A family of semistable elliptic curves with large Tate-Shafarevitch groups
A family of semistable elliptic curves with large Tate-Shafarevitch groups
复制标题
具有大 Tate-Shafarevitch 群的半稳定椭圆曲线族
DOI：
10.1090/s0002-9939-1983-0715850-1
复制
发表时间：
1983
期刊：
影响因子：
--
通讯作者：
K. Kramer
中科院分区：
文献类型：
--
作者：
K. Kramer
我们提出了一个家庭的椭圆曲线定义的有理数Q，使每一条曲线只承认良好的或乘法的减少，并为每一个整数n有一条曲线，其Tate-Shafarevitch群在Q有超过n个元素的顺序2。以前已知的大Tate-Shafarevitch群的例子是通过强制许多地方的加法还原来构造的。
We present a family of elliptic curves defined over the rationals Q such that each curve admits only good or multiplicative reduction and for every integer n there is a curve whose Tate-Shafarevitch group over Q has more than n elements of order 2. Previously known examples of large Tate-Shafarevitch groups were con- structed by forcing many places of additive reduction.