Geodesic
Torsion Points on Certain Families of Elliptic Curves
Canadian mathematical bulletin, Tome 46 (2003) no. 1, pp. 157-160

Voir la notice de l'article provenant de la source Cambridge University Press

Fix an elliptic curve ${{y}^{2}}\,=\,{{x}^{3}}\,+\,Ax\,+\,B$ , satisfying $A,\,B\,\in \,\mathbb{Z},\,A\ge \,\left| B \right|\,>\,0$ . We prove that the $\mathbb{Q}$ -torsion subgroup is one of $(0),\,\mathbb{Z}/3\mathbb{Z},\,\mathbb{Z}/9\mathbb{Z}$ . Related numerical calculations are discussed.
DOI : 10.4153/CMB-2003-016-6
Mots-clés : 11G05 
Wieczorek, Małgorzata. Torsion Points on Certain Families of Elliptic Curves. Canadian mathematical bulletin, Tome 46 (2003) no. 1, pp. 157-160. doi: 10.4153/CMB-2003-016-6
@article{10_4153_CMB_2003_016_6,
     author = {Wieczorek, Ma{\l}gorzata},
     title = {Torsion {Points} on {Certain} {Families} of {Elliptic} {Curves}},
     journal = {Canadian mathematical bulletin},
     pages = {157--160},
     year = {2003},
     volume = {46},
     number = {1},
     doi = {10.4153/CMB-2003-016-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2003-016-6/}
}
TY  - JOUR
AU  - Wieczorek, Małgorzata
TI  - Torsion Points on Certain Families of Elliptic Curves
JO  - Canadian mathematical bulletin
PY  - 2003
SP  - 157
EP  - 160
VL  - 46
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2003-016-6/
DO  - 10.4153/CMB-2003-016-6
ID  - 10_4153_CMB_2003_016_6
ER  - 
%0 Journal Article
%A Wieczorek, Małgorzata
%T Torsion Points on Certain Families of Elliptic Curves
%J Canadian mathematical bulletin
%D 2003
%P 157-160
%V 46
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2003-016-6/
%R 10.4153/CMB-2003-016-6
%F 10_4153_CMB_2003_016_6

[1] [1] Dąbrowski, A. and Wieczorek, M., Families of elliptic curves with trivial Mordell-Weil group. Bull. Austral.Math. Soc. 62 (2000), 303–306. Google Scholar

[2] [2] Dąbrowski, A. and Wieczorek, M., Arithmetic on certain families of elliptic curves. Bull. Austral.Math. Soc. 61 (2000), 319–327. Google Scholar

[3] [3] Kubert, D. S., Universal bounds on the torsion of elliptic curves. Proc. London Math. Soc. 33 (1976), 193–237. Google Scholar

[4] [4] Mazur, B., Rational isogenies of prime degree. Invent.Math. 44 (1978), 129–162. Google Scholar

[5] [5] Olson, L. D., Points of finite order on elliptic curves with complex multiplication. Manuscripta Math. 14 (1974), 195–205. Google Scholar

[6] [6] Qiu, D. and Zhang, X., Explicit classification for torsion subgroups of rational points of elliptic curves. Preprint No 131 (Algebraic number theory archives, September 3, 1998). Google Scholar

Cité par Sources :