## Abstract

Let E be an elliptic curve over Q with prime conductor p. For each positive integer n we put Kn:=Q(E[pn]). The aim of this paper is to estimate the order of the p-Sylow group of the ideal class group of K_{n}. We give a lower bound in terms of the Mordell-Weil rank of E(Q). As an application of our result, we give an example such that p^{2n} divides the class number of the field K_{n} in the case of p=5077 for each positive integer n.

Original language | English |
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Pages (from-to) | 277-289 |

Number of pages | 13 |

Journal | Journal of Number Theory |

Volume | 156 |

DOIs | |

Publication status | Published - 2015 Nov 1 |

Externally published | Yes |

## Keywords

- Class number
- Elliptic curve
- Mordell-Weil rank

## ASJC Scopus subject areas

- Algebra and Number Theory

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