Arithmetic Information of Rational Elliptic Surfaces, and Shioda's Rank 68 Elliptic Surface

Blair Butler, Andreas-Stephan Elsenhans

The field of definition of the Mordell-Weil group of an elliptic surface $E\to {\mathbb{P}}^1$ defined over $\mathbb{Q}$ is the smallest number field $k$ such that all of it…