Journal of the Ramanujan Mathematical Society

Suman Ahmed ¹, Sudhanshu Shekhar ²

Affiliations
1 Department of Mathematics, University of Burdwan, Golapbag, Burdwan-713104, West Bengal, IN
2 Ruprecht-Karls-Universitadt Heidelberg Mathematisches Institut Im Neuenheimer Feld 288, 69120 Heidelberg, Raum 232, DE

Abstract

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.

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