### Abstract

We construct a family of cyclic extensions of number fields, in which every finite place is unramified, from an elliptic curve with a rational torsion point. As an application, we obtain such polynomials F(X) of rational coefficients that have the following property: For a rational number ξ chosen at random, the class number of the field generated by the square root of F(ξ) is "often" divisible by 3, 5 or by 7.

Original language | English |
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Pages (from-to) | 375-390 |

Number of pages | 16 |

Journal | Osaka Journal of Mathematics |

Volume | 45 |

Issue number | 2 |

Publication status | Published - 2008 Jun 1 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Sato, A. (2008). On the class numbers of certain number fields obtained from points on elliptic curves II.

*Osaka Journal of Mathematics*,*45*(2), 375-390.