MAGMA code main.m load "basicdefinitions.m"; // These divisors will be used to generate the entire Xxxxxx group, // by considering their orbits under a subgroup G of the // automorphism group, as well as under the Galois group of K2. // They are, in order, Xxx, X0, X0, X0. InitialDivisors := [ [xˆ2 + yˆ2 + zˆ2,w-b0 x y z], [xˆ2 + yˆ2 + xxxx0 xˆ0, w-b1 x y z], [xˆ2 + zeta3 yˆ2 + xxxx0ˆ0 xˆ0, w-b0 x y z], [xˆ2-d/3 yˆ2+zˆ2,3 r3 w+b0 b1 b2 yˆ3], [2 x y-c0 zˆ2,xˆ3-yˆ3-w], [r3/9 (b0 b1+b1 b2+b2 b0+d) xˆ2-r3/3 (yˆ2+zˆ2)-y z, r3/27 ((b0+b1+b2)ˆ3-(b0ˆ3+b1ˆ3+b2ˆ3)) xˆ3\ -(b0+b1+b2) x y z-w], [c0 xˆ2\ +2 ((3 c0+2 d) (3 c0-d))/((c0-c1) (c1-c2) (c2-c0)) x y\ +2 yˆ2-zˆ2, (2 c0+c2) (c0 xˆ3\ +(9 c0+6 d) 4 c0/((c0-c1) (c1-c2) (c2-c0)) xˆ2 y+\
