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, 9566, 22617169]	C₁₀₀₅		167)	[22617169, 4783, 64980]	C₁₀₀₅
2)	[8, 6446, 10346257]	C₁₀₀₅		162)	[10346257, 3223, 10368]	C₁₀₀₅
3)	[8, 6110, 9307937]	C₁₀₀₅		160)	[9307937, 3055, 6272]	C₁₀₀₅
4)	[13, 5742, 8201873]	C₁₀₀₅		158)	[8201873, 2871, 10192]	C₁₀₀₅
5)	[17, 2702, 1032049]	C₁₀₀₅		137)	[1032049, 1351, 198288]	C₁₀₀₅
6)	[29, 4214, 4409753]	C₁₀₀₅		152)	[4409753, 2107, 7424]	C₁₀₀₅
7)	[41, 2254, 511793]	C₁₀₀₅		130)	[511793, 1127, 189584]	C₁₀₀₅
8)	[53, 3694, 3136657]	C₁₀₀₅		148)	[3136657, 1847, 68688]	C₁₀₀₅
9)	[53, 5390, 7208753]	C₁₀₀₅		157)	[7208753, 2695, 13568]	C₁₀₀₅
10)	[73, 3326, 1251841]	C₁₀₀₅		143)	[1251841, 1663, 378432]	C₁₀₀₅
11)	[89, 1886, 200033]	C₁₀₀₅		---)	[200033, 943, 172304]	C₃ x C₃₀₁₅
12)	[101, 3574, 3167513]	C₁₀₀₅		149)	[3167513, 1787, 6464]	C₁₀₀₅
13)	[101, 3214, 2168753]	C₁₀₀₅		---)	[2168753, 1607, 103424]	C₇₀₃₅
14)	[109, 2334, 1250273]	C₁₀₀₅		---)	[1250273, 1167, 27904]	C₅ x C₁₀₀₅
15)	[109, 2814, 1868033]	C₁₀₀₅		145)	[1868033, 1407, 27904]	C₁₀₀₅
16)	[109, 3990, 3533561]	C₁₀₀₅		150)	[3533561, 1995, 111616]	C₁₀₀₅
17)	[181, 3534, 1164593]	C₁₀₀₅		142)	[1164593, 1767, 489424]	C₁₀₀₅
18)	[181, 2238, 1066817]	C₁₀₀₅		139)	[1066817, 1119, 46336]	C₁₀₀₅
19)	[241, 702, 107777]	C₁₀₀₅		116)	[107777, 351, 3856]	C₁₀₀₅
20)	[269, 1574, 602153]	C₁₀₀₅		132)	[602153, 787, 4304]	C₁₀₀₅
21)	[293, 3262, 784961]	C₁₀₀₅		135)	[784961, 1631, 468800]	C₁₀₀₅
22)	[389, 3230, 2508641]	C₁₀₀₅		146)	[2508641, 1615, 24896]	C₁₀₀₅
23)	[397, 1662, 665153]	C₁₀₀₅		133)	[665153, 831, 6352]	C₁₀₀₅
24)	[409, 606, 65633]	C₁₀₀₅		---)	[65633, 303, 6544]	C₁₇₀₈₅
25)	[521, 1326, 406225]	C₁₀₀₅		96)	[16249, 663, 8336]	C₁₀₀₅
26)	[569, 946, 221453]	C₁₀₀₅		124)	[221453, 473, 569]	C₁₀₀₅
27)	[761, 299, 13028]	C₁₀₀₅		---)	[3257, 598, 37289]	C₃₃₅
28)	[1097, 2667, 66628]	C₁₀₀₅		97)	[16657, 3447, 2966288]	C₁₀₀₅
29)	[1301, 2081, 1074509]	C₁₀₀₅		140)	[1074509, 4162, 32525]	C₁₀₀₅
30)	[1429, 381, 35933]	C₁₀₀₅		110)	[35933, 762, 1429]	C₁₀₀₅
31)	[1801, 3474, 416525]	C₁₀₀₅		---)	[16661, 1737, 650161]	C₃ x C₁₀₀₅
32)	[1877, 921, 132757]	C₁₀₀₅		120)	[132757, 1842, 317213]	C₁₀₀₅
33)	[1889, 959, 191668]	C₁₀₀₅		114)	[47917, 1918, 153009]	C₁₀₀₅
34)	[2141, 873, 189997]	C₁₀₀₅		122)	[189997, 1746, 2141]	C₁₀₀₅
35)	[2141, 869, 183973]	C₁₀₀₅		---)	[183973, 1738, 19269]	C₇₀₃₅
36)	[2273, 2727, 140176]	C₁₀₀₅		---)	[8761, 4151, 1309248]	C₃ x C₉₀₄₅
37)	[2273, 454, 15161]	C₁₀₀₅		92)	[15161, 227, 9092]	C₁₀₀₅
38)	[2557, 1569, 614801]	C₁₀₀₅		57)	[5081, 3138, 2557]	C₁₀₀₅
39)	[2917, 3030, 8297]	C₁₀₀₅		---)	[8297, 1515, 571732]	C₃₃₅
40)	[3001, 1122, 14621]	C₁₀₀₅		89)	[14621, 561, 75025]	C₁₀₀₅
41)	[3221, 665, 13121]	C₁₀₀₅		---)	[13121, 1330, 389741]	C₃₃₅
42)	[3361, 2375, 602676]	C₁₀₀₅		---)	[16741, 4750, 3229921]	C₅ x C₁₀₀₅
43)	[3449, 4947, 736900]	C₁₀₀₅		70)	[7369, 4555, 1117476]	C₁₀₀₅
44)	[3449, 4315, 59876]	C₁₀₀₅		---)	[14969, 7495, 3531776]	C₃ x C₁₀₀₅
45)	[3637, 5885, 1456137]	C₁₀₀₅		100)	[17977, 5555, 6415668]	C₁₀₀₅
46)	[3877, 4969, 5466157]	C₁₀₀₅		79)	[10333, 4105, 1399597]	C₁₀₀₅
47)	[3929, 2071, 953408]	C₁₀₀₅		91)	[14897, 4142, 475409]	C₁₀₀₅
48)	[3929, 2199, 1042900]	C₁₀₀₅		80)	[10429, 4398, 664001]	C₁₀₀₅
49)	[4001, 867, 162916]	C₁₀₀₅		---)	[241, 763, 144036]	C₃₃₅
50)	[4261, 3262, 205825]	C₁₀₀₅		74)	[8233, 1631, 613584]	C₁₀₀₅
51)	[4457, 2471, 589376]	C₁₀₀₅		77)	[9209, 4942, 3748337]	C₁₀₀₅
52)	[4513, 2282, 850581]	C₁₀₀₅		81)	[10501, 1141, 112825]	C₁₀₀₅
53)	[4597, 354, 12941]	C₁₀₀₅		---)	[12941, 177, 4597]	C₃₃₅
54)	[4597, 1613, 42489]	C₁₀₀₅		---)	[4721, 3226, 2431813]	C₃₃₅
55)	[4789, 2318, 117297]	C₁₀₀₅		---)	[13033, 1159, 306496]	C₁₃₀₆₅
56)	[4889, 1883, 885200]	C₁₀₀₅		---)	[2213, 2873, 4889]	C₃ x C₂₀₁
57)	[5081, 3138, 2557]	C₁₀₀₅		38)	[2557, 1569, 614801]	C₁₀₀₅
58)	[5081, 243, 13492]	C₁₀₀₅		---)	[3373, 486, 5081]	C₃₃₅
59)	[5113, 1922, 903069]	C₁₀₀₅		84)	[11149, 961, 5113]	C₁₀₀₅
60)	[5261, 5201, 132425]	C₁₀₀₅		61)	[5297, 4871, 336704]	C₁₀₀₅
61)	[5297, 4871, 336704]	C₁₀₀₅		60)	[5261, 5201, 132425]	C₁₀₀₅
62)	[5641, 6379, 6786900]	C₁₀₀₅		71)	[7541, 3469, 141025]	C₁₀₀₅
63)	[5669, 5825, 3549209]	C₁₀₀₅		---)	[12281, 8011, 566900]	C₁₁₀₅₅
64)	[5749, 1169, 167733]	C₁₀₀₅		104)	[18637, 2338, 695629]	C₁₀₀₅
65)	[5801, 2203, 306896]	C₁₀₀₅		106)	[19181, 4406, 3625625]	C₁₀₀₅
66)	[6113, 4747, 3541328]	C₁₀₀₅		---)	[4517, 2965, 299537]	C₂₀₁
67)	[6481, 5071, 4871700]	C₁₀₀₅		---)	[5413, 3781, 2858121]	C₂₀₁
68)	[6637, 1613, 51453]	C₁₀₀₅		---)	[5717, 3226, 2395957]	C₃₃₅
69)	[6949, 3041, 183789]	C₁₀₀₅		---)	[2269, 2821, 840829]	C₂₀₁
70)	[7369, 4555, 1117476]	C₁₀₀₅		43)	[3449, 4947, 736900]	C₁₀₀₅
71)	[7541, 3469, 141025]	C₁₀₀₅		62)	[5641, 6379, 6786900]	C₁₀₀₅
72)	[7673, 1986, 955357]	C₁₀₀₅		---)	[5653, 993, 7673]	C₃₃₅
73)	[7753, 5027, 20308]	C₁₀₀₅		---)	[5077, 4045, 3419073]	C₃₃₅
74)	[8233, 1631, 613584]	C₁₀₀₅		50)	[4261, 3262, 205825]	C₁₀₀₅
75)	[8597, 3433, 4049]	C₁₀₀₅		---)	[4049, 6247, 3438800]	C₃₃₅
76)	[8597, 4769, 1333609]	C₁₀₀₅		---)	[2521, 3027, 1685012]	C₃₃₅
77)	[9209, 4942, 3748337]	C₁₀₀₅		51)	[4457, 2471, 589376]	C₁₀₀₅
78)	[9281, 5663, 478900]	C₁₀₀₅		---)	[4789, 4145, 4092921]	C₃₃₅
79)	[10333, 4105, 1399597]	C₁₀₀₅		46)	[3877, 4969, 5466157]	C₁₀₀₅
80)	[10429, 4398, 664001]	C₁₀₀₅		48)	[3929, 2199, 1042900]	C₁₀₀₅
81)	[10501, 1141, 112825]	C₁₀₀₅		52)	[4513, 2282, 850581]	C₁₀₀₅
82)	[10613, 2413, 688853]	C₁₀₀₅		---)	[5693, 4826, 3067157]	C₂₀₁
83)	[11057, 3047, 2318288]	C₁₀₀₅		---)	[2957, 6017, 3195473]	C₃₃₅
84)	[11149, 961, 5113]	C₁₀₀₅		59)	[5113, 1922, 903069]	C₁₀₀₅
85)	[11273, 3798, 720313]	C₁₀₀₅		---)	[5953, 1899, 721472]	C₂₀₁
86)	[12197, 3886, 2018881]	C₁₀₀₅		---)	[1201, 1943, 439092]	C₃₃₅
87)	[12821, 1249, 361153]	C₁₀₀₅		---)	[2137, 2498, 115389]	C₃₃₅
88)	[14197, 2818, 1928493]	C₁₀₀₅		---)	[4373, 1409, 14197]	C₃₃₅
89)	[14621, 561, 75025]	C₁₀₀₅		40)	[3001, 1122, 14621]	C₁₀₀₅
90)	[14653, 3277, 1362249]	C₁₀₀₅		---)	[3089, 6554, 5289733]	C₃₃₅
91)	[14897, 4142, 475409]	C₁₀₀₅		47)	[3929, 2071, 953408]	C₁₀₀₅
92)	[15161, 227, 9092]	C₁₀₀₅		37)	[2273, 454, 15161]	C₁₀₀₅
93)	[15641, 671, 14804]	C₁₀₀₅		---)	[3701, 1342, 391025]	C₃₃₅
94)	[15661, 3902, 1551217]	C₁₀₀₅		---)	[4297, 1951, 563796]	C₃₃₅
95)	[15881, 631, 63808]	C₁₀₀₅		---)	[997, 1262, 142929]	C₃₃₅
96)	[16249, 663, 8336]	C₁₀₀₅		25)	[521, 1326, 406225]	C₁₀₀₅
97)	[16657, 3447, 2966288]	C₁₀₀₅		28)	[1097, 2667, 66628]	C₁₀₀₅
98)	[17053, 3149, 1963197]	C₁₀₀₅		---)	[2693, 6298, 2063413]	C₃₃₅
99)	[17581, 9013, 16612137]	C₁₀₀₅		---)	[5113, 5059, 2531664]	C₃₃₅
100)	[17977, 5555, 6415668]	C₁₀₀₅		45)	[3637, 5885, 1456137]	C₁₀₀₅
101)	[18269, 1789, 685949]	C₁₀₀₅		---)	[5669, 3578, 456725]	C₃₃₅
102)	[18353, 4779, 89104]	C₁₀₀₅		---)	[5569, 9558, 22482425]	C₂₀₁
103)	[18433, 2951, 845316]	C₁₀₀₅		---)	[2609, 5902, 5327137]	C₂₀₁
104)	[18637, 2338, 695629]	C₁₀₀₅		64)	[5749, 1169, 167733]	C₁₀₀₅
105)	[18701, 1797, 690421]	C₁₀₀₅		---)	[2389, 3594, 467525]	C₃₃₅
106)	[19181, 4406, 3625625]	C₁₀₀₅		65)	[5801, 2203, 306896]	C₁₀₀₅
107)	[29221, 722, 13437]	C₁₀₀₅		---)	[1493, 361, 29221]	C₃₃₅
108)	[29989, 1273, 337657]	C₁₀₀₅		---)	[97, 1423, 479824]	C₃₃₅
109)	[31513, 818, 41229]	C₁₀₀₅		---)	[509, 409, 31513]	C₃₃₅
110)	[35933, 762, 1429]	C₁₀₀₅		30)	[1429, 381, 35933]	C₁₀₀₅
111)	[37781, 2141, 1136525]	C₁₀₀₅		---)	[269, 2849, 944525]	C₂₀₁
112)	[39569, 695, 110864]	C₁₀₀₅		---)	[41, 1390, 39569]	C₃₃₅
113)	[42437, 826, 821]	C₁₀₀₅		---)	[821, 413, 42437]	C₂₀₁
114)	[47917, 1918, 153009]	C₁₀₀₅		33)	[1889, 959, 191668]	C₁₀₀₅
115)	[74293, 1114, 13077]	C₁₀₀₅		---)	[1453, 557, 74293]	C₃₃₅
116)	[107777, 351, 3856]	C₁₀₀₅		19)	[241, 702, 107777]	C₁₀₀₅
117)	[116437, 349, 1341]	C₁₀₀₅		---)	[149, 698, 116437]	C₂₀₁
118)	[119701, 1490, 76221]	C₁₀₀₅		---)	[941, 745, 119701]	C₃₃₅
119)	[123817, 2719, 1074384]	C₁₀₀₅		---)	[829, 5438, 3095425]	C₃₃₅
120)	[132757, 1842, 317213]	C₁₀₀₅		32)	[1877, 921, 132757]	C₁₀₀₅
121)	[157037, 513, 26533]	C₁₀₀₅		---)	[157, 1026, 157037]	C₂₀₁
122)	[189997, 1746, 2141]	C₁₀₀₅		34)	[2141, 873, 189997]	C₁₀₀₅
123)	[208253, 457, 149]	C₁₀₀₅		---)	[149, 914, 208253]	C₂₀₁
124)	[221453, 473, 569]	C₁₀₀₅		26)	[569, 946, 221453]	C₁₀₀₅
125)	[287537, 2819, 189584]	C₁₀₀₅		---)	[41, 2591, 1150148]	C₆₇
126)	[288817, 1895, 825552]	C₁₀₀₅		---)	[13, 1189, 288817]	C₃₃₅
127)	[313997, 561, 181]	C₁₀₀₅		---)	[181, 1122, 313997]	C₃₃₅
128)	[389569, 637, 4050]	C₁₀₀₅		---)	[8, 1274, 389569]	C₂₀₁
129)	[497969, 2411, 332800]	C₁₀₀₅		---)	[13, 1413, 497969]	C₂₀₁
130)	[511793, 1127, 189584]	C₁₀₀₅		7)	[41, 2254, 511793]	C₁₀₀₅
131)	[514853, 2882, 17069]	C₁₀₀₅		---)	[101, 1441, 514853]	C₃₃₅
132)	[602153, 787, 4304]	C₁₀₀₅		20)	[269, 1574, 602153]	C₁₀₀₅
133)	[665153, 831, 6352]	C₁₀₀₅		23)	[397, 1662, 665153]	C₁₀₀₅
134)	[691661, 881, 21125]	C₁₀₀₅		---)	[5, 1762, 691661]	C₆₇
135)	[784961, 1631, 468800]	C₁₀₀₅		21)	[293, 3262, 784961]	C₁₀₀₅
136)	[927013, 965, 1053]	C₁₀₀₅		---)	[13, 1930, 927013]	C₃₃₅
137)	[1032049, 1351, 198288]	C₁₀₀₅		5)	[17, 2702, 1032049]	C₁₀₀₅
138)	[1066561, 1183, 83232]	C₁₀₀₅		---)	[8, 2366, 1066561]	C₃₃₅
139)	[1066817, 1119, 46336]	C₁₀₀₅		18)	[181, 2238, 1066817]	C₁₀₀₅
140)	[1074509, 4162, 32525]	C₁₀₀₅		29)	[1301, 2081, 1074509]	C₁₀₀₅
141)	[1106909, 1153, 55625]	C₁₀₀₅		---)	[89, 2306, 1106909]	C₃₃₅
142)	[1164593, 1767, 489424]	C₁₀₀₅		17)	[181, 3534, 1164593]	C₁₀₀₅
143)	[1251841, 1663, 378432]	C₁₀₀₅		10)	[73, 3326, 1251841]	C₁₀₀₅
144)	[1709261, 1729, 320045]	C₁₀₀₅		---)	[5, 2657, 1709261]	C₂₀₁
145)	[1868033, 1407, 27904]	C₁₀₀₅		15)	[109, 2814, 1868033]	C₁₀₀₅
146)	[2508641, 1615, 24896]	C₁₀₀₅		22)	[389, 3230, 2508641]	C₁₀₀₅
147)	[2553017, 4799, 13312]	C₁₀₀₅		---)	[13, 3825, 2553017]	C₃₃₅
148)	[3136657, 1847, 68688]	C₁₀₀₅		8)	[53, 3694, 3136657]	C₁₀₀₅
149)	[3167513, 1787, 6464]	C₁₀₀₅		12)	[101, 3574, 3167513]	C₁₀₀₅
150)	[3533561, 1995, 111616]	C₁₀₀₅		16)	[109, 3990, 3533561]	C₁₀₀₅
151)	[4356041, 2179, 98000]	C₁₀₀₅		---)	[5, 4358, 4356041]	C₃₃₅
152)	[4409753, 2107, 7424]	C₁₀₀₅		6)	[29, 4214, 4409753]	C₁₀₀₅
153)	[4555409, 2903, 968000]	C₁₀₀₅		---)	[5, 4309, 4555409]	C₃₃₅
154)	[4672769, 2167, 5780]	C₁₀₀₅		---)	[5, 4334, 4672769]	C₂₀₁
155)	[4896809, 2227, 15680]	C₁₀₀₅		---)	[5, 4454, 4896809]	C₃₃₅
156)	[6499601, 2551, 2000]	C₁₀₀₅		---)	[5, 5102, 6499601]	C₃₃₅
157)	[7208753, 2695, 13568]	C₁₀₀₅		9)	[53, 5390, 7208753]	C₁₀₀₅
158)	[8201873, 2871, 10192]	C₁₀₀₅		4)	[13, 5742, 8201873]	C₁₀₀₅
159)	[9252041, 3107, 100352]	C₁₀₀₅		---)	[8, 6214, 9252041]	C₃₃₅
160)	[9307937, 3055, 6272]	C₁₀₀₅		3)	[8, 6110, 9307937]	C₁₀₀₅
161)	[9612569, 3163, 98000]	C₁₀₀₅		---)	[5, 6326, 9612569]	C₃₃₅
162)	[10346257, 3223, 10368]	C₁₀₀₅		2)	[8, 6446, 10346257]	C₁₀₀₅
163)	[12151169, 3487, 2000]	C₁₀₀₅		---)	[5, 6974, 12151169]	C₃₃₅
164)	[13205849, 3643, 16400]	C₁₀₀₅		---)	[41, 7286, 13205849]	C₃₃₅
165)	[14859113, 3859, 8192]	C₁₀₀₅		---)	[8, 7718, 14859113]	C₃₃₅
166)	[15213449, 3907, 12800]	C₁₀₀₅		---)	[8, 7814, 15213449]	C₃₃₅
167)	[22617169, 4783, 64980]	C₁₀₀₅		1)	[5, 9566, 22617169]	C₁₀₀₅

Class number: [Non-normal] [Cyclic]

Class group C1005 non-normal (D4) quartic CM field invariants: 167 fields

Class group C₁₀₀₅ non-normal (D₄) quartic CM field invariants: 167 fields