On rational torsion points of central ℚ-curves

Fumio Sairaiji, Takuya Yamauchi

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1 Citation (Scopus)


Let E be a central ℚ-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 Etors(k) (see Theorems 1.1 and 1.2). The notion of central ℚ-curves is a generalization of that of elliptic curves over ℚ. 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].

Original languageEnglish
Pages (from-to)465-483
Number of pages19
JournalJournal de Theorie des Nombres de Bordeaux
Issue number2
Publication statusPublished - 2008


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