%0 Journal Article
%T On the class numbers of the fields of the p^n-torsion points of certain elliptic curves over Q
%A Fumio Sairaiji
%A Takuya Yamauchi
%J Mathematics
%D 2013
%I arXiv
%X Let E be an elliptic curve over Q with prime conductor p. For each non-negative integer n we put K_n:=Q(E[p^n]). 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 bounds 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.
%U http://arxiv.org/abs/1307.7691v3