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 |
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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