Journal of the Ramanujan Mathematical Society

Volume 30, Issue 1, March 2015 pp. 115–133.

λ-invariants of Selmer groups of elliptic curves with positive μ-invariant

Authors: Suman Ahmed and Sudhanshu Shekhar
Author institution:Department of Mathematics, University of Burdwan, Golapbag, Burdwan, West Bengal 713 104.

Summary: Let E1 and E2 be two elliptic curves defined over Q with good ordinary reduction at an odd prime p such that the pn-torsion points of the elliptic curves are isomorphic as Galois modules for some n. Assuming n=1 and μ-invariant of one of the curves vanish at p, Greenberg and Vatsal compared the λ-invariants of the Selmer groups of E1 and E2. In this paper, we compare the λ-invariants for the curves E1 and E2 with positive μ-invariant and n > μ. We also discuss a few numerical examples.

Keywords: Elliptic curves, Iwasawa invariants, Selmer groups.

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