Le résultat de Merel sur la forme forte de la conjecture de borne uniforme a mis en valeur la classification des parties de torsion des groupes de Mordell–Weil des courbes elliptiques définies sur les corps de nombres de degré fixé . Dans cet article, nous étudions les sous-groupes de torsion cycliques des courbes elliptiques sur les corps de nombres cubiques. Pour ou , nous montrons que n’est pas un sous-groupe de pour toute courbe elliptique sur un corps de nombres cubique .
Merel’s result on the strong uniform boundedness conjecture made it meaningful to classify the torsion part of the Mordell–Weil groups of all elliptic curves defined over number fields of fixed degree . In this paper, we discuss the cyclic torsion subgroup of elliptic curves over cubic number fields. For or , we show that is not a subgroup of for any elliptic curve over a cubic number field .
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Classification : 11G05, 11G18
Mots clés : torsion subgroup, elliptic curves, modular curves
@article{JTNB_2019__31_3_663_0, author = {Wang, Jian}, title = {On the cyclic torsion of elliptic curves over cubic number fields {(II)}}, journal = {Journal de Th\'eorie des Nombres de Bordeaux}, pages = {663--670}, publisher = {Soci\'et\'e Arithm\'etique de Bordeaux}, volume = {31}, number = {3}, year = {2019}, doi = {10.5802/jtnb.1100}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/jtnb.1100/} }
TY - JOUR AU - Wang, Jian TI - On the cyclic torsion of elliptic curves over cubic number fields (II) JO - Journal de Théorie des Nombres de Bordeaux PY - 2019 DA - 2019/// SP - 663 EP - 670 VL - 31 IS - 3 PB - Société Arithmétique de Bordeaux UR - http://archive.numdam.org/articles/10.5802/jtnb.1100/ UR - https://doi.org/10.5802/jtnb.1100 DO - 10.5802/jtnb.1100 LA - en ID - JTNB_2019__31_3_663_0 ER -
Wang, Jian. On the cyclic torsion of elliptic curves over cubic number fields (II). Journal de Théorie des Nombres de Bordeaux, Tome 31 (2019) no. 3, pp. 663-670. doi : 10.5802/jtnb.1100. http://archive.numdam.org/articles/10.5802/jtnb.1100/
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