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.

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 d. Dans cet article, nous étudions les sous-groupes de torsion cycliques des courbes elliptiques sur les corps de nombres cubiques. Pour N=49,40,25 ou 22, nous montrons que /N n’est pas un sous-groupe de E(K) tor pour toute courbe elliptique E sur un corps de nombres cubique K.

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 d. In this paper, we discuss the cyclic torsion subgroup of elliptic curves over cubic number fields. For N=49,40,25 or 22, we show that /N is not a subgroup of E(K) tor for any elliptic curve E over a cubic number field K.

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DOI : https://doi.org/10.5802/jtnb.1100
Classification : 11G05,  11G18
Mots clés : torsion subgroup, elliptic curves, modular curves
@article{JTNB_2019__31_3_663_0,
     author = {Jian Wang},
     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 = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1100/}
}
Jian Wang. 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. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1100/

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