Abstract
In this chapter we study the group of rational points on an elliptic curve defined over a field which is complete with respect to a discrete valuation. We start with some basic facts concerning Weierstrass equations and “reduction modulo π”.This enables us to break our problem up into several pieces; and then by examining each piece individually, we will be able to deduce a great deal about the group of rational points as a whole. Unless explicitly stated otherwise, we will use the following notation.
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© 1986 Springer Science+Business Media New York
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Silverman, J.H. (1986). Elliptic Curves over Local Fields. In: The Arithmetic of Elliptic Curves. Graduate Texts in Mathematics, vol 106. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-1920-8_8
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DOI: https://doi.org/10.1007/978-1-4757-1920-8_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4757-1922-2
Online ISBN: 978-1-4757-1920-8
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