First, we give a coarse classification by means of the 3-class numbers of the
four associated complex cubic fields
(L1,L2,L3,L4).
Most interesting are the cases with one or more occurrences of 3-class number 9 or 27.
(Computed by Fung and Williams in 1990 at the University of Manitoba, Winnipeg City [3,4].
Class field theoretic and group theoretic interpretation in May 2006
by our most recent sophisticated theorems [5].)
It should be pointed out that Brink has determined the capitulation type
of all fields with discriminant marked by an asterisk (*)
in his 1984 thesis [2],
based on class group computations of Wada [1]
for odd discriminants d > -24000 and even discriminants d > -96000.
Our own table of
capitulation types
for all discriminants d > -50000
has been constructed in 2003 without the knowledge of Brink's thesis,
which came to our disposal with delay in 2006.
It is contained in [6] and confirms Brink's results
with a single exception d=-49128 (type D.10 instead of D.5).
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