Elliptic threefolds with high Mordell–Weil rank

We present the first examples of smooth elliptic Calabi-Yau threefolds with Mordell-Weil rank 10, highest currently known value. They are given by Schoen introduced Namikawa. explicitly compute Shioda homomorphism for generators group and their induced height pairing. There six isolated fibers Kodaira Type IV. Compactification F-theory on these gives an effective theory in dimensions which contains ten abelian gauge factors. charges multiplicities massless hypermultiplets as Gopakumar-Vafa invariants show that they satisfy gravitational anomaly cancellation conditions. describe a Weierstrass model over $\mathbb P^2$ log canonical relate it to construction Elkies.