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A note on Iwasawa µ-invariants of elliptic curves

A note on Iwasawa µ-invariants of elliptic curves Suppose that E 1 and E 2 are elliptic curves defined over ℚ and p is an odd prime where E 1 and E 2 have good ordinary reduction. In this paper, we generalize a theorem of Greenberg and Vatsal [3] and prove that if E 1[p i ] and E 2[p i ] are isomorphic as Galois modules for i = µ(E 1), then µ(E 1) ≤ µ(E 2). If the isomorphism holds for i = µ(E 1) + 1, then both the curves have same µ-invariants. We also discuss one numerical example. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the Brazilian Mathematical Society, New Series Springer Journals

A note on Iwasawa µ-invariants of elliptic curves

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References (3)

Publisher
Springer Journals
Copyright
Copyright © 2010 by Springer
Subject
Mathematics; Theoretical, Mathematical and Computational Physics; Mathematics, general
ISSN
1678-7544
eISSN
1678-7714
DOI
10.1007/s00574-010-0018-8
Publisher site
See Article on Publisher Site

Abstract

Suppose that E 1 and E 2 are elliptic curves defined over ℚ and p is an odd prime where E 1 and E 2 have good ordinary reduction. In this paper, we generalize a theorem of Greenberg and Vatsal [3] and prove that if E 1[p i ] and E 2[p i ] are isomorphic as Galois modules for i = µ(E 1), then µ(E 1) ≤ µ(E 2). If the isomorphism holds for i = µ(E 1) + 1, then both the curves have same µ-invariants. We also discuss one numerical example.

Journal

Bulletin of the Brazilian Mathematical Society, New Series – Springer Journals

Published: Sep 1, 2010

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