Vol. 261, No. 1, 2013

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ISSN: 0030-8730
Formal groups of elliptic curves with potential good supersingular reduction

Álvaro Lozano-Robledo

Vol. 261 (2013), No. 1, 145–164

Let L be a number field and let E∕L be an elliptic curve with potentially supersingular reduction at a prime ideal of L above a rational prime p. In this article we describe a formula for the slopes of the Newton polygon associated to the multiplication-by-p map in the formal group of E, depending only on the congruence class of p mod 12, the -adic valuation of the discriminant of a model for E over L, and the valuation of the j-invariant of E. The formula is applied to prove a divisibility formula for the ramification indices in the field of definition of a p-torsion point.

elliptic curves, supersingular, formal group, torsion points
Mathematical Subject Classification 2010
Primary: 11G05, 11G07
Secondary: 14H52, 14L05
Received: 23 May 2012
Revised: 9 August 2012
Accepted: 27 August 2012
Published: 28 February 2013
Álvaro Lozano-Robledo
Department of Mathematics
University of Connecticut
196 Auditorium Road, Unit 3009
Storrs CT 06269
United States