Torsion Points on Elliptic Curves over Global Fields
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...
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| Format: | Others |
| Language: | en_US |
| Published: |
2005
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| Online Access: | http://ndltd.ncl.edu.tw/handle/87000636265723272512 |
| Summary: | 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.
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