Journal of the Ramanujan Mathematical Society

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λ-Invariants of Selmer Groups of Elliptic Curves With Positive μ-Invariant


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

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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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  • λ-Invariants of Selmer Groups of Elliptic Curves With Positive μ-Invariant

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Authors

Suman Ahmed
Department of Mathematics, University of Burdwan, Golapbag, Burdwan-713104, West Bengal, India
Sudhanshu Shekhar
Ruprecht-Karls-Universitadt Heidelberg Mathematisches Institut Im Neuenheimer Feld 288, 69120 Heidelberg, Raum 232, Germany

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.