On rational torsion points of central ℚ -curves

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

Journal de Théorie des Nombres de Bordeaux (2008)

  • Volume: 20, Issue: 2, page 465-483
  • ISSN: 1246-7405

Abstract

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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 E t o r s ( 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].

How to cite

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Sairaiji, Fumio, and Yamauchi, Takuya. "On rational torsion points of central $\mathbb{Q}$-curves." Journal de Théorie des Nombres de Bordeaux 20.2 (2008): 465-483. <http://eudml.org/doc/10846>.

@article{Sairaiji2008,
abstract = {Let $E$ be a central $\mathbb\{Q\}$-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 $E_\{tors\}(k)$ (see Theorems 1.1 and 1.2). The notion of central $\mathbb\{Q\}$-curves is a generalization of that of elliptic curves over $\mathbb\{Q\}$. 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].},
affiliation = {Hiroshima International University, Hiro, Hiroshima 737-0112, Japan; Faculty of Liberal Arts and Sciences, Osaka Prefecture University, 1-1 Gakuen-cho, Nakaku, Sakai, Osaka 599-8531, Japan},
author = {Sairaiji, Fumio, Yamauchi, Takuya},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {class of -curves without complex multiplications; Oesterlé bound},
language = {eng},
number = {2},
pages = {465-483},
publisher = {Université Bordeaux 1},
title = {On rational torsion points of central $\mathbb\{Q\}$-curves},
url = {http://eudml.org/doc/10846},
volume = {20},
year = {2008},
}

TY - JOUR
AU - Sairaiji, Fumio
AU - Yamauchi, Takuya
TI - On rational torsion points of central $\mathbb{Q}$-curves
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2008
PB - Université Bordeaux 1
VL - 20
IS - 2
SP - 465
EP - 483
AB - Let $E$ be a central $\mathbb{Q}$-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 $E_{tors}(k)$ (see Theorems 1.1 and 1.2). The notion of central $\mathbb{Q}$-curves is a generalization of that of elliptic curves over $\mathbb{Q}$. 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].
LA - eng
KW - class of -curves without complex multiplications; Oesterlé bound
UR - http://eudml.org/doc/10846
ER -

References

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