Local Root Numbers of Elliptic Curves over Dyadic Fields

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J. Math. Sci. Univ. Tokyo
Vol. 22 (2015), No. 1, Page 247–260.

Imai, Naoki
Local Root Numbers of Elliptic Curves over Dyadic Fields
[Full Article (PDF)] [MathSciNet Review (HTML)] [MathSciNet Review (PDF)]

Abstract:
We consider an elliptic curve over a dyadic field with additive, potentially good reduction. We study the finite Galois extension of the dyadic field generated by the three-torsion points of the elliptic curve. As an application, we give a formula to calculate the local root number of the elliptic curve over the dyadic field.

Keywords: Root number, elliptic curve.

Mathematics Subject Classification (2010): 11G07, 11S40.

Mathematical Reviews Number: MR3329196

Received: 2014-06-27

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