## Abstract

Let E be an elliptic curve over Q which has multiplicative reduction at a fixed prime p. Assume E has multiplicative reduction or potentially good reduction at any prime not equal to p. For each positive integer n we put K _{n} := Q(E[p ^{n} ]). The aim of this paper is to extend the authors’ previous results in [13] concerning with the order of the p-Sylow group of the ideal class group of K _{n} to more general setting. We also modify the previous lower bound of the order given in terms of the Mordell–Weil rank of E(Q) and the ramification related to E.

Original language | English |
---|---|

Pages (from-to) | 893-915 |

Number of pages | 23 |

Journal | Journal de Theorie des Nombres de Bordeaux |

Volume | 30 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2018 Jan 1 |

## Keywords

- Class number
- Elliptic curves
- Mordell-Weil rank

## ASJC Scopus subject areas

- Algebra and Number Theory