Classical Invariants and 2-descent on Elliptic Curves
Classical Invariants and 2-descent on Elliptic Curves
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椭圆曲线上的经典不变量和 2-下降
DOI：
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发表时间：
2001
影响因子：
0.7
通讯作者：
J. Cremona
中科院分区：
文献类型：
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作者：
J. Cremona
将经典的二元四分次不变量理论应用于确定域K上由2阶下降定义的椭圆曲线上的有理点群的问题。这些结果对Birch和Swinnerton-Dyer（1963）首次提出的方法进行了一些简化，并且可以应用于给出一个更有效的算法来确定莫德尔？在Q上有更多的群，并且更容易扩展到其他数域。本文主要局限于一般理论，它在特征为非2或非3的任意域上有效。
The classical theory of invariants of binary quartics is applied to the problem of determining the group of rational points of an elliptic curve defined over a field K by 2-descent. The results lead to some simplifications to the method first presented in Birch and Swinnerton-Dyer (1963), and can be applied to give a more efficient algorithm for determining Mordell?Weil groups over Q, as well as being more readily extended to other number fields. In this paper we mainly restrict ourselves to general theory, valid over arbitrary fields of characteristic neither 2 nor 3.