Local Root Numbers of Elliptic Curves over Dyadic Fields

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

Imai, Naoki
Local Root Numbers of Elliptic Curves over Dyadic Fields
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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