This example has been investigated by
Scholz and Taussky [1],
Heider and Schmithals [2],
Brink [3],
and in our previous papers [4,5].
We give the complete data needed to determine the capitulation type and the group G=Gal(K_{2}K).
Computed in October, 1989, at the University of Graz, Computer Centre [4].
Counter, n = 2  Discriminant, d = 4027  3class group of type (3,3)  3class number, h = 9  Conductor, f = 1 

The nonGalois absolute cubic subfields (L_{1},L_{2},L_{3},L_{4}) of the four unramified cyclic cubic relative extensions NK  
Regulators, R  2.3  2.5  4.70  4.75 
Class numbers, h  6  6  3  3 
Polynomials, p(X) = X^{3} + C*X + D, with d(p) = i^{2}*d  
(C,D)  (10,1)  (44,113)  (43,56)  (8,15) 
Indices, i  1  1  10  1 
Fundamental units, e = (U + V*x + W*x^{2})/T, with P(x) = 0  
U  0  28  18  7 
V  1  4  13  2 
W  0  1  1  0 
T  1  1  10  1 
Splitting primes, q  43  13  19  61 
Associated quadratic forms, F = a*X^{2} + b*X*Y + c*Y^{2}  
(a,b,c)  (29,27,41)  (13,9,79)  (19,1,53)  (17,11,61) 
Represented primes, q  29, 43  13  19  17, 61 
Associated ideal cubes, (x + y*d^{1/2})/2, with 4*q^{3} = x^{2}  d*y^{2}  
(x,y)  (182,4)  (69,1)  (153,1)  (125,1) 
Principalization  2  3  3  1 
Capitulation type D.10: (2,3,3,1)  Group G in CBF^{1a}(4,5)  Contents 

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