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, 6542, 10698929]	C₉₃₃		---)	[10698929, 3271, 128]	C₆₅₃₁
2)	[8, 5726, 8178337]	C₉₃₃		101)	[8178337, 2863, 4608]	C₉₃₃
3)	[13, 9081, 20387909]	C₉₃₃		106)	[20387909, 16753, 24292957]	C₉₃₃
4)	[17, 3326, 2761217]	C₉₃₃		95)	[2761217, 1663, 1088]	C₉₃₃
5)	[37, 3342, 2328113]	C₉₃₃		93)	[2328113, 1671, 116032]	C₉₃₃
6)	[53, 3982, 3960689]	C₉₃₃		98)	[3960689, 1991, 848]	C₉₃₃
7)	[73, 2510, 1196593]	C₉₃₃		---)	[1196593, 1255, 94608]	C₄₆₆₅
8)	[97, 1334, 406089]	C₉₃₃		85)	[45121, 667, 9700]	C₉₃₃
9)	[181, 3774, 2402369]	C₉₃₃		94)	[2402369, 1887, 289600]	C₉₃₃
10)	[241, 1547, 591012]	C₉₃₃		73)	[16417, 1963, 926404]	C₉₃₃
11)	[293, 2374, 940169]	C₉₃₃		91)	[940169, 1187, 117200]	C₉₃₃
12)	[449, 430, 17489]	C₉₃₃		77)	[17489, 215, 7184]	C₉₃₃
13)	[617, 1258, 333941]	C₉₃₃		89)	[333941, 629, 15425]	C₉₃₃
14)	[761, 1242, 17317]	C₉₃₃		---)	[17317, 621, 92081]	C₃₁₁
15)	[761, 1067, 275300]	C₉₃₃		---)	[2753, 1003, 3044]	C₃₁₁
16)	[941, 1793, 577637]	C₉₃₃		---)	[577637, 3586, 904301]	C₃ x C₉₃₃
17)	[977, 2271, 1136704]	C₉₃₃		81)	[17761, 3883, 35172]	C₉₃₃
18)	[1489, 635, 55764]	C₉₃₃		---)	[1549, 1270, 180169]	C₃₁₁
19)	[1609, 411, 41828]	C₉₃₃		---)	[10457, 822, 1609]	C₃ x C₉₃₃
20)	[2381, 1621, 442025]	C₉₃₃		80)	[17681, 3242, 859541]	C₉₃₃
21)	[2633, 2846, 508321]	C₉₃₃		38)	[4201, 1423, 379152]	C₉₃₃
22)	[2729, 2966, 2155625]	C₉₃₃		29)	[3449, 1483, 10916]	C₉₃₃
23)	[2801, 1346, 441725]	C₉₃₃		79)	[17669, 673, 2801]	C₉₃₃
24)	[2897, 771, 26212]	C₉₃₃		54)	[6553, 1542, 489593]	C₉₃₃
25)	[2917, 405, 5273]	C₉₃₃		---)	[5273, 810, 142933]	C₂₁₇₇
26)	[3169, 2031, 269888]	C₉₃₃		40)	[4217, 4062, 3045409]	C₉₃₃
27)	[3221, 322, 13037]	C₉₃₃		---)	[13037, 161, 3221]	C₃₁₁
28)	[3313, 4551, 4381952]	C₉₃₃		75)	[17117, 8173, 5569153]	C₉₃₃
29)	[3449, 1483, 10916]	C₉₃₃		22)	[2729, 2966, 2155625]	C₉₃₃
30)	[3457, 5831, 1654416]	C₉₃₃		61)	[11489, 3431, 2710288]	C₉₃₃
31)	[3541, 2153, 74421]	C₉₃₃		58)	[8269, 4306, 4337725]	C₉₃₃
32)	[3673, 2983, 2201616]	C₉₃₃		71)	[15289, 5966, 91825]	C₉₃₃
33)	[3877, 261, 16061]	C₉₃₃		---)	[16061, 522, 3877]	C₃₁₁
34)	[4049, 6707, 1324900]	C₉₃₃		65)	[13249, 4383, 1619600]	C₉₃₃
35)	[4073, 267, 16804]	C₉₃₃		39)	[4201, 534, 4073]	C₉₃₃
36)	[4093, 6649, 4338757]	C₉₃₃		69)	[15013, 4861, 5603317]	C₉₃₃
37)	[4153, 1979, 429876]	C₉₃₃		63)	[11941, 3958, 2196937]	C₉₃₃
38)	[4201, 1423, 379152]	C₉₃₃		21)	[2633, 2846, 508321]	C₉₃₃
39)	[4201, 534, 4073]	C₉₃₃		35)	[4073, 267, 16804]	C₉₃₃
40)	[4217, 4062, 3045409]	C₉₃₃		26)	[3169, 2031, 269888]	C₉₃₃
41)	[4273, 7855, 13800448]	C₉₃₃		66)	[13477, 4429, 1234897]	C₉₃₃
42)	[4597, 2405, 341577]	C₉₃₃		---)	[4217, 4810, 4417717]	C₃₁₁
43)	[4649, 2703, 1630132]	C₉₃₃		---)	[8317, 5406, 785681]	C₃₁₁
44)	[4721, 4983, 3600400]	C₉₃₃		59)	[9001, 4295, 2719296]	C₉₃₃
45)	[4789, 9293, 4061025]	C₉₃₃		82)	[18049, 6851, 6206544]	C₉₃₃
46)	[4817, 3035, 76148]	C₉₃₃		84)	[19037, 6070, 8906633]	C₉₃₃
47)	[4861, 7009, 10433125]	C₉₃₃		74)	[16693, 8761, 10737949]	C₉₃₃
48)	[4937, 5627, 2701076]	C₉₃₃		67)	[13781, 8477, 597377]	C₉₃₃
49)	[5077, 5897, 7626213]	C₉₃₃		76)	[17293, 7505, 3701133]	C₉₃₃
50)	[5081, 307, 22292]	C₉₃₃		---)	[5573, 614, 5081]	C₃₁₁
51)	[5393, 651, 72244]	C₉₃₃		83)	[18061, 1302, 134825]	C₉₃₃
52)	[5581, 1209, 364025]	C₉₃₃		68)	[14561, 2418, 5581]	C₉₃₃
53)	[5749, 9930, 2552069]	C₉₃₃		70)	[15101, 4965, 5524789]	C₉₃₃
54)	[6553, 1542, 489593]	C₉₃₃		24)	[2897, 771, 26212]	C₉₃₃
55)	[6997, 2629, 46881]	C₉₃₃		---)	[5209, 5258, 6724117]	C₃₁₁
56)	[7753, 155, 4068]	C₉₃₃		---)	[113, 310, 7753]	C₃₁₁
57)	[8069, 4185, 4037641]	C₉₃₃		---)	[4801, 4631, 290484]	C₃₁₁
58)	[8269, 4306, 4337725]	C₉₃₃		31)	[3541, 2153, 74421]	C₉₃₃
59)	[9001, 4295, 2719296]	C₉₃₃		44)	[4721, 4983, 3600400]	C₉₃₃
60)	[10301, 3205, 1638341]	C₉₃₃		---)	[5669, 6410, 3718661]	C₃₁₁
61)	[11489, 3431, 2710288]	C₉₃₃		30)	[3457, 5831, 1654416]	C₉₃₃
62)	[11821, 3369, 990509]	C₉₃₃		---)	[5861, 6738, 7388125]	C₃₁₁
63)	[11941, 3958, 2196937]	C₉₃₃		37)	[4153, 1979, 429876]	C₉₃₃
64)	[12821, 4249, 3971813]	C₉₃₃		---)	[4133, 6373, 3705269]	C₃₁₁
65)	[13249, 4383, 1619600]	C₉₃₃		34)	[4049, 6707, 1324900]	C₉₃₃
66)	[13477, 4429, 1234897]	C₉₃₃		41)	[4273, 7855, 13800448]	C₉₃₃
67)	[13781, 8477, 597377]	C₉₃₃		48)	[4937, 5627, 2701076]	C₉₃₃
68)	[14561, 2418, 5581]	C₉₃₃		52)	[5581, 1209, 364025]	C₉₃₃
69)	[15013, 4861, 5603317]	C₉₃₃		36)	[4093, 6649, 4338757]	C₉₃₃
70)	[15101, 4965, 5524789]	C₉₃₃		53)	[5749, 9930, 2552069]	C₉₃₃
71)	[15289, 5966, 91825]	C₉₃₃		32)	[3673, 2983, 2201616]	C₉₃₃
72)	[15773, 541, 37681]	C₉₃₃		---)	[769, 1082, 141957]	C₃₁₁
73)	[16417, 1963, 926404]	C₉₃₃		10)	[241, 1547, 591012]	C₉₃₃
74)	[16693, 8761, 10737949]	C₉₃₃		47)	[4861, 7009, 10433125]	C₉₃₃
75)	[17117, 8173, 5569153]	C₉₃₃		28)	[3313, 4551, 4381952]	C₉₃₃
76)	[17293, 7505, 3701133]	C₉₃₃		49)	[5077, 5897, 7626213]	C₉₃₃
77)	[17489, 215, 7184]	C₉₃₃		12)	[449, 430, 17489]	C₉₃₃
78)	[17609, 1758, 490897]	C₉₃₃		---)	[4057, 879, 70436]	C₃₁₁
79)	[17669, 673, 2801]	C₉₃₃		23)	[2801, 1346, 441725]	C₉₃₃
80)	[17681, 3242, 859541]	C₉₃₃		20)	[2381, 1621, 442025]	C₉₃₃
81)	[17761, 3883, 35172]	C₉₃₃		17)	[977, 2271, 1136704]	C₉₃₃
82)	[18049, 6851, 6206544]	C₉₃₃		45)	[4789, 9293, 4061025]	C₉₃₃
83)	[18061, 1302, 134825]	C₉₃₃		51)	[5393, 651, 72244]	C₉₃₃
84)	[19037, 6070, 8906633]	C₉₃₃		46)	[4817, 3035, 76148]	C₉₃₃
85)	[45121, 667, 9700]	C₉₃₃		8)	[97, 1334, 406089]	C₉₃₃
86)	[45641, 2815, 52724]	C₉₃₃		---)	[269, 2449, 1141025]	C₃₁₁
87)	[100469, 1298, 19325]	C₉₃₃		---)	[773, 649, 100469]	C₃₁₁
88)	[209357, 505, 11417]	C₉₃₃		---)	[233, 1010, 209357]	C₃₁₁
89)	[333941, 629, 15425]	C₉₃₃		13)	[617, 1258, 333941]	C₉₃₃
90)	[807113, 931, 14912]	C₉₃₃		---)	[233, 1862, 807113]	C₃₁₁
91)	[940169, 1187, 117200]	C₉₃₃		11)	[293, 2374, 940169]	C₉₃₃
92)	[1945729, 1727, 259200]	C₉₃₃		---)	[8, 3454, 1945729]	C₃₁₁
93)	[2328113, 1671, 116032]	C₉₃₃		5)	[37, 3342, 2328113]	C₉₃₃
94)	[2402369, 1887, 289600]	C₉₃₃		9)	[181, 3774, 2402369]	C₉₃₃
95)	[2761217, 1663, 1088]	C₉₃₃		4)	[17, 3326, 2761217]	C₉₃₃
96)	[3069769, 1987, 219600]	C₉₃₃		---)	[61, 3974, 3069769]	C₃₁₁
97)	[3342601, 1891, 58320]	C₉₃₃		---)	[5, 3782, 3342601]	C₃₁₁
98)	[3960689, 1991, 848]	C₉₃₃		6)	[53, 3982, 3960689]	C₉₃₃
99)	[4032361, 2323, 340992]	C₉₃₃		---)	[37, 4646, 4032361]	C₃₁₁
100)	[4480361, 2291, 192080]	C₉₃₃		---)	[5, 4582, 4480361]	C₃₁₁
101)	[8178337, 2863, 4608]	C₉₃₃		2)	[8, 5726, 8178337]	C₉₃₃
102)	[10970777, 3515, 346112]	C₉₃₃		---)	[8, 7030, 10970777]	C₃₁₁
103)	[11279969, 3407, 81920]	C₉₃₃		---)	[5, 6814, 11279969]	C₃₁₁
104)	[15163033, 3899, 9792]	C₉₃₃		---)	[17, 7798, 15163033]	C₃₁₁
105)	[15936329, 4579, 1257728]	C₉₃₃		---)	[17, 9158, 15936329]	C₃₁₁
106)	[20387909, 16753, 24292957]	C₉₃₃		3)	[13, 9081, 20387909]	C₉₃₃

Class number: [Non-normal] [Cyclic]

Class group C933 non-normal (D4) quartic CM field invariants: 106 fields

Class group C₉₃₃ non-normal (D₄) quartic CM field invariants: 106 fields