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, 5614, 7878097]	C₈₁₉		---)	[7878097, 2807, 288]	C₁₃₉₂₃
2)	[13, 3502, 2459473]	C₈₁₉		137)	[2459473, 1751, 151632]	C₈₁₉
3)	[17, 2398, 1349473]	C₈₁₉		129)	[1349473, 1199, 22032]	C₈₁₉
4)	[17, 2318, 1325873]	C₈₁₉		128)	[1325873, 1159, 4352]	C₈₁₉
5)	[17, 2014, 925921]	C₈₁₉		---)	[925921, 1007, 22032]	C₃ x C₈₁₉
6)	[17, 2894, 2024177]	C₈₁₉		136)	[2024177, 1447, 17408]	C₈₁₉
7)	[17, 1646, 638161]	C₈₁₉		122)	[638161, 823, 9792]	C₈₁₉
8)	[29, 5686, 7897049]	C₈₁₉		144)	[7897049, 2843, 46400]	C₈₁₉
9)	[29, 4742, 4723337]	C₈₁₉		---)	[4723337, 2371, 224576]	C₄₀₉₅
10)	[29, 3302, 2679401]	C₈₁₉		---)	[2679401, 1651, 11600]	C₃ x C₈₁₉
11)	[37, 3822, 3637121]	C₈₁₉		141)	[3637121, 1911, 3700]	C₈₁₉
12)	[37, 2925, 1899137]	C₈₁₉		134)	[1899137, 5850, 959077]	C₈₁₉
13)	[41, 2510, 1060721]	C₈₁₉		126)	[1060721, 1255, 128576]	C₈₁₉
14)	[53, 3662, 3230449]	C₈₁₉		140)	[3230449, 1831, 30528]	C₈₁₉
15)	[53, 3598, 3151601]	C₈₁₉		139)	[3151601, 1799, 21200]	C₈₁₉
16)	[53, 3438, 2737873]	C₈₁₉		138)	[2737873, 1719, 54272]	C₈₁₉
17)	[53, 3833, 3667129]	C₈₁₉		142)	[3667129, 7666, 23373]	C₈₁₉
18)	[61, 5294, 6971473]	C₈₁₉		143)	[6971473, 2647, 8784]	C₈₁₉
19)	[61, 2646, 1090553]	C₈₁₉		---)	[1090553, 1323, 164944]	C₄₀₉₅
20)	[89, 582, 49081]	C₈₁₉		---)	[49081, 291, 8900]	C₄₀₉₅
21)	[101, 3526, 1013833]	C₈₁₉		125)	[1013833, 1763, 523584]	C₈₁₉
22)	[109, 2742, 1433177]	C₈₁₉		131)	[1433177, 1371, 111616]	C₈₁₉
23)	[241, 2795, 1783764]	C₈₁₉		104)	[49549, 3025, 1284289]	C₈₁₉
24)	[317, 2533, 1381409]	C₈₁₉		130)	[1381409, 5066, 890453]	C₈₁₉
25)	[353, 1186, 350237]	C₈₁₉		118)	[350237, 593, 353]	C₈₁₉
26)	[373, 2702, 1610353]	C₈₁₉		132)	[1610353, 1351, 53712]	C₈₁₉
27)	[389, 989, 236653]	C₈₁₉		115)	[236653, 1978, 31509]	C₈₁₉
28)	[457, 1830, 829913]	C₈₁₉		90)	[16937, 915, 1828]	C₈₁₉
29)	[509, 1661, 358753]	C₈₁₉		119)	[358753, 3322, 1323909]	C₈₁₉
30)	[577, 1298, 31149]	C₈₁₉		---)	[3461, 649, 97513]	C₁₁₇
31)	[757, 3502, 2956993]	C₈₁₉		92)	[17497, 1751, 27252]	C₈₁₉
32)	[773, 1238, 370793]	C₈₁₉		120)	[370793, 619, 3092]	C₈₁₉
33)	[997, 870, 173273]	C₈₁₉		112)	[173273, 435, 3988]	C₈₁₉
34)	[1009, 727, 111700]	C₈₁₉		---)	[1117, 857, 9081]	C₁₁₇
35)	[1069, 1041, 270653]	C₈₁₉		117)	[270653, 2082, 1069]	C₈₁₉
36)	[1217, 842, 172373]	C₈₁₉		111)	[172373, 421, 1217]	C₈₁₉
37)	[1361, 406, 19433]	C₈₁₉		95)	[19433, 203, 5444]	C₈₁₉
38)	[1621, 2525, 977521]	C₈₁₉		---)	[977521, 5050, 2465541]	C₄₀₉₅
39)	[1777, 1507, 194148]	C₈₁₉		66)	[5393, 3014, 1494457]	C₈₁₉
40)	[1877, 3097, 2341073]	C₈₁₉		101)	[47777, 6194, 227117]	C₈₁₉
41)	[2029, 1986, 4013]	C₈₁₉		---)	[4013, 993, 245509]	C₁₁₇
42)	[2593, 1822, 166113]	C₈₁₉		94)	[18457, 911, 165952]	C₈₁₉
43)	[2729, 3655, 277136]	C₈₁₉		91)	[17321, 6719, 11177984]	C₈₁₉
44)	[2729, 1295, 303956]	C₈₁₉		106)	[75989, 2590, 461201]	C₈₁₉
45)	[2753, 1831, 804416]	C₈₁₉		83)	[12569, 3662, 134897]	C₈₁₉
46)	[2801, 4278, 2379337]	C₈₁₉		75)	[8233, 2139, 548996]	C₈₁₉
47)	[2833, 4055, 540468]	C₈₁₉		87)	[15013, 7073, 7368633]	C₈₁₉
48)	[3217, 967, 52816]	C₈₁₉		49)	[3301, 1934, 723825]	C₈₁₉
49)	[3301, 1934, 723825]	C₈₁₉		48)	[3217, 967, 52816]	C₈₁₉
50)	[3373, 2573, 95913]	C₈₁₉		80)	[10657, 5146, 6236677]	C₈₁₉
51)	[3457, 6635, 9407808]	C₈₁₉		---)	[16333, 4297, 169393]	C₉₀₀₉
52)	[3541, 2801, 1641825]	C₈₁₉		72)	[7297, 4651, 1713844]	C₈₁₉
53)	[3613, 7285, 4415053]	C₈₁₉		---)	[15277, 4585, 4946197]	C₇ x C₈₁₉
54)	[3613, 6113, 9081153]	C₈₁₉		82)	[12457, 3691, 14452]	C₈₁₉
55)	[3709, 2726, 1798425]	C₈₁₉		74)	[7993, 1363, 14836]	C₈₁₉
56)	[3833, 8443, 17743444]	C₈₁₉		---)	[15349, 4597, 4174137]	C₃ x C₈₁₉
57)	[3833, 5102, 374801]	C₈₁₉		73)	[7649, 2551, 1533200]	C₈₁₉
58)	[4021, 7677, 16217]	C₈₁₉		---)	[16217, 4383, 4117504]	C₇ x C₈₁₉
59)	[4229, 1369, 2293]	C₈₁₉		---)	[2293, 2738, 1864989]	C₁₁₇
60)	[4241, 3055, 550976]	C₈₁₉		76)	[8609, 6110, 7129121]	C₈₁₉
61)	[4241, 6139, 251728]	C₈₁₉		---)	[15733, 5509, 6450561]	C₃ x C₈₁₉
62)	[4549, 5877, 2574377]	C₈₁₉		88)	[15233, 8723, 891604]	C₈₁₉
63)	[4733, 8053, 15193]	C₈₁₉		---)	[15193, 7599, 302912]	C₃ x C₈₁₉
64)	[5021, 2629, 9473]	C₈₁₉		78)	[9473, 5258, 6873749]	C₈₁₉
65)	[5153, 2867, 1899044]	C₈₁₉		79)	[9689, 5734, 623513]	C₈₁₉
66)	[5393, 3014, 1494457]	C₈₁₉		39)	[1777, 1507, 194148]	C₈₁₉
67)	[5449, 8315, 16564176]	C₈₁₉		84)	[12781, 4733, 1226025]	C₈₁₉
68)	[5581, 5485, 878521]	C₈₁₉		---)	[17929, 10879, 4375504]	C₃ x C₈₁₉
69)	[5641, 6426, 7593125]	C₈₁₉		81)	[12149, 3213, 682561]	C₈₁₉
70)	[5813, 662, 16553]	C₈₁₉		---)	[16553, 331, 23252]	C₃ x C₈₁₉
71)	[6421, 881, 179593]	C₈₁₉		113)	[179593, 1762, 57789]	C₈₁₉
72)	[7297, 4651, 1713844]	C₈₁₉		52)	[3541, 2801, 1641825]	C₈₁₉
73)	[7649, 2551, 1533200]	C₈₁₉		57)	[3833, 5102, 374801]	C₈₁₉
74)	[7993, 1363, 14836]	C₈₁₉		55)	[3709, 2726, 1798425]	C₈₁₉
75)	[8233, 2139, 548996]	C₈₁₉		46)	[2801, 4278, 2379337]	C₈₁₉
76)	[8609, 6110, 7129121]	C₈₁₉		60)	[4241, 3055, 550976]	C₈₁₉
77)	[9049, 5883, 6478400]	C₈₁₉		---)	[4049, 3127, 904900]	C₁₁₇
78)	[9473, 5258, 6873749]	C₈₁₉		64)	[5021, 2629, 9473]	C₈₁₉
79)	[9689, 5734, 623513]	C₈₁₉		65)	[5153, 2867, 1899044]	C₈₁₉
80)	[10657, 5146, 6236677]	C₈₁₉		50)	[3373, 2573, 95913]	C₈₁₉
81)	[12149, 3213, 682561]	C₈₁₉		69)	[5641, 6426, 7593125]	C₈₁₉
82)	[12457, 3691, 14452]	C₈₁₉		54)	[3613, 6113, 9081153]	C₈₁₉
83)	[12569, 3662, 134897]	C₈₁₉		45)	[2753, 1831, 804416]	C₈₁₉
84)	[12781, 4733, 1226025]	C₈₁₉		67)	[5449, 8315, 16564176]	C₈₁₉
85)	[13049, 530, 18029]	C₈₁₉		---)	[149, 265, 13049]	C₁₁₇
86)	[13457, 659, 78292]	C₈₁₉		---)	[37, 501, 13457]	C₆₃
87)	[15013, 7073, 7368633]	C₈₁₉		47)	[2833, 4055, 540468]	C₈₁₉
88)	[15233, 8723, 891604]	C₈₁₉		62)	[4549, 5877, 2574377]	C₈₁₉
89)	[15377, 2091, 443392]	C₈₁₉		---)	[433, 1611, 246032]	C₆₃
90)	[16937, 915, 1828]	C₈₁₉		28)	[457, 1830, 829913]	C₈₁₉
91)	[17321, 6719, 11177984]	C₈₁₉		43)	[2729, 3655, 277136]	C₈₁₉
92)	[17497, 1751, 27252]	C₈₁₉		31)	[757, 3502, 2956993]	C₈₁₉
93)	[17989, 4066, 4061133]	C₈₁₉		---)	[853, 2033, 17989]	C₉₁
94)	[18457, 911, 165952]	C₈₁₉		42)	[2593, 1822, 166113]	C₈₁₉
95)	[19433, 203, 5444]	C₈₁₉		37)	[1361, 406, 19433]	C₈₁₉
96)	[21613, 757, 8181]	C₈₁₉		---)	[101, 1514, 540325]	C₆₃
97)	[33941, 2498, 338125]	C₈₁₉		---)	[541, 1249, 305469]	C₁₁₇
98)	[38977, 311, 14436]	C₈₁₉		---)	[401, 622, 38977]	C₄₅₅
99)	[39089, 2135, 348004]	C₈₁₉		---)	[241, 2375, 1407204]	C₁₁₇
100)	[47093, 1525, 569633]	C₈₁₉		---)	[113, 1919, 188372]	C₉₁
101)	[47777, 6194, 227117]	C₈₁₉		40)	[1877, 3097, 2341073]	C₈₁₉
102)	[48121, 427, 33552]	C₈₁₉		---)	[233, 854, 48121]	C₉₁
103)	[48973, 673, 100989]	C₈₁₉		---)	[229, 1346, 48973]	C₂₇₃
104)	[49549, 3025, 1284289]	C₈₁₉		23)	[241, 2795, 1783764]	C₈₁₉
105)	[75401, 323, 7232]	C₈₁₉		---)	[113, 646, 75401]	C₆₃
106)	[75989, 2590, 461201]	C₈₁₉		44)	[2729, 1295, 303956]	C₈₁₉
107)	[82373, 301, 2057]	C₈₁₉		---)	[17, 602, 82373]	C₆₃
108)	[83273, 1091, 276752]	C₈₁₉		---)	[353, 2182, 83273]	C₉₁
109)	[100493, 321, 637]	C₈₁₉		---)	[13, 642, 100493]	C₆₃
110)	[130457, 443, 16448]	C₈₁₉		---)	[257, 886, 130457]	C₃ x C₁₁₇
111)	[172373, 421, 1217]	C₈₁₉		36)	[1217, 842, 172373]	C₈₁₉
112)	[173273, 435, 3988]	C₈₁₉		33)	[997, 870, 173273]	C₈₁₉
113)	[179593, 1762, 57789]	C₈₁₉		71)	[6421, 881, 179593]	C₈₁₉
114)	[207833, 1435, 462848]	C₈₁₉		---)	[113, 2870, 207833]	C₁₁₇
115)	[236653, 1978, 31509]	C₈₁₉		27)	[389, 989, 236653]	C₈₁₉
116)	[264889, 963, 165620]	C₈₁₉		---)	[5, 1069, 264889]	C₉₁
117)	[270653, 2082, 1069]	C₈₁₉		35)	[1069, 1041, 270653]	C₈₁₉
118)	[350237, 593, 353]	C₈₁₉		25)	[353, 1186, 350237]	C₈₁₉
119)	[358753, 3322, 1323909]	C₈₁₉		29)	[509, 1661, 358753]	C₈₁₉
120)	[370793, 619, 3092]	C₈₁₉		32)	[773, 1238, 370793]	C₈₁₉
121)	[545789, 2917, 899197]	C₈₁₉		---)	[13, 1509, 545789]	C₁₁₇
122)	[638161, 823, 9792]	C₈₁₉		7)	[17, 1646, 638161]	C₈₁₉
123)	[709769, 937, 42050]	C₈₁₉		---)	[8, 1874, 709769]	C₆₃
124)	[984421, 3233, 398125]	C₈₁₉		---)	[13, 2009, 984421]	C₁₁₇
125)	[1013833, 1763, 523584]	C₈₁₉		21)	[101, 3526, 1013833]	C₈₁₉
126)	[1060721, 1255, 128576]	C₈₁₉		13)	[41, 2510, 1060721]	C₈₁₉
127)	[1170373, 3857, 1085773]	C₈₁₉		---)	[13, 2165, 1170373]	C₁₁₇
128)	[1325873, 1159, 4352]	C₈₁₉		4)	[17, 2318, 1325873]	C₈₁₉
129)	[1349473, 1199, 22032]	C₈₁₉		3)	[17, 2398, 1349473]	C₈₁₉
130)	[1381409, 5066, 890453]	C₈₁₉		24)	[317, 2533, 1381409]	C₈₁₉
131)	[1433177, 1371, 111616]	C₈₁₉		22)	[109, 2742, 1433177]	C₈₁₉
132)	[1610353, 1351, 53712]	C₈₁₉		26)	[373, 2702, 1610353]	C₈₁₉
133)	[1639481, 1291, 6800]	C₈₁₉		---)	[17, 2582, 1639481]	C₉₁
134)	[1899137, 5850, 959077]	C₈₁₉		12)	[37, 2925, 1899137]	C₈₁₉
135)	[1973417, 1523, 86528]	C₈₁₉		---)	[8, 3046, 1973417]	C₁₁₇
136)	[2024177, 1447, 17408]	C₈₁₉		6)	[17, 2894, 2024177]	C₈₁₉
137)	[2459473, 1751, 151632]	C₈₁₉		2)	[13, 3502, 2459473]	C₈₁₉
138)	[2737873, 1719, 54272]	C₈₁₉		16)	[53, 3438, 2737873]	C₈₁₉
139)	[3151601, 1799, 21200]	C₈₁₉		15)	[53, 3598, 3151601]	C₈₁₉
140)	[3230449, 1831, 30528]	C₈₁₉		14)	[53, 3662, 3230449]	C₈₁₉
141)	[3637121, 1911, 3700]	C₈₁₉		11)	[37, 3822, 3637121]	C₈₁₉
142)	[3667129, 7666, 23373]	C₈₁₉		17)	[53, 3833, 3667129]	C₈₁₉
143)	[6971473, 2647, 8784]	C₈₁₉		18)	[61, 5294, 6971473]	C₈₁₉
144)	[7897049, 2843, 46400]	C₈₁₉		8)	[29, 5686, 7897049]	C₈₁₉

Class number: [Non-normal] [Cyclic]

Class group C819 non-normal (D4) quartic CM field invariants: 144 fields

Class group C₈₁₉ non-normal (D₄) quartic CM field invariants: 144 fields