Points algébriques sur une courbe hyperelliptique de Nils Bruin
DOI: 10.54647/mathematics110421 83 Downloads 162161 Views
Author(s)
Abstract
We give the set of algebraic points of degree ≤5 over Q on the hyperelliptic curveC: y²=6x(x^4+3). This result extends a previous result of Bruin of who described in [1] the set of Q-rational points on this curve.
Keywords
Degree of algebraic points - Rational points - Algebraic extensions - Jacobian.
Cite this paper
El Hadji SOW, Moussa FALL, Oumar SALL,
Points algébriques sur une courbe hyperelliptique de Nils Bruin
, SCIREA Journal of Mathematics.
Volume 8, Issue 4, August 2023 | PP. 130-138.
10.54647/mathematics110421
References
[ 1 ] | N. Bruin, On powers as sums of two cubes, International Algorithmic Number Theory Symposium. Springer, Berlin, Heidelberg, 2000. |
[ 2 ] | P. A. Griffiths, Introduction to algebraic curves, Translations of mathematical monographs volume 76. American Mathematical Society, Providence, 1989. |
[ 3 ] | M. Hindry and J. H. Silverman, Diophantie geometry, an introduction, springer verlage,2000. |
[ 4 ] | J. TH. Mulholland, Elliptic curves with rational 2-torsion and related ternary Diophantine equations. ProQuest LLC. Ann Arbor, MI, 2006. |
[ 5 ] | E. H. Sow, M. Fall, O. Sall, Points algébriques de degrésau-plus 5 sur la courbe d'équation affine , SCIREA Journal of Mathematics, Volume 6, Issue 6, 2021. |