  We present the first examples of smooth elliptic Calabi-Yau threefolds with
Mordell-Weil rank 10, the highest currently known value. They are given by the
Schoen threefolds introduced by Namikawa; there are six isolated fibers of
Kodaira Type IV. We explicitly compute the Shioda homomorphism for the
generators of the Mordell-Weil group and their induced height pairing.
Compactification of F-theory on these threefolds gives an effective theory in
six dimensions which contains ten abelian gauge group factors. We compute the
massless matter spectrum. In particular, we show that the charged singlet
matter need not reside at enhancement loci of Type $I_2$, as previously
believed. We relate the multiplicities of the massless spectrum to genus-zero
Gopakumar-Vafa invariants and other geometric quantities of the Calabi-Yau. We
show that the gravitational and abelian anomaly cancellation conditions are
satisfied. We prove a Geometric Anomaly Cancellation equation and we deduce
birational equivalence for the quantities in the spectrum. We explicitly
describe a Weierstrass model over $\mathbb P^2$ of the Calabi-Yau threefolds as
a log canonical model and compare it to a construction by Elkies and classical
results of Burkhardt.
