This example has neither been investigated by Brink [1]
nor in our previous paper [2].
We give the complete data needed to determine the capitulation type and the group G=Gal(K_{2}K).
Computed on July 31, 2007, at the University of Graz, Computer Centre [3,4].
Counter, n = 78  Discriminant, d = 50739  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  18.0  21.5  24.7  29.8 
Class numbers, h  3  3  3  3 
Polynomials, p(X) = X^{3} + C*X + D, with d(p) = i^{2}*d  
(C,D)  (48,23)  (204,1129)  (42,167)  (186,985) 
Indices, i  3  3  3  3 
Fundamental units, e = (U + V*x + W*x^{2})/T, with P(x) = 0  
U  134  345974  219811  75804979 
V  518  18319  109904  4682296 
W  497  2380  17330  602102 
T  3  1  3  3 
Splitting primes, q  127  43  823  61 
Associated quadratic forms, F = a*X^{2} + b*X*Y + c*Y^{2}  
(a,b,c)  (105,51,127)  (43,1,295)  (55,31,235)  (61,47,217) 
Represented primes, q  127  43  823  61 
Associated ideal cubes, (x + y*d^{1/2})/2, with 4*q^{3} = x^{2}  d*y^{2}  
(x,y)  (2389,7)  (517,1)  (41623,99)  (310,4) 
Principalization  3  1  4  4 
Capitulation type D.10: (3,1,4,4)  Group G in CBF^{1a}(4,5)  Contents 

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