Parametrization of algebraic points of low degrees on the affine curve y^{2}= x^{5}+144^{2}

Authors

  • El Hadji SOW Université Assane SECK Ziguinchor
  • Pape Modou SARR
  • OUMAR SALL

DOI:

https://doi.org/10.53555/ephms.v7i12.1865

Keywords:

Planes curves, Degree of algebraic points, Rational 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 y^{2}= x^{5}+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.

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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 y^2 = x^5 + 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 $x^{3} + y^{4} + z^{5} = 0$, Bull. London Math. Soc. 44 (2012) 151-166.

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Published

2021-12-30

How to Cite

SOW, E. H., SARR, P. M., & SALL, O. (2021). Parametrization of algebraic points of low degrees on the affine curve y^{2}= x^{5}+144^{2}. EPH - International Journal of Mathematics and Statistics, 7(12), 1–5. https://doi.org/10.53555/ephms.v7i12.1865

Issue

Vol. 7 No. 12 (2021): EPH - International Journal of Mathematics and Statistics (ISSN: 2208-2212)

Section

Articles

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