Points algébriques de degrés au plus $5$ sur la courbe C d'équation affine y^{2}= 4x^{5}+1
DOI: 10.54647/mathematics11300 73 Downloads 4513 Views
Author(s)
Abstract
In this work, we determine the set of algebraic points of degree at most Q over on the curve C given by the affine equation y^{2}= 4x^{5}+1. This result extends a result of Andrew R. Booker, Jeroen Sijsling, Andrew V. Sutherland, John Voight and Dan Yasak who described in [1] the set of rational points on this curve
Keywords
Planes curves - Degree of algebraic points - Rationals points - Algebraic extensions - Jacobian-Linear system
Cite this paper
EL Hadji SOW, Moussa FALL, Oumar SALL,
Points algébriques de degrés au plus $5$ sur la courbe C d'équation affine y^{2}= 4x^{5}+1
, SCIREA Journal of Mathematics.
Volume 6, Issue 6, December 2021 | PP. 73-86.
10.54647/mathematics11300
References
[ 1 ] | Andrew R. Booker, Jeroen Sijsling, Andrew V. Sutherland, John Voight and Dan Yasak, (2016). A database of genus-2 curves over the rational numbers. LMS Journal of Computation and Mathematics, 19(A), 235-254. |
[ 2 ] | P. A. Griffiths, Introduction to algebraic curves, Translations of mathematical monographs volume 76. American Mathematical Society, Providence (1989). |
[ 3 ] | The LMFDB Collaboration, The L-functions and Modular Forms Database. Available at: http://www.lmfdb.org. [Online; accessed 8 November 2021] |
[ 4 ] | O. Sall, Points algébriques sur certains quotients de courbes de Fermat, C. R. Acad. Sci. Paris Ser. I 336 (2003) 117-120. |
[ 5 ] | O. Sall, M. Fall, C. M. Coly, Points algébriques de degré donné sur la courbe d'équation affine , International Journal Of Development Research Vol. 06, Issue, 11, pp. 10295-10300, November, 2016. |