本篇論文主要是計算橢圓曲線在大域體上扭點的計算。計算橢圓曲線上的扭點我們主要用兩種方法，一種是利用division polynomial，而另一種則是利用推廣的Lutz-Nagell定理

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.

[1] Henri Cohen.
A Course in Computational Algebraic Number Theory. GTM 138 Springer-Verlag,
Berlin Heidelberg, 1993
[2] I.F.Blake, G.Seroussi, N.P.Smart.
Elliptic Curves in Cryptography. London Mathematical Society Lecture Note Series;
265, 1999
[3] Joseph H. Sliverman.
The Arithmetic of Elliptic Curves. GTM 106 Springer-Verlag, New York, 1986.
[4] Serge Lang.
Elliptic curves :Diophantine Analysis. Springer-Verlag, Berlin, 1978
[5] Susanne Schmitt * Host G.Zimmer.
Elliptic Curves :A Computational Approach. Berlin ;Walter de Gruyter,New York,
2003.
[6] Washington, Lawrence C.
Elliptic Curves :Number theory and Cryptography. Chapman & Hall/CRC, 2003.
[7] Cassels, J.W.S: A note on the division values of }(u). Proc. Cambridge Phil. Soc.
45, 167-172, 1949.
[8] Cremona, J.E., Whitley, E.:Periods of cusp forms and elliptic curves over imaginary
quadratic fields. Math. Comp. 62, 407 − 429, 1994.
[9] Zimmer, H.G.: Torsion points on elliptic curves over a global field. Manuscripta
Math. 29 , 119-145, 1979.
[10] David A. Cox, Walter R. Parry.: Torsion in elliptic curves over k(t). Compositio
Mathematica. Vol 41, Fasc 3, 337-354, 1980.