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, 5853, 7946641]	C₅₇₁		192)	[7946641, 3511, 1095120]	C₅₇₁
2)	[5, 10454, 27275449]	C₅₇₁		---)	[27275449, 5227, 11520]	C₁₇₁₃
3)	[5, 6478, 8443121]	C₅₇₁		194)	[8443121, 3239, 512000]	C₅₇₁
4)	[5, 10846, 29327009]	C₅₇₁		---)	[29327009, 5423, 20480]	C₁₇₁₃
5)	[5, 4462, 4044241]	C₅₇₁		---)	[4044241, 2231, 233280]	C₁₇₁₃
6)	[5, 8654, 17329009]	C₅₇₁		200)	[17329009, 4327, 348480]	C₅₇₁
7)	[8, 5182, 5788481]	C₅₇₁		---)	[5788481, 2591, 231200]	C₁₃₁₃₃
8)	[8, 4366, 4760881]	C₅₇₁		---)	[4760881, 2183, 1152]	C₁₇₁₃
9)	[8, 4462, 4682449]	C₅₇₁		186)	[4682449, 2231, 73728]	C₅₇₁
10)	[8, 11062, 30366169]	C₅₇₁		203)	[30366169, 5531, 56448]	C₅₇₁
11)	[8, 6526, 7370369]	C₅₇₁		190)	[7370369, 3263, 819200]	C₅₇₁
12)	[8, 11558, 33316841]	C₅₇₁		---)	[33316841, 5779, 20000]	C₁₇₁₃
13)	[8, 3326, 2679041]	C₅₇₁		178)	[2679041, 1663, 21632]	C₅₇₁
14)	[8, 4030, 4053953]	C₅₇₁		182)	[4053953, 2015, 1568]	C₅₇₁
15)	[8, 9238, 21040249]	C₅₇₁		---)	[21040249, 4619, 73728]	C₈₅₆₅
16)	[8, 8198, 16728073]	C₅₇₁		199)	[16728073, 4099, 18432]	C₅₇₁
17)	[8, 4798, 5668673]	C₅₇₁		189)	[5668673, 2399, 21632]	C₅₇₁
18)	[8, 5678, 8034833]	C₅₇₁		193)	[8034833, 2839, 6272]	C₅₇₁
19)	[8, 2638, 1683313]	C₅₇₁		---)	[1683313, 1319, 14112]	C₁₇₁₃
20)	[13, 6326, 9884761]	C₅₇₁		195)	[9884761, 3163, 29952]	C₅₇₁
21)	[13, 11150, 31013233]	C₅₇₁		---)	[31013233, 5575, 16848]	C₁₇₁₃
22)	[13, 9734, 23320777]	C₅₇₁		201)	[23320777, 4867, 91728]	C₅₇₁
23)	[13, 5046, 3756377]	C₅₇₁		181)	[3756377, 2523, 652288]	C₅₇₁
24)	[13, 4374, 4569977]	C₅₇₁		184)	[4569977, 2187, 53248]	C₅₇₁
25)	[29, 3278, 2084977]	C₅₇₁		176)	[2084977, 1639, 150336]	C₅₇₁
26)	[29, 6454, 10227929]	C₅₇₁		197)	[10227929, 3227, 46400]	C₅₇₁
27)	[29, 5606, 4887209]	C₅₇₁		188)	[4887209, 2803, 742400]	C₅₇₁
28)	[29, 4454, 4773929]	C₅₇₁		187)	[4773929, 2227, 46400]	C₅₇₁
29)	[37, 3558, 2700713]	C₅₇₁		---)	[2700713, 1779, 116032]	C₆₅₆₆₅
30)	[37, 2134, 371257]	C₅₇₁		163)	[371257, 1067, 191808]	C₅₇₁
31)	[41, 1022, 166657]	C₅₇₁		156)	[166657, 511, 23616]	C₅₇₁
32)	[41, 2110, 598721]	C₅₇₁		167)	[598721, 1055, 128576]	C₅₇₁
33)	[41, 2506, 1450453]	C₅₇₁		174)	[1450453, 1253, 29889]	C₅₇₁
34)	[53, 3806, 2858209]	C₅₇₁		179)	[2858209, 1903, 190800]	C₅₇₁
35)	[53, 2654, 1692241]	C₅₇₁		---)	[1692241, 1327, 17172]	C₁₇₁₃
36)	[61, 4950, 3486521]	C₅₇₁		180)	[3486521, 2475, 659776]	C₅₇₁
37)	[73, 4326, 4673897]	C₅₇₁		185)	[4673897, 2163, 1168]	C₅₇₁
38)	[89, 8294, 16628009]	C₅₇₁		198)	[16628009, 4147, 142400]	C₅₇₁
39)	[89, 6326, 9913433]	C₅₇₁		196)	[9913433, 3163, 22784]	C₅₇₁
40)	[89, 5606, 7765673]	C₅₇₁		191)	[7765673, 2803, 22784]	C₅₇₁
41)	[97, 10214, 26025577]	C₅₇₁		202)	[26025577, 5107, 13968]	C₅₇₁
42)	[113, 4102, 4141513]	C₅₇₁		183)	[4141513, 2051, 16272]	C₅₇₁
43)	[113, 1155, 206692]	C₅₇₁		151)	[51673, 2310, 507257]	C₅₇₁
44)	[137, 1210, 361093]	C₅₇₁		162)	[361093, 605, 1233]	C₅₇₁
45)	[149, 6629, 6344225]	C₅₇₁		158)	[253769, 3659, 238400]	C₅₇₁
46)	[157, 3878, 1498921]	C₅₇₁		175)	[1498921, 1939, 565200]	C₅₇₁
47)	[157, 3366, 260201]	C₅₇₁		---)	[260201, 1683, 643072]	C₂₅₆₉₅
48)	[173, 1198, 347729]	C₅₇₁		161)	[347729, 599, 2768]	C₅₇₁
49)	[173, 2542, 275729]	C₅₇₁		159)	[275729, 1271, 334928]	C₅₇₁
50)	[193, 1530, 547397]	C₅₇₁		166)	[547397, 765, 9457]	C₅₇₁
51)	[241, 1754, 760453]	C₅₇₁		171)	[760453, 877, 2169]	C₅₇₁
52)	[277, 1481, 353817]	C₅₇₁		150)	[39313, 2962, 778093]	C₅₇₁
53)	[293, 1098, 300229]	C₅₇₁		160)	[300229, 549, 293]	C₅₇₁
54)	[293, 1882, 884309]	C₅₇₁		---)	[884309, 941, 293]	C₂₈₅₅
55)	[313, 3174, 2198057]	C₅₇₁		---)	[2198057, 1587, 80128]	C₃₉₉₇
56)	[433, 1782, 766169]	C₅₇₁		172)	[766169, 891, 6928]	C₅₇₁
57)	[449, 1047, 214672]	C₅₇₁		126)	[13417, 2094, 237521]	C₅₇₁
58)	[449, 1330, 426061]	C₅₇₁		165)	[426061, 665, 4041]	C₅₇₁
59)	[457, 2214, 1196201]	C₅₇₁		173)	[1196201, 1107, 7312]	C₅₇₁
60)	[461, 1790, 328961]	C₅₇₁		---)	[328961, 895, 118016]	C₃₉₉₇
61)	[617, 3190, 609113]	C₅₇₁		168)	[609113, 1595, 483728]	C₅₇₁
62)	[653, 1318, 173081]	C₅₇₁		157)	[173081, 659, 65300]	C₅₇₁
63)	[857, 586, 82421]	C₅₇₁		154)	[82421, 293, 857]	C₅₇₁
64)	[929, 655, 107024]	C₅₇₁		116)	[6689, 1310, 929]	C₅₇₁
65)	[953, 1127, 277268]	C₅₇₁		153)	[69317, 2254, 161057]	C₅₇₁
66)	[953, 1546, 136277]	C₅₇₁		155)	[136277, 773, 115313]	C₅₇₁
67)	[1193, 1630, 645137]	C₅₇₁		169)	[645137, 815, 4772]	C₅₇₁
68)	[1201, 1559, 520848]	C₅₇₁		89)	[3617, 1827, 811876]	C₅₇₁
69)	[1201, 3155, 2452176]	C₅₇₁		138)	[17029, 3269, 10809]	C₅₇₁
70)	[1249, 1710, 711041]	C₅₇₁		170)	[711041, 855, 4996]	C₅₇₁
71)	[1409, 3427, 2284772]	C₅₇₁		122)	[11657, 3331, 952484]	C₅₇₁
72)	[2017, 4198, 3599001]	C₅₇₁		118)	[8161, 2099, 201700]	C₅₇₁
73)	[2137, 790, 121833]	C₅₇₁		---)	[13537, 395, 8548]	C₁₇₁₃
74)	[2137, 1494, 421241]	C₅₇₁		164)	[421241, 747, 34192]	C₅₇₁
75)	[2293, 546, 65357]	C₅₇₁		152)	[65357, 273, 2293]	C₅₇₁
76)	[2297, 1414, 352841]	C₅₇₁		---)	[352841, 707, 36752]	C₂₈₅₅
77)	[2381, 3382, 1907081]	C₅₇₁		136)	[15761, 1691, 238100]	C₅₇₁
78)	[2477, 1614, 17137]	C₅₇₁		139)	[17137, 807, 158528]	C₅₇₁
79)	[2609, 434, 36653]	C₅₇₁		---)	[36653, 217, 2609]	C₁₇₁₃
80)	[2797, 1489, 396949]	C₅₇₁		---)	[8101, 2978, 629325]	C₇₄₂₃
81)	[2833, 1178, 63621]	C₅₇₁		117)	[7069, 589, 70825]	C₅₇₁
82)	[2957, 3433, 12289]	C₅₇₁		125)	[12289, 5979, 4731200]	C₅₇₁
83)	[3037, 6069, 7804337]	C₅₇₁		131)	[14753, 4295, 595252]	C₅₇₁
84)	[3037, 393, 37853]	C₅₇₁		149)	[37853, 786, 3037]	C₅₇₁
85)	[3209, 6563, 3527936]	C₅₇₁		128)	[13781, 4345, 3209]	C₅₇₁
86)	[3301, 2422, 1255257]	C₅₇₁		135)	[15497, 1211, 52816]	C₅₇₁
87)	[3329, 6311, 7253200]	C₅₇₁		145)	[18133, 4881, 402809]	C₅₇₁
88)	[3517, 6469, 10440009]	C₅₇₁		129)	[14321, 4167, 900352]	C₅₇₁
89)	[3617, 1827, 811876]	C₅₇₁		68)	[1201, 1559, 520848]	C₅₇₁
90)	[3637, 2773, 1848733]	C₅₇₁		115)	[6397, 4933, 1923973]	C₅₇₁
91)	[3673, 2427, 590144]	C₅₇₁		120)	[9221, 4854, 3529753]	C₅₇₁
92)	[3697, 3795, 3444308]	C₅₇₁		140)	[17573, 7590, 624793]	C₅₇₁
93)	[3733, 1697, 383049]	C₅₇₁		---)	[4729, 3394, 1347613]	C₁₇₁₃
94)	[3989, 973, 12301]	C₅₇₁		---)	[12301, 1946, 897525]	C₂₈₅₅
95)	[4013, 2709, 1472497]	C₅₇₁		---)	[8713, 5418, 1448693]	C₁₇₁₃
96)	[4253, 6345, 4704913]	C₅₇₁		---)	[13033, 4763, 5511888]	C₇₄₂₃
97)	[4289, 1583, 59252]	C₅₇₁		132)	[14813, 3166, 2268881]	C₅₇₁
98)	[4289, 5266, 3072589]	C₅₇₁		146)	[18181, 2633, 965025]	C₅₇₁
99)	[4337, 5562, 6883909]	C₅₇₁		148)	[19069, 2781, 212513]	C₅₇₁
100)	[4349, 8377, 16968377]	C₅₇₁		141)	[17657, 7651, 14630036]	C₅₇₁
101)	[4721, 3883, 3758800]	C₅₇₁		121)	[9397, 5721, 4721]	C₅₇₁
102)	[4817, 619, 65684]	C₅₇₁		137)	[16421, 1238, 120425]	C₅₇₁
103)	[4817, 2471, 1178432]	C₅₇₁		147)	[18413, 4942, 1392113]	C₅₇₁
104)	[4937, 7698, 2472301]	C₅₇₁		130)	[14629, 3849, 3085625]	C₅₇₁
105)	[5189, 622, 13697]	C₅₇₁		127)	[13697, 311, 20756]	C₅₇₁
106)	[5197, 4374, 2704169]	C₅₇₁		---)	[16001, 2187, 519700]	C₂₈₅₅
107)	[5309, 7393, 8396257]	C₅₇₁		119)	[8737, 4107, 4162256]	C₅₇₁
108)	[5393, 6623, 286544]	C₅₇₁		144)	[17909, 9497, 9971657]	C₅₇₁
109)	[5437, 6018, 7988429]	C₅₇₁		134)	[15101, 3009, 266413]	C₅₇₁
110)	[5657, 7306, 5175701]	C₅₇₁		143)	[17909, 3653, 2042177]	C₅₇₁
111)	[5693, 5213, 17749]	C₅₇₁		142)	[17749, 9773, 22595517]	C₅₇₁
112)	[5717, 573, 12049]	C₅₇₁		123)	[12049, 1146, 280133]	C₅₇₁
113)	[5801, 3931, 3792128]	C₅₇₁		133)	[14813, 7862, 284249]	C₅₇₁
114)	[5881, 7555, 435924]	C₅₇₁		124)	[12109, 5033, 5651641]	C₅₇₁
115)	[6397, 4933, 1923973]	C₅₇₁		90)	[3637, 2773, 1848733]	C₅₇₁
116)	[6689, 1310, 929]	C₅₇₁		64)	[929, 655, 107024]	C₅₇₁
117)	[7069, 589, 70825]	C₅₇₁		81)	[2833, 1178, 63621]	C₅₇₁
118)	[8161, 2099, 201700]	C₅₇₁		72)	[2017, 4198, 3599001]	C₅₇₁
119)	[8737, 4107, 4162256]	C₅₇₁		107)	[5309, 7393, 8396257]	C₅₇₁
120)	[9221, 4854, 3529753]	C₅₇₁		91)	[3673, 2427, 590144]	C₅₇₁
121)	[9397, 5721, 4721]	C₅₇₁		101)	[4721, 3883, 3758800]	C₅₇₁
122)	[11657, 3331, 952484]	C₅₇₁		71)	[1409, 3427, 2284772]	C₅₇₁
123)	[12049, 1146, 280133]	C₅₇₁		112)	[5717, 573, 12049]	C₅₇₁
124)	[12109, 5033, 5651641]	C₅₇₁		114)	[5881, 7555, 435924]	C₅₇₁
125)	[12289, 5979, 4731200]	C₅₇₁		82)	[2957, 3433, 12289]	C₅₇₁
126)	[13417, 2094, 237521]	C₅₇₁		57)	[449, 1047, 214672]	C₅₇₁
127)	[13697, 311, 20756]	C₅₇₁		105)	[5189, 622, 13697]	C₅₇₁
128)	[13781, 4345, 3209]	C₅₇₁		85)	[3209, 6563, 3527936]	C₅₇₁
129)	[14321, 4167, 900352]	C₅₇₁		88)	[3517, 6469, 10440009]	C₅₇₁
130)	[14629, 3849, 3085625]	C₅₇₁		104)	[4937, 7698, 2472301]	C₅₇₁
131)	[14753, 4295, 595252]	C₅₇₁		83)	[3037, 6069, 7804337]	C₅₇₁
132)	[14813, 3166, 2268881]	C₅₇₁		97)	[4289, 1583, 59252]	C₅₇₁
133)	[14813, 7862, 284249]	C₅₇₁		113)	[5801, 3931, 3792128]	C₅₇₁
134)	[15101, 3009, 266413]	C₅₇₁		109)	[5437, 6018, 7988429]	C₅₇₁
135)	[15497, 1211, 52816]	C₅₇₁		86)	[3301, 2422, 1255257]	C₅₇₁
136)	[15761, 1691, 238100]	C₅₇₁		77)	[2381, 3382, 1907081]	C₅₇₁
137)	[16421, 1238, 120425]	C₅₇₁		102)	[4817, 619, 65684]	C₅₇₁
138)	[17029, 3269, 10809]	C₅₇₁		69)	[1201, 3155, 2452176]	C₅₇₁
139)	[17137, 807, 158528]	C₅₇₁		78)	[2477, 1614, 17137]	C₅₇₁
140)	[17573, 7590, 624793]	C₅₇₁		92)	[3697, 3795, 3444308]	C₅₇₁
141)	[17657, 7651, 14630036]	C₅₇₁		100)	[4349, 8377, 16968377]	C₅₇₁
142)	[17749, 9773, 22595517]	C₅₇₁		111)	[5693, 5213, 17749]	C₅₇₁
143)	[17909, 3653, 2042177]	C₅₇₁		110)	[5657, 7306, 5175701]	C₅₇₁
144)	[17909, 9497, 9971657]	C₅₇₁		108)	[5393, 6623, 286544]	C₅₇₁
145)	[18133, 4881, 402809]	C₅₇₁		87)	[3329, 6311, 7253200]	C₅₇₁
146)	[18181, 2633, 965025]	C₅₇₁		98)	[4289, 5266, 3072589]	C₅₇₁
147)	[18413, 4942, 1392113]	C₅₇₁		103)	[4817, 2471, 1178432]	C₅₇₁
148)	[19069, 2781, 212513]	C₅₇₁		99)	[4337, 5562, 6883909]	C₅₇₁
149)	[37853, 786, 3037]	C₅₇₁		84)	[3037, 393, 37853]	C₅₇₁
150)	[39313, 2962, 778093]	C₅₇₁		52)	[277, 1481, 353817]	C₅₇₁
151)	[51673, 2310, 507257]	C₅₇₁		43)	[113, 1155, 206692]	C₅₇₁
152)	[65357, 273, 2293]	C₅₇₁		75)	[2293, 546, 65357]	C₅₇₁
153)	[69317, 2254, 161057]	C₅₇₁		65)	[953, 1127, 277268]	C₅₇₁
154)	[82421, 293, 857]	C₅₇₁		63)	[857, 586, 82421]	C₅₇₁
155)	[136277, 773, 115313]	C₅₇₁		66)	[953, 1546, 136277]	C₅₇₁
156)	[166657, 511, 23616]	C₅₇₁		31)	[41, 1022, 166657]	C₅₇₁
157)	[173081, 659, 65300]	C₅₇₁		62)	[653, 1318, 173081]	C₅₇₁
158)	[253769, 3659, 238400]	C₅₇₁		45)	[149, 6629, 6344225]	C₅₇₁
159)	[275729, 1271, 334928]	C₅₇₁		49)	[173, 2542, 275729]	C₅₇₁
160)	[300229, 549, 293]	C₅₇₁		53)	[293, 1098, 300229]	C₅₇₁
161)	[347729, 599, 2768]	C₅₇₁		48)	[173, 1198, 347729]	C₅₇₁
162)	[361093, 605, 1233]	C₅₇₁		44)	[137, 1210, 361093]	C₅₇₁
163)	[371257, 1067, 191808]	C₅₇₁		30)	[37, 2134, 371257]	C₅₇₁
164)	[421241, 747, 34192]	C₅₇₁		74)	[2137, 1494, 421241]	C₅₇₁
165)	[426061, 665, 4041]	C₅₇₁		58)	[449, 1330, 426061]	C₅₇₁
166)	[547397, 765, 9457]	C₅₇₁		50)	[193, 1530, 547397]	C₅₇₁
167)	[598721, 1055, 128576]	C₅₇₁		32)	[41, 2110, 598721]	C₅₇₁
168)	[609113, 1595, 483728]	C₅₇₁		61)	[617, 3190, 609113]	C₅₇₁
169)	[645137, 815, 4772]	C₅₇₁		67)	[1193, 1630, 645137]	C₅₇₁
170)	[711041, 855, 4996]	C₅₇₁		70)	[1249, 1710, 711041]	C₅₇₁
171)	[760453, 877, 2169]	C₅₇₁		51)	[241, 1754, 760453]	C₅₇₁
172)	[766169, 891, 6928]	C₅₇₁		56)	[433, 1782, 766169]	C₅₇₁
173)	[1196201, 1107, 7312]	C₅₇₁		59)	[457, 2214, 1196201]	C₅₇₁
174)	[1450453, 1253, 29889]	C₅₇₁		33)	[41, 2506, 1450453]	C₅₇₁
175)	[1498921, 1939, 565200]	C₅₇₁		46)	[157, 3878, 1498921]	C₅₇₁
176)	[2084977, 1639, 150336]	C₅₇₁		25)	[29, 3278, 2084977]	C₅₇₁
177)	[2181209, 1499, 16448]	C₅₇₁		---)	[257, 2998, 2181209]	C₁₇₁₃
178)	[2679041, 1663, 21632]	C₅₇₁		13)	[8, 3326, 2679041]	C₅₇₁
179)	[2858209, 1903, 190800]	C₅₇₁		34)	[53, 3806, 2858209]	C₅₇₁
180)	[3486521, 2475, 659776]	C₅₇₁		36)	[61, 4950, 3486521]	C₅₇₁
181)	[3756377, 2523, 652288]	C₅₇₁		23)	[13, 5046, 3756377]	C₅₇₁
182)	[4053953, 2015, 1568]	C₅₇₁		14)	[8, 4030, 4053953]	C₅₇₁
183)	[4141513, 2051, 16272]	C₅₇₁		42)	[113, 4102, 4141513]	C₅₇₁
184)	[4569977, 2187, 53248]	C₅₇₁		24)	[13, 4374, 4569977]	C₅₇₁
185)	[4673897, 2163, 1168]	C₅₇₁		37)	[73, 4326, 4673897]	C₅₇₁
186)	[4682449, 2231, 73728]	C₅₇₁		9)	[8, 4462, 4682449]	C₅₇₁
187)	[4773929, 2227, 46400]	C₅₇₁		28)	[29, 4454, 4773929]	C₅₇₁
188)	[4887209, 2803, 742400]	C₅₇₁		27)	[29, 5606, 4887209]	C₅₇₁
189)	[5668673, 2399, 21632]	C₅₇₁		17)	[8, 4798, 5668673]	C₅₇₁
190)	[7370369, 3263, 819200]	C₅₇₁		11)	[8, 6526, 7370369]	C₅₇₁
191)	[7765673, 2803, 22784]	C₅₇₁		40)	[89, 5606, 7765673]	C₅₇₁
192)	[7946641, 3511, 1095120]	C₅₇₁		1)	[5, 5853, 7946641]	C₅₇₁
193)	[8034833, 2839, 6272]	C₅₇₁		18)	[8, 5678, 8034833]	C₅₇₁
194)	[8443121, 3239, 512000]	C₅₇₁		3)	[5, 6478, 8443121]	C₅₇₁
195)	[9884761, 3163, 29952]	C₅₇₁		20)	[13, 6326, 9884761]	C₅₇₁
196)	[9913433, 3163, 22784]	C₅₇₁		39)	[89, 6326, 9913433]	C₅₇₁
197)	[10227929, 3227, 46400]	C₅₇₁		26)	[29, 6454, 10227929]	C₅₇₁
198)	[16628009, 4147, 142400]	C₅₇₁		38)	[89, 8294, 16628009]	C₅₇₁
199)	[16728073, 4099, 18432]	C₅₇₁		16)	[8, 8198, 16728073]	C₅₇₁
200)	[17329009, 4327, 348480]	C₅₇₁		6)	[5, 8654, 17329009]	C₅₇₁
201)	[23320777, 4867, 91728]	C₅₇₁		22)	[13, 9734, 23320777]	C₅₇₁
202)	[26025577, 5107, 13968]	C₅₇₁		41)	[97, 10214, 26025577]	C₅₇₁
203)	[30366169, 5531, 56448]	C₅₇₁		10)	[8, 11062, 30366169]	C₅₇₁

Class number: [Non-normal] [Cyclic]

Class number 571 non-normal (D4) quartic CM field invariants: 203 fields

Class number 571 non-normal (D₄) quartic CM field invariants: 203 fields