ALGEBRAIC POINTS OF GIVEN DEGREE ON THE AFFINE CURVE C : y2 = x5

被引：0
作者：
Sow, E. L. Hadji [1 ]
Fall, Moussa [1 ]
Sall, Oumar [1 ]
机构：
[1] Assane SECK Univ Ziguinchor, UFR Sci & Technol Math & Applicat Lab, Ziguinchor, Senegal
来源：
JP JOURNAL OF ALGEBRA NUMBER THEORY AND APPLICATIONS | 2023年 / 60卷 / 02期
关键词：
planes curves; degree of algebraic points; rational points; algebraic extensions; Jacobian;
D O I：
10.17654/0972555523004
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this work, we determine the set of algebraic points of a given degree over Q on the curve of affine equation y2 = x5 + 42. This note extends a result of Mulholland in [8] who gave a description of the set of Q-rational points, i.e., the set of points of degree one over Q on this curve.
引用
收藏
页码：59 / 68
页数：10
相关论文
共 12 条
  • [1] [Anonymous], 1989, TRANSLATIONS MATH MO
  • [2] A database of genus-2 curves over the rational numbers
    Booker, Andrew R.
    Sijsling, Jeroen
    Sutherland, Andrew V.
    Voight, John
    Yasaki, Dan
    [J]. LMS JOURNAL OF COMPUTATION AND MATHEMATICS, 2016, 19 : 235 - 254
  • [3] Bruin N, 2000, LECT NOTES COMPUT SC, V1838, P169
  • [4] Chenciner A., 2008, COURBES ALGEBRIQUES
  • [5] Garcia E. L., 2021, DIOPHANTINE GEOMETRY
  • [6] LMFDB Collaboration, L FUNCT MOD FORMS DA
  • [7] Mulholland J. TH., 2006, ELLIPTIC CURVES RATI
  • [8] Sall O., 2016, INT J DEV RES, V6, P10295
  • [9] Explicit Chabauty over number fields
    Siksek, Samir
    [J]. ALGEBRA & NUMBER THEORY, 2013, 7 (04) : 765 - 793
  • [10] Silverman JH., 2000, DIOPHANTINE GEOMETRY, DOI [10.1007/978-1-4612-1210-2, DOI 10.1007/978-1-4612-1210-2]
12