A quartic CM field field K is represented by invariants [D,A,B], where K = Q[x]/(x⁴+Ax²+B), and D is the discriminant of the totally real quadratic subfield (hence A²-4B = m²D for some m).

K	Quartic invariants	Cl(O_K)	Igusa invariants	K^r	Reflex invariants	Cl(O_K^r)	Igusa invariants
1)	[229, 657, 107397]	C₃ x C₆ x C₃₀		---)	[11933, 1314, 2061]	C₃ x C₆₀
2)	[257, 1654, 618137]	C₃ x C₆ x C₃₀		---)	[618137, 827, 16448]	C₃ x C₁₂ x C₁₂₀
3)	[316, 2806, 1948185]	C₃ x C₆ x C₃₀		---)	[216465, 1403, 5056]	C₆ x C₆₀
4)	[316, 286, 15393]	C₃ x C₆ x C₃₀		---)	[15393, 143, 1264]	C₆ x C₆₀
5)	[316, 250, 2274]	C₃ x C₆ x C₃₀		---)	[9096, 500, 53404]	C₆ x C₆₀
6)	[321, 155, 5926]	C₃ x C₆ x C₃₀		---)	[23704, 310, 321]	C₆ x C₃₀
7)	[321, 1303, 347332]	C₃ x C₆ x C₃₀		---)	[86833, 2606, 308481]	C₃ x C₆₀
8)	[321, 1910, 398425]	C₃ x C₆ x C₃₀		---)	[15937, 955, 128400]	C₆ x C₃₀
9)	[469, 1033, 69675]	C₃ x C₆ x C₃₀		---)	[11148, 2066, 788389]	C₆ x C₆₀
10)	[469, 898, 109677]	C₃ x C₆ x C₃₀		---)	[109677, 449, 22981]	C₃ x C₆₀
11)	[473, 471, 54396]	C₃ x C₆ x C₃₀		---)	[6044, 942, 4257]	C₆ x C₃₀
12)	[568, 1222, 146121]	C₃ x C₆ x C₃₀		---)	[146121, 611, 56800]	C₆ x C₆₀
13)	[568, 666, 42161]	C₃ x C₆ x C₃₀		---)	[42161, 333, 17182]	C₃ x C₆ x C₁₈₀
14)	[568, 650, 23833]	C₃ x C₆ x C₃₀		---)	[23833, 325, 20448]	C₆ x C₃₀
15)	[733, 610, 90093]	C₃ x C₆ x C₃₀		---)	[90093, 305, 733]	C₂ x C₆ x C₃₀
16)	[785, 1258, 317141]	C₃ x C₆ x C₃₀		---)	[2621, 629, 19625]	C₃ x C₃₀
17)	[892, 286, 6177]	C₃ x C₆ x C₃₀		---)	[6177, 143, 3568]	C₆ x C₆₀
18)	[993, 503, 63004]	C₃ x C₆ x C₃₀		---)	[63004, 1006, 993]	C₂ x C₆ x C₃₀
19)	[1436, 206, 1634]	C₃ x C₆ x C₃₀		---)	[6536, 412, 35900]	C₆ x C₆₀
20)	[1509, 434, 41053]	C₃ x C₆ x C₃₀		---)	[41053, 217, 1509]	C₂ x C₃₀ x C₃₀
21)	[1901, 1338, 379125]	C₃ x C₆ x C₃₀		---)	[1685, 669, 17109]	C₂ x C₆ x C₃₀
22)	[2713, 725, 98172]	C₃ x C₆ x C₃₀		---)	[1212, 1450, 132937]	C₆ x C₆₀
23)	[2777, 85, 1112]	C₃ x C₆ x C₃₀		---)	[1112, 170, 2777]	C₆ x C₃₀
24)	[2777, 489, 3546]	C₃ x C₆ x C₃₀		---)	[1576, 978, 224937]	C₆ x C₆₀
25)	[4481, 214, 6968]	C₃ x C₆ x C₃₀		---)	[6968, 428, 17924]	C₆ x C₆₀
26)	[5613, 367, 32269]	C₃ x C₆ x C₃₀		---)	[61, 543, 50517]	C₆ x C₃₀
27)	[7148, 1234, 266321]	C₃ x C₆ x C₃₀		---)	[2201, 617, 28592]	C₃ x C₆₀
28)	[7388, 694, 2201]	C₃ x C₆ x C₃₀		---)	[2201, 347, 29552]	C₃ x C₆₀
29)	[8572, 190, 453]	C₃ x C₆ x C₃₀		---)	[453, 95, 2143]	C₃ x C₆₀
30)	[11885, 442, 1301]	C₃ x C₆ x C₃₀		---)	[1301, 221, 11885]	C₃ x C₃₀
31)	[12248, 728, 22264]	C₃ x C₆ x C₃₀		---)	[184, 364, 27558]	C₃ x C₆₀
32)	[13269, 888, 144060]	C₃ x C₆ x C₃₀		---)	[60, 444, 13269]	C₆ x C₆₀
33)	[13589, 173, 4085]	C₃ x C₆ x C₃₀		---)	[4085, 346, 13589]	C₆ x C₆₀
34)	[15349, 143, 1275]	C₃ x C₆ x C₃₀		---)	[204, 286, 15349]	C₂ x C₆ x C₃₀
35)	[16661, 478, 40460]	C₃ x C₆ x C₃₀		---)	[140, 956, 66644]	C₆ x C₆₀
36)	[20549, 1293, 1845]	C₃ x C₆ x C₃₀		---)	[205, 2586, 1664469]	C₆ x C₆₀
37)	[24952, 694, 20601]	C₃ x C₆ x C₃₀		---)	[2289, 347, 24952]	C₆ x C₁₂₀
38)	[28473, 1727, 681568]	C₃ x C₆ x C₃₀		---)	[472, 3454, 256257]	C₃ x C₆₀
39)	[29221, 382, 7260]	C₃ x C₆ x C₃₀		---)	[60, 764, 116884]	C₆ x C₆₀
40)	[32009, 253, 8000]	C₃ x C₆ x C₃₀		---)	[5, 359, 32009]	C₆₀
41)	[32197, 2010, 881237]	C₃ x C₆ x C₃₀		---)	[917, 1005, 32197]	C₃ x C₆₀
42)	[37085, 193, 41]	C₃ x C₆ x C₃₀		---)	[41, 386, 37085]	C₃ x C₃₀
43)	[52149, 567, 67335]	C₃ x C₆ x C₃₀		---)	[60, 1134, 52149]	C₆ x C₆₀
44)	[57677, 241, 101]	C₃ x C₆ x C₃₀		---)	[101, 482, 57677]	C₃ x C₃₀
45)	[67313, 1342, 180989]	C₃ x C₆ x C₃₀		---)	[29, 671, 67313]	C₆ x C₃₀
46)	[80101, 301, 2625]	C₃ x C₆ x C₃₀		---)	[105, 602, 80101]	C₆ x C₆₀
47)	[97001, 461, 28880]	C₃ x C₆ x C₃₀		---)	[5, 623, 97001]	C₃ x C₆₀
48)	[104332, 2036, 97336]	C₃ x C₆ x C₃₀		---)	[184, 1018, 234747]	C₃ x C₆₀
49)	[105401, 325, 56]	C₃ x C₆ x C₃₀		---)	[56, 650, 105401]	C₆ x C₃₀
50)	[142616, 758, 1025]	C₃ x C₆ x C₃₀		---)	[41, 379, 35654]	C₆ x C₃₀
51)	[146161, 609, 56180]	C₃ x C₆ x C₃₀		---)	[5, 767, 146161]	C₃ x C₆₀
52)	[186401, 3454, 113]	C₃ x C₆ x C₃₀		---)	[113, 1727, 745604]	C₃ x C₃₀
53)	[196369, 445, 414]	C₃ x C₆ x C₃₀		---)	[184, 890, 196369]	C₃ x C₆₀
54)	[201129, 627, 48000]	C₃ x C₆ x C₃₀		---)	[120, 1254, 201129]	C₆ x C₆₀
55)	[264757, 1545, 1053]	C₃ x C₆ x C₃₀		---)	[13, 3090, 2382813]	C₆ x C₃₀
56)	[418469, 683, 12005]	C₃ x C₆ x C₃₀		---)	[5, 1366, 418469]	C₆ x C₃₀
57)	[698869, 973, 61965]	C₃ x C₆ x C₃₀		---)	[85, 1946, 698869]	C₂ x C₆ x C₃₀
58)	[906601, 1171, 116160]	C₃ x C₆ x C₃₀		---)	[60, 2342, 906601]	C₆ x C₆₀

Class number: [Non-normal] [Cyclic]

Class group C3 x C6 x C30 non-normal (D4) quartic CM field invariants: 58 fields

Class group C₃ x C₆ x C₃₀ non-normal (D₄) quartic CM field invariants: 58 fields