A numerical approach toward the p-adic Beilinson conjecture for elliptic curves over Q

Restricting ourselves to elliptic curves over Q , we reformulate the p -adic Beilinson conjecture due to Perrin-Riou, which is customized to our computational approach. We then develop a new algorithm for numerical verifications of the p -adic Beilinson conjecture, which is based on the theory of rigid cohomology and F -isocrystals.