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)	[8, 10610, 28142953]	C₃ x C₂₀₁		105)	[28142953, 5305, 18]	C₃ x C₂₀₁
2)	[8, 6350, 5362033]	C₃ x C₂₀₁		102)	[5362033, 3175, 1179648]	C₃ x C₂₀₁
3)	[41, 13190, 43452041]	C₃ x C₂₀₁		---)	[43452041, 6595, 10496]	C₃ x C₁₀₀₅
4)	[53, 3454, 2968961]	C₃ x C₂₀₁		---)	[2968961, 1727, 3392]	C₃ x C₃ x C₂₀₁
5)	[89, 5606, 7851113]	C₃ x C₂₀₁		---)	[7851113, 2803, 1424]	C₃ x C₃ x C₂₀₁
6)	[229, 742, 5737]	C₃ x C₂₀₁		---)	[5737, 371, 32976]	C₂₀₁
7)	[257, 306, 22381]	C₃ x C₂₀₁		---)	[22381, 153, 257]	C₂₀₁
8)	[257, 1619, 644432]	C₃ x C₂₀₁		---)	[40277, 3238, 43433]	C₂₀₁
9)	[257, 2274, 33469]	C₃ x C₂₀₁		---)	[33469, 1137, 314825]	C₂₀₁
10)	[733, 462, 6449]	C₃ x C₂₀₁		---)	[6449, 231, 11728]	C₂₀₁
11)	[1373, 1245, 98833]	C₃ x C₂₀₁		---)	[2017, 1191, 87872]	C₂₀₁
12)	[1889, 1882, 877925]	C₃ x C₂₀₁		73)	[35117, 941, 1889]	C₃ x C₂₀₁
13)	[2113, 3939, 62324]	C₃ x C₂₀₁		59)	[15581, 5009, 2030593]	C₃ x C₂₀₁
14)	[2213, 2873, 4889]	C₃ x C₂₀₁		---)	[4889, 1883, 885200]	C₁₀₀₅
15)	[2477, 1670, 63113]	C₃ x C₂₀₁		77)	[63113, 835, 158528]	C₃ x C₂₀₁
16)	[2557, 3737, 1414369]	C₃ x C₂₀₁		---)	[11689, 5543, 6392500]	C₂₀₁
17)	[2677, 818, 156573]	C₃ x C₂₀₁		---)	[1933, 409, 2677]	C₂₀₁
18)	[2677, 169, 1117]	C₃ x C₂₀₁		---)	[1117, 338, 24093]	C₂₀₁
19)	[2801, 4063, 1347700]	C₃ x C₂₀₁		55)	[13477, 6213, 7868009]	C₃ x C₂₀₁
20)	[2857, 3267, 953408]	C₃ x C₂₀₁		---)	[14897, 6534, 6859657]	C₂₀₁
21)	[2917, 169, 577]	C₃ x C₂₀₁		---)	[577, 338, 26253]	C₁₄₀₇
22)	[3209, 4831, 1078100]	C₃ x C₂₀₁		51)	[10781, 4429, 3931025]	C₃ x C₂₀₁
23)	[3221, 1598, 174577]	C₃ x C₂₀₁		---)	[1033, 799, 115956]	C₂₀₁
24)	[3221, 117, 2617]	C₃ x C₂₀₁		---)	[2617, 234, 3221]	C₂₀₁
25)	[3469, 1041, 228425]	C₃ x C₂₀₁		46)	[9137, 2082, 169981]	C₃ x C₂₀₁
26)	[3877, 2001, 651101]	C₃ x C₂₀₁		---)	[5381, 4002, 1399597]	C₂₀₁
27)	[3889, 1003, 242752]	C₃ x C₂₀₁		---)	[3793, 2006, 35001]	C₂₀₁
28)	[4493, 1145, 3137]	C₃ x C₂₀₁		---)	[3137, 2290, 1298477]	C₃ x C₆₀₃
29)	[4813, 8085, 15907433]	C₃ x C₂₀₁		---)	[16553, 5655, 2329492]	C₃ x C₃ x C₂₀₁
30)	[4933, 5293, 431973]	C₃ x C₂₀₁		37)	[5333, 3873, 4933]	C₃ x C₂₀₁
31)	[4933, 985, 34137]	C₃ x C₂₀₁		---)	[3793, 1970, 833677]	C₂₀₁
32)	[4937, 4538, 705061]	C₃ x C₂₀₁		---)	[14389, 2269, 1110825]	C₃ x C₃ x C₂₀₁
33)	[5297, 4771, 1080896]	C₃ x C₂₀₁		---)	[16889, 9542, 18438857]	C₂₀₁
34)	[5297, 259, 4852]	C₃ x C₂₀₁		---)	[1213, 518, 47673]	C₂₀₁
35)	[5297, 1819, 603392]	C₃ x C₂₀₁		---)	[2357, 3433, 895193]	C₂₀₁
36)	[5333, 890, 6037]	C₃ x C₂₀₁		---)	[6037, 445, 47997]	C₂₀₁
37)	[5333, 3873, 4933]	C₃ x C₂₀₁		30)	[4933, 5293, 431973]	C₃ x C₂₀₁
38)	[5573, 4337, 788753]	C₃ x C₂₀₁		60)	[16097, 8674, 15654557]	C₃ x C₂₀₁
39)	[5741, 4085, 140189]	C₃ x C₂₀₁		---)	[2861, 2137, 694661]	C₂₀₁
40)	[5821, 750, 47489]	C₃ x C₂₀₁		---)	[281, 375, 23284]	C₂₀₁
41)	[6053, 3497, 1954093]	C₃ x C₂₀₁		---)	[5413, 5285, 6591717]	C₂₀₁
42)	[6053, 3258, 1467253]	C₃ x C₂₀₁		---)	[5077, 1629, 296597]	C₂₀₁
43)	[7537, 2039, 615424]	C₃ x C₂₀₁		---)	[601, 1391, 482368]	C₂₀₁
44)	[7753, 367, 16228]	C₃ x C₂₀₁		---)	[4057, 734, 69777]	C₂₀₁
45)	[8597, 6537, 2685733]	C₃ x C₂₀₁		---)	[5077, 6165, 3103517]	C₂₀₁
46)	[9137, 2082, 169981]	C₃ x C₂₀₁		25)	[3469, 1041, 228425]	C₃ x C₂₀₁
47)	[9293, 517, 45913]	C₃ x C₂₀₁		---)	[937, 1034, 83637]	C₂₀₁
48)	[10301, 942, 57025]	C₃ x C₂₀₁		---)	[2281, 471, 41204]	C₂₀₁
49)	[10301, 1601, 638225]	C₃ x C₂₀₁		---)	[521, 1715, 41204]	C₂₀₁
50)	[10733, 4249, 2957]	C₃ x C₂₀₁		---)	[2957, 3905, 3101837]	C₂₀₁
51)	[10781, 4429, 3931025]	C₃ x C₂₀₁		22)	[3209, 4831, 1078100]	C₃ x C₂₀₁
52)	[11197, 2154, 40229]	C₃ x C₂₀₁		---)	[821, 1077, 279925]	C₂₀₁
53)	[12197, 3209, 2546977]	C₃ x C₂₀₁		---)	[1153, 2459, 439092]	C₂₀₁
54)	[12401, 1850, 806021]	C₃ x C₂₀₁		---)	[2789, 925, 12401]	C₂₀₁
55)	[13477, 6213, 7868009]	C₃ x C₂₀₁		19)	[2801, 4063, 1347700]	C₃ x C₂₀₁
56)	[13577, 746, 84821]	C₃ x C₂₀₁		---)	[701, 373, 13577]	C₂₀₁
57)	[15193, 1706, 180661]	C₃ x C₂₀₁		---)	[1069, 853, 136737]	C₂₀₁
58)	[15193, 8694, 17924057]	C₃ x C₂₀₁		---)	[4817, 4347, 243088]	C₂₀₁
59)	[15581, 5009, 2030593]	C₃ x C₂₀₁		13)	[2113, 3939, 62324]	C₃ x C₂₀₁
60)	[16097, 8674, 15654557]	C₃ x C₂₀₁		38)	[5573, 4337, 788753]	C₃ x C₂₀₁
61)	[16477, 3209, 1647589]	C₃ x C₂₀₁		---)	[5701, 6418, 3707325]	C₂₀₁
62)	[16481, 5650, 3821]	C₃ x C₂₀₁		---)	[3821, 2825, 1994201]	C₂₀₁
63)	[16553, 1679, 204032]	C₃ x C₂₀₁		---)	[797, 3358, 2002913]	C₂₀₁
64)	[17609, 5879, 500900]	C₃ x C₂₀₁		---)	[5009, 9335, 3451364]	C₂₀₁
65)	[18701, 5914, 6873749]	C₃ x C₂₀₁		---)	[5021, 2957, 467525]	C₂₀₁
66)	[22397, 185, 2957]	C₃ x C₂₀₁		---)	[2957, 370, 22397]	C₂₀₁
67)	[23297, 2667, 1073488]	C₃ x C₂₀₁		---)	[397, 2357, 209673]	C₂₀₁
68)	[24281, 762, 48037]	C₃ x C₂₀₁		---)	[397, 381, 24281]	C₂₀₁
69)	[26113, 2067, 904916]	C₃ x C₂₀₁		---)	[269, 1849, 26113]	C₂₀₁
70)	[27617, 231, 6436]	C₃ x C₂₀₁		---)	[1609, 462, 27617]	C₂₀₁
71)	[29629, 517, 157]	C₃ x C₂₀₁		---)	[157, 1034, 266661]	C₂₀₁
72)	[31121, 2194, 83053]	C₃ x C₂₀₁		---)	[157, 1097, 280089]	C₂₀₁
73)	[35117, 941, 1889]	C₃ x C₂₀₁		12)	[1889, 1882, 877925]	C₃ x C₂₀₁
74)	[39157, 826, 13941]	C₃ x C₂₀₁		---)	[1549, 413, 39157]	C₂₀₁
75)	[42709, 1297, 153621]	C₃ x C₂₀₁		---)	[101, 1885, 42709]	C₂₀₁
76)	[53633, 1854, 1201]	C₃ x C₂₀₁		---)	[1201, 927, 214532]	C₂₀₁
77)	[63113, 835, 158528]	C₃ x C₂₀₁		15)	[2477, 1670, 63113]	C₃ x C₂₀₁
78)	[85517, 1258, 53573]	C₃ x C₂₀₁		---)	[317, 629, 85517]	C₂₀₁
79)	[101273, 827, 145664]	C₃ x C₂₀₁		---)	[569, 1654, 101273]	C₂₀₁
80)	[111121, 1506, 122525]	C₃ x C₂₀₁		---)	[29, 753, 111121]	C₂₀₁
81)	[113417, 2814, 164977]	C₃ x C₂₀₁		---)	[457, 1407, 453668]	C₂₀₁
82)	[158233, 403, 1044]	C₃ x C₂₀₁		---)	[29, 806, 158233]	C₂₀₁
83)	[185441, 975, 191296]	C₃ x C₂₀₁		---)	[61, 1950, 185441]	C₂₀₁
84)	[194581, 541, 24525]	C₃ x C₂₀₁		---)	[109, 1082, 194581]	C₂₀₁
85)	[209317, 2098, 263133]	C₃ x C₂₀₁		---)	[173, 1049, 209317]	C₂₀₁
86)	[218797, 481, 3141]	C₃ x C₂₀₁		---)	[349, 962, 218797]	C₂₀₁
87)	[254437, 733, 70713]	C₃ x C₂₀₁		---)	[97, 1466, 254437]	C₂₀₁
88)	[283501, 649, 34425]	C₃ x C₂₀₁		---)	[17, 1298, 283501]	C₂₀₁
89)	[299701, 549, 425]	C₃ x C₂₀₁		---)	[17, 1098, 299701]	C₂₀₁
90)	[373453, 625, 4293]	C₃ x C₂₀₁		---)	[53, 1250, 373453]	C₂₀₁
91)	[376097, 2195, 358288]	C₃ x C₂₀₁		---)	[457, 4390, 3384873]	C₂₀₁
92)	[550757, 845, 40817]	C₃ x C₂₀₁		---)	[17, 1690, 550757]	C₂₀₁
93)	[999529, 1651, 431568]	C₃ x C₂₀₁		---)	[37, 3302, 999529]	C₂₀₁
94)	[1484137, 1475, 172872]	C₃ x C₂₀₁		---)	[8, 2950, 1484137]	C₂₀₁
95)	[1754617, 1483, 111168]	C₃ x C₂₀₁		---)	[193, 2966, 1754617]	C₂₀₁
96)	[2897689, 1883, 162000]	C₃ x C₂₀₁		---)	[5, 3766, 2897689]	C₂₀₁
97)	[3045457, 2647, 990288]	C₃ x C₂₀₁		---)	[13, 5294, 3045457]	C₂₀₁
98)	[3078661, 2421, 695645]	C₃ x C₂₀₁		---)	[5, 3533, 3078661]	C₂₀₁
99)	[3467833, 1985, 118098]	C₃ x C₂₀₁		---)	[8, 3970, 3467833]	C₂₀₁
100)	[3843221, 2621, 756605]	C₃ x C₂₀₁		---)	[5, 3973, 3843221]	C₂₀₁
101)	[4487449, 2171, 56448]	C₃ x C₂₀₁		---)	[8, 4342, 4487449]	C₂₀₁
102)	[5362033, 3175, 1179648]	C₃ x C₂₀₁		2)	[8, 6350, 5362033]	C₃ x C₂₀₁
103)	[5502949, 3973, 2570445]	C₃ x C₂₀₁		---)	[5, 4749, 5502949]	C₂₀₁
104)	[13703897, 3803, 189728]	C₃ x C₂₀₁		---)	[8, 7606, 13703897]	C₂₀₁
105)	[28142953, 5305, 18]	C₃ x C₂₀₁		1)	[8, 10610, 28142953]	C₃ x C₂₀₁

Class number: [Non-normal] [Cyclic]

Class group C3 x C201 non-normal (D4) quartic CM field invariants: 105 fields

Class group C₃ x C₂₀₁ non-normal (D₄) quartic CM field invariants: 105 fields