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

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].

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].

DOI : 10.5802/jtnb.637
Fumio Sairaiji 1 ; Takuya Yamauchi 2

1 Hiroshima International University, Hiro, Hiroshima 737-0112, Japan
2 Faculty of Liberal Arts and Sciences, Osaka Prefecture University, 1-1 Gakuen-cho, Nakaku, Sakai, Osaka 599-8531, Japan
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Fumio Sairaiji; Takuya Yamauchi. On rational torsion points of central $\mathbb{Q}$-curves. Journal de théorie des nombres de Bordeaux, Tome 20 (2008) no. 2, pp. 465-483. doi : 10.5802/jtnb.637. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.637/

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