Torsion Points on Elliptic Curves over Global Fields

• Main Author: 姜焙元
• Other Authors: 于靖
• Format: Others
• Language: en_US
• Published: 2005
• Online Access: http://ndltd.ncl.edu.tw/handle/87000636265723272512

碩士 === 國立清華大學 === 數學系 === 93 === Let $E$ be an elliptic curve defined over a global field $K$. By a global field $K$ we mean an algebraic number field or an algebraic function field of one variable over a field $k$ as its field of constants. For technical reason we may assume that our function field has characteristic $\neq 2$. Our main interest is to compute torsion points of $E$ over $K$. In this paper we provide two methods. One is to use division polynomials, and the other is to use the generalized Nagell-Lutz theorem.