On rational torsion points of central -curves
Journal de théorie des nombres de Bordeaux, Volume 20 (2008) no. 2, p. 465-483

Let E be a central -curve over a polyquadratic field k. In this article we give an upper bound for prime divisors of the order of the k-rational torsion subgroup E tors (k) (see Theorems 1.1 and 1.2). The notion of central -curves is a generalization of that of elliptic curves over . Our result is a generalization of Theorem 2 of Mazur [12], and it is a precision of the upper bounds of Merel [15] and Oesterlé [17].

Soit E une -courbe centrale sur un corps polyquadratique k. Dans cet article, nous donnons une borne supérieure des diviseurs premiers de l’ordre du sous-groupe de torsion k-rationnel E tors (k) (voir Théorèmes 1.1 et 1.2). La notion de -courbe centrale est une généralisation de celle de courbe elliptique sur . Notre résultat est une généralisation du Théorème de Mazur [12], et c’est une précision des bornes supérieures de Merel [15] et Oesterlé [17].

@article{JTNB_2008__20_2_465_0,
     author = {Sairaiji, Fumio and Yamauchi, Takuya},
     title = {On rational torsion points of central $\mathbb{Q}$-curves},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     publisher = {Universit\'e Bordeaux 1},
     volume = {20},
     number = {2},
     year = {2008},
     pages = {465-483},
     doi = {10.5802/jtnb.637},
     mrnumber = {2477514},
     zbl = {1171.11037},
     language = {en},
     url = {http://www.numdam.org/item/JTNB_2008__20_2_465_0}
}
Sairaiji, Fumio; Yamauchi, Takuya. On rational torsion points of central $\mathbb{Q}$-curves. Journal de théorie des nombres de Bordeaux, Volume 20 (2008) no. 2, pp. 465-483. doi : 10.5802/jtnb.637. http://www.numdam.org/item/JTNB_2008__20_2_465_0/

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