A family of semistable elliptic curves with large Tate-Shafarevitch groups

We present a family of elliptic curves defined over the rationals Q {\mathbf {Q}} such that each curve admits only good or multiplicative reduction and for every integer n n there is a curve whose Tate-Shafarevitch group over Q {\mathbf {Q}} has more than n n elements of order 2. Previously known examples of large Tate-Shafarevitch groups were constructed by forcing many places of additive reduction.