In this study, we construct four-dimensional F-theory models with 3 to 8 U(1) factors on products of K3 surfaces. We provide explicit Weierstrass equations elliptic surfaces Mordell–Weil ranks 8. utilize the method quadratic base change glue pairs rational together yield aforementioned types The moduli constructed in study include Kummer specific complex structures. show that tadpole cancels co...

Let E be an elliptic curve having Complex Multiplication by the full ring OK of integers of K = Q( √ −D), let H = K(j(E)) be the Hilbert class field of K. Then the Mordell-Weil group E(H) is an OK-module, and its Steinitz class St(E) is studied. When D is a prime number, it is proved that St(E) = 1 if D ≡ 3 (mod 4); and St(E) = [P]t if p ≡ 1 (mod 4), where [P] is the ideal class of K represente...