Equation 677 Database

Size-65 Latin eq677 magma: a permutation-twisted 5x13 fibre bundle. See the size-65 page comment for the general family. There is a 5-class congruence theta with five 13-element classes. Coordinates (i,u): i in F_5 is the class index, u in F_13 is the fibre coordinate; each row Ci lists the elements with u=0,1,...,12: C0: 60,4,57,6,20,52,47,37,43,11,15,32,25 C1: 61,1,56,7,22,51,46,35,41,12,17,30,27 C2: 62,0,55,5,21,50,45,36,42,10,16,31,26 C3: 64,3,59,9,24,54,49,39,44,14,19,34,29 C4: 63,2,58,8,23,53,48,38,40,13,18,33,28 The quotient M/theta is magma#e549b5f8, the F_5 affine law i*j = 2i+4j. Every theta-class is a copy of magma#babb8d44, the F_13 affine law u*v = 9u+11v. In these coordinates: (i,u)*(j,v) = (2i+4j, 9u+11v) if i=j (i,u)*(j,v) = (2i+4j, p^-1(9 p(u)+11 p(v))) if i!=j with off-diagonal twist permutation p = (1,10,9,5,11,2,3,7,8,4,0,12,6), i.e. p(0)=1, p(1)=10, ..., p(12)=6. Right-cancellative, non-idempotent. [text written by Claude]