CURVE Y2 = X5 + 1442

Authors

  • EL Hadji SOW Department of Mathematics Facutly of Science and Technology University Assane SECK of Ziguinchor (SENEGAL)
  • Pape Modou SARR Department of Mathematics Facutly of Science and Technology University Assane SECK of Ziguinchor (SENEGAL)
  • Oumar SALL Department of Mathematics Facutly of Science and Technology University Assane SECK of Ziguinchor (SENEGAL)

DOI:

https://doi.org/10.53555/eijms.v7i1.57

Keywords:

Planes curves - Degree of algebraic points - Rationals points - Algebraic extensions – Jacobian

Abstract

In this work, we determine a parametrization of algebraic points of degrees at most 3 over Q on curve C of affine equation y2 = x5 + 20736. This result extends a result of S. Siksek and M. Stoll who described in [4] the set of Q-rational points on this curve.

References

P. A. Griffiths, Introduction to algebraic curves, Translations of mathematical monographs volume 76. American Mathematical Society, Providence (1989).

O. Sall, Points algébriques sur certains quotients de courbes de Fermat, C. R. Acad. Sci. Paris Ser. I 336 (2003) 117-120.

O. Sall, M. Fall, C. M. Coly, Points algébriques de degré donné sur la courbe d’équation affine y2 = x5 + 1, International Journal Of Development Research Vol. 06, Issue, 11, pp. 10295-10300, November, 2016.

S. Siksek, M. Stoll, Partial descent on hyperelliptic curves and the generalized Fermat equation x3 + y4 + z5 = 0, Bull. London Math. Soc. 44 (2012) 151-166.

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Published

2021-06-27

Issue

Vol. 7 No. 1 (2021): EPH - International Journal of Mathematics and Statistics (ISSN: 2208-2212)

Section

Articles

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Copyright (c) 2021 EPH-International Journal of Mathematics and Statistics

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