For an elliptic curve $E/\mathbb{Q}$ we show that there are infinitely many cyclic sextic extensions $K/\mathbb{Q}$ such that the Mordell-Weil group $E(K)$ has rank greater than the subgroup of $E(K)$ generated by all the $E(F)$ for the proper subfields $F \subset K$. For certain curves $E/\mathbb{Q}$ we show that the number of such fields $K$ of conductor less than $X$ is $>> \sqrt X$.

Bio: Kisilevsky is a Canadian number theorist. He obtained his doctorate at MIT and taught at Caltech and Concordia. He is currently Emeritus Professor at Concordia.