Counterexamples to O'Neil's Period-Index Problem on Elliptic Curves

Xiaoguang Shang, Cheng Niu

Let $E/K$ be an elliptic curve over a number field $K$, and let $[C]\in H^1(K,E(\overline{K}))$ be a homogeneous space under $E$. Suppose that $C$ has period $n$ and index $d$. O'N…