Iwasawa μ-invariants of elliptic curves and their symmetric powers

[摘要] In an earlier paper we considered the effects that finite submodules can have on mu-invariants of Selmer groups. In this paper we examine some of the consequences of that theory to elliptic curves and their symmetric powers. One main result is the construction of an isogeny class of elliptic curves, all of which have positive mu-invariants. A second result is a connection between the behaviors of mu-invariants associated with the symmetric powers of an elliptic curve over Q, and the behavior of the mu-invariant of that elliptic curve over different extensions of Q. (C) 2003 Elsevier Inc. All rights reserved.

[发布日期] 2003-10-01

[关键词] Iwasawa theory;elliptic curves;mu-invariants