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On rational torsion points of central -curves

Fumio Sairaiji, Takuya Yamauchi (2008)

Journal de Théorie des Nombres de Bordeaux

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 t o r s ( 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].

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