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)	[5, 13774, 47038769]	C₈₄₇		---)	[47038769, 6887, 98000]	C₂₅₄₁
2)	[5, 12494, 35497009]	C₈₄₇		84)	[35497009, 6247, 882000]	C₈₄₇
3)	[8, 6494, 10491809]	C₈₄₇		83)	[10491809, 3247, 12800]	C₈₄₇
4)	[13, 5742, 8159441]	C₈₄₇		---)	[8159441, 2871, 20800]	C₂₅₄₁
5)	[13, 6414, 10271537]	C₈₄₇		---)	[10271537, 3207, 3328]	C₂₅₄₁
6)	[37, 2550, 1339097]	C₈₄₇		---)	[1339097, 1275, 71632]	C₇₆₂₃
7)	[109, 3782, 2571337]	C₈₄₇		82)	[2571337, 1891, 251136]	C₈₄₇
8)	[173, 4030, 2720513]	C₈₄₇		---)	[2720513, 2015, 334928]	C₂₅₄₁
9)	[233, 4006, 3773417]	C₈₄₇		---)	[3773417, 2003, 59648]	C₁₂₇₀₅
10)	[281, 1115, 82564]	C₈₄₇		70)	[20641, 2230, 912969]	C₈₄₇
11)	[317, 2782, 1914593]	C₈₄₇		81)	[1914593, 1391, 5072]	C₈₄₇
12)	[353, 1050, 274213]	C₈₄₇		76)	[274213, 525, 353]	C₈₄₇
13)	[1009, 682, 15381]	C₈₄₇		---)	[1709, 341, 25225]	C₁₂₁
14)	[1021, 205, 8209]	C₈₄₇		46)	[8209, 410, 9189]	C₈₄₇
15)	[1181, 1193, 355517]	C₈₄₇		78)	[355517, 2386, 1181]	C₈₄₇
16)	[1433, 2134, 15017]	C₈₄₇		57)	[15017, 1067, 280868]	C₈₄₇
17)	[1601, 351, 11188]	C₈₄₇		---)	[2797, 702, 78449]	C₁₂₁
18)	[1601, 446, 24113]	C₈₄₇		---)	[24113, 223, 6404]	C₁₂₁
19)	[1601, 2818, 134525]	C₈₄₇		---)	[5381, 1409, 462689]	C₁₂₁
20)	[1801, 5279, 6768400]	C₈₄₇		63)	[16921, 4195, 3176964]	C₈₄₇
21)	[2029, 642, 94925]	C₈₄₇		---)	[3797, 321, 2029]	C₁₂₁
22)	[2029, 905, 179901]	C₈₄₇		---)	[2221, 1810, 99421]	C₁₂₁
23)	[2269, 5769, 15233]	C₈₄₇		58)	[15233, 3247, 1778896]	C₈₄₇
24)	[2281, 4403, 329652]	C₈₄₇		49)	[9157, 3581, 1005921]	C₈₄₇
25)	[2789, 4773, 3586201]	C₈₄₇		---)	[12409, 3627, 1349876]	C₇₆₂₃
26)	[2861, 5213, 6775961]	C₈₄₇		54)	[12809, 3515, 11444]	C₈₄₇
27)	[2897, 1123, 53828]	C₈₄₇		---)	[13457, 2246, 1045817]	C₁₁₀₁₁
28)	[3089, 2922, 1529077]	C₈₄₇		52)	[12637, 1461, 151361]	C₈₄₇
29)	[3257, 3207, 283984]	C₈₄₇		66)	[17749, 6414, 9148913]	C₈₄₇
30)	[3449, 2595, 234064]	C₈₄₇		56)	[14629, 5190, 5797769]	C₈₄₇
31)	[3593, 1110, 250537]	C₈₄₇		37)	[5113, 555, 14372]	C₈₄₇
32)	[3697, 4887, 202448]	C₈₄₇		53)	[12653, 5833, 5061193]	C₈₄₇
33)	[4201, 4835, 4078836]	C₈₄₇		---)	[12589, 5509, 1214089]	C₁₁ x C₈₄₇
34)	[4217, 323, 25028]	C₈₄₇		45)	[6257, 646, 4217]	C₈₄₇
35)	[4229, 893, 113725]	C₈₄₇		---)	[4549, 1786, 342549]	C₁₂₁
36)	[4801, 5919, 7605200]	C₈₄₇		68)	[19013, 8193, 235249]	C₈₄₇
37)	[5113, 555, 14372]	C₈₄₇		31)	[3593, 1110, 250537]	C₈₄₇
38)	[5413, 549, 9041]	C₈₄₇		48)	[9041, 1098, 265237]	C₈₄₇
39)	[5581, 5370, 757589]	C₈₄₇		59)	[15461, 2685, 1612909]	C₈₄₇
40)	[5653, 757, 141849]	C₈₄₇		60)	[15761, 1514, 5653]	C₈₄₇
41)	[5701, 946, 18493]	C₈₄₇		67)	[18493, 473, 51309]	C₈₄₇
42)	[5801, 7554, 1990813]	C₈₄₇		62)	[16453, 3777, 3068729]	C₈₄₇
43)	[5861, 329, 13873]	C₈₄₇		55)	[13873, 658, 52749]	C₈₄₇
44)	[5897, 10170, 19040293]	C₈₄₇		69)	[19813, 5085, 1704233]	C₈₄₇
45)	[6257, 646, 4217]	C₈₄₇		34)	[4217, 323, 25028]	C₈₄₇
46)	[8209, 410, 9189]	C₈₄₇		14)	[1021, 205, 8209]	C₈₄₇
47)	[9029, 2621, 306629]	C₈₄₇		---)	[1061, 1885, 442421]	C₁₂₁
48)	[9041, 1098, 265237]	C₈₄₇		38)	[5413, 549, 9041]	C₈₄₇
49)	[9157, 3581, 1005921]	C₈₄₇		24)	[2281, 4403, 329652]	C₈₄₇
50)	[10313, 6359, 2866916]	C₈₄₇		---)	[4241, 4723, 4125200]	C₁₂₁
51)	[12497, 2807, 17156]	C₈₄₇		---)	[4289, 5614, 7810625]	C₁₂₁
52)	[12637, 1461, 151361]	C₈₄₇		28)	[3089, 2922, 1529077]	C₈₄₇
53)	[12653, 5833, 5061193]	C₈₄₇		32)	[3697, 4887, 202448]	C₈₄₇
54)	[12809, 3515, 11444]	C₈₄₇		26)	[2861, 5213, 6775961]	C₈₄₇
55)	[13873, 658, 52749]	C₈₄₇		43)	[5861, 329, 13873]	C₈₄₇
56)	[14629, 5190, 5797769]	C₈₄₇		30)	[3449, 2595, 234064]	C₈₄₇
57)	[15017, 1067, 280868]	C₈₄₇		16)	[1433, 2134, 15017]	C₈₄₇
58)	[15233, 3247, 1778896]	C₈₄₇		23)	[2269, 5769, 15233]	C₈₄₇
59)	[15461, 2685, 1612909]	C₈₄₇		39)	[5581, 5370, 757589]	C₈₄₇
60)	[15761, 1514, 5653]	C₈₄₇		40)	[5653, 757, 141849]	C₈₄₇
61)	[16217, 1115, 306752]	C₈₄₇		---)	[4793, 2230, 16217]	C₁₂₁
62)	[16453, 3777, 3068729]	C₈₄₇		42)	[5801, 7554, 1990813]	C₈₄₇
63)	[16921, 4195, 3176964]	C₈₄₇		20)	[1801, 5279, 6768400]	C₈₄₇
64)	[17569, 2935, 884196]	C₈₄₇		---)	[2729, 5870, 5077441]	C₁₂₁
65)	[17569, 1787, 56052]	C₈₄₇		---)	[173, 1149, 17569]	C₁₂₁
66)	[17749, 6414, 9148913]	C₈₄₇		29)	[3257, 3207, 283984]	C₈₄₇
67)	[18493, 473, 51309]	C₈₄₇		41)	[5701, 946, 18493]	C₈₄₇
68)	[19013, 8193, 235249]	C₈₄₇		36)	[4801, 5919, 7605200]	C₈₄₇
69)	[19813, 5085, 1704233]	C₈₄₇		44)	[5897, 10170, 19040293]	C₈₄₇
70)	[20641, 2230, 912969]	C₈₄₇		10)	[281, 1115, 82564]	C₈₄₇
71)	[23629, 946, 129213]	C₈₄₇		---)	[293, 473, 23629]	C₁₂₁
72)	[46817, 946, 36461]	C₈₄₇		---)	[101, 473, 46817]	C₁₂₁
73)	[71569, 279, 1568]	C₈₄₇		---)	[8, 558, 71569]	C₁₂₁
74)	[183329, 589, 40898]	C₈₄₇		---)	[8, 1178, 183329]	C₁₂₁
75)	[236297, 515, 7232]	C₈₄₇		---)	[113, 1030, 236297]	C₁₂₁
76)	[274213, 525, 353]	C₈₄₇		12)	[353, 1050, 274213]	C₈₄₇
77)	[324529, 789, 74498]	C₈₄₇		---)	[8, 1578, 324529]	C₁₂₁
78)	[355517, 2386, 1181]	C₈₄₇		15)	[1181, 1193, 355517]	C₈₄₇
79)	[1142593, 1111, 22932]	C₈₄₇		---)	[13, 2222, 1142593]	C₁₂₁
80)	[1416713, 1475, 189728]	C₈₄₇		---)	[8, 2950, 1416713]	C₁₂₁
81)	[1914593, 1391, 5072]	C₈₄₇		11)	[317, 2782, 1914593]	C₈₄₇
82)	[2571337, 1891, 251136]	C₈₄₇		7)	[109, 3782, 2571337]	C₈₄₇
83)	[10491809, 3247, 12800]	C₈₄₇		3)	[8, 6494, 10491809]	C₈₄₇
84)	[35497009, 6247, 882000]	C₈₄₇		2)	[5, 12494, 35497009]	C₈₄₇

Class number: [Non-normal] [Cyclic]

Class group C847 non-normal (D4) quartic CM field invariants: 84 fields

Class group C₈₄₇ non-normal (D₄) quartic CM field invariants: 84 fields