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, 11542, 27472441]	C₉₅₇		---)	[27472441, 5771, 1458000]	C₁₆₂₆₉
2)	[5, 12982, 41998601]	C₉₅₇		---)	[41998601, 6491, 33620]	C₃ x C₉₅₇
3)	[5, 13934, 48089089]	C₉₅₇		---)	[48089089, 6967, 112500]	C₃ x C₉₅₇
4)	[5, 9493, 19675361]	C₉₅₇		117)	[19675361, 5231, 1922000]	C₉₅₇
5)	[8, 6542, 10681009]	C₉₅₇		---)	[10681009, 3271, 4608]	C₃ x C₂₈₇₁
6)	[13, 6582, 10789913]	C₉₅₇		113)	[10789913, 3291, 10192]	C₉₅₇
7)	[13, 6606, 10896497]	C₉₅₇		114)	[10896497, 3303, 3328]	C₉₅₇
8)	[17, 1934, 826289]	C₉₅₇		104)	[826289, 967, 27200]	C₉₅₇
9)	[17, 2350, 1028113]	C₉₅₇		105)	[1028113, 1175, 88128]	C₉₅₇
10)	[53, 3334, 1137161]	C₉₅₇		107)	[1137161, 1667, 410432]	C₉₅₇
11)	[61, 2358, 1327577]	C₉₅₇		108)	[1327577, 1179, 15616]	C₉₅₇
12)	[181, 3862, 3543417]	C₉₅₇		---)	[393713, 1931, 46336]	C₃ x C₂₈₇₁
13)	[197, 2014, 900577]	C₉₅₇		---)	[900577, 1007, 28368]	C₃ x C₉₅₇
14)	[229, 634, 26293]	C₉₅₇		---)	[26293, 317, 18549]	C₃₁₉
15)	[229, 453, 48497]	C₉₅₇		---)	[48497, 906, 11221]	C₃₁₉
16)	[229, 3894, 2852825]	C₉₅₇		---)	[114113, 1947, 234496]	C₃₁₉
17)	[281, 995, 92324]	C₉₅₇		84)	[23081, 1990, 620729]	C₉₅₇
18)	[521, 1815, 238864]	C₉₅₇		71)	[14929, 2187, 1102436]	C₉₅₇
19)	[773, 1046, 224057]	C₉₅₇		95)	[224057, 523, 12368]	C₉₅₇
20)	[857, 1475, 70628]	C₉₅₇		78)	[17657, 2950, 1893113]	C₉₅₇
21)	[953, 994, 243197]	C₉₅₇		97)	[243197, 497, 953]	C₉₅₇
22)	[1297, 539, 69712]	C₉₅₇		---)	[4357, 1078, 11673]	C₄₃₅
23)	[1609, 1798, 164601]	C₉₅₇		80)	[18289, 899, 160900]	C₉₅₇
24)	[2269, 1082, 65781]	C₉₅₇		53)	[7309, 541, 56725]	C₉₅₇
25)	[2377, 2923, 205264]	C₉₅₇		69)	[12829, 5473, 3995737]	C₉₅₇
26)	[2417, 4670, 4833473]	C₉₅₇		55)	[9137, 2335, 154688]	C₉₅₇
27)	[2557, 2497, 23913]	C₉₅₇		---)	[2657, 2167, 163648]	C₃₁₉
28)	[2593, 2651, 70852]	C₉₅₇		79)	[17713, 5302, 6744393]	C₉₅₇
29)	[2689, 2239, 607248]	C₉₅₇		38)	[4217, 2823, 43024]	C₉₅₇
30)	[2833, 6650, 165573]	C₉₅₇		81)	[18397, 3325, 2722513]	C₉₅₇
31)	[3041, 4631, 4205200]	C₉₅₇		60)	[10513, 3851, 109476]	C₉₅₇
32)	[3109, 1822, 382225]	C₉₅₇		72)	[15289, 911, 111924]	C₉₅₇
33)	[3617, 3691, 41156]	C₉₅₇		58)	[10289, 5111, 5787200]	C₉₅₇
34)	[3701, 3357, 18481]	C₉₅₇		82)	[18481, 6714, 11195525]	C₉₅₇
35)	[3853, 2165, 1009017]	C₉₅₇		66)	[12457, 4330, 651157]	C₉₅₇
36)	[3889, 2734, 1619793]	C₉₅₇		---)	[3673, 1367, 62224]	C₃₁₉
37)	[3889, 3171, 1182800]	C₉₅₇		---)	[2957, 2121, 1123921]	C₃₁₉
38)	[4217, 2823, 43024]	C₉₅₇		29)	[2689, 2239, 607248]	C₉₅₇
39)	[4241, 5683, 7301200]	C₉₅₇		---)	[18253, 8289, 14762921]	C₄₇₈₅
40)	[4621, 7102, 114417]	C₉₅₇		67)	[12713, 3551, 3123796]	C₉₅₇
41)	[4721, 6506, 10563125]	C₉₅₇		---)	[16901, 3253, 4721]	C₆₆₉₉
42)	[4729, 514, 47133]	C₉₅₇		---)	[5237, 257, 4729]	C₃₁₉
43)	[4789, 697, 91521]	C₉₅₇		57)	[10169, 1394, 119725]	C₉₅₇
44)	[5021, 2917, 2095841]	C₉₅₇		76)	[17321, 5834, 125525]	C₉₅₇
45)	[5209, 4623, 1685012]	C₉₅₇		---)	[8597, 4909, 2755561]	C₃ x C₉₅₇
46)	[5261, 4881, 5954725]	C₉₅₇		---)	[4861, 3861, 3288125]	C₃₁₉
47)	[5333, 1109, 7489]	C₉₅₇		---)	[7489, 2218, 1199925]	C₃₁₉
48)	[5333, 401, 6869]	C₉₅₇		---)	[6869, 802, 133325]	C₃₁₉
49)	[5477, 394, 16901]	C₉₅₇		---)	[16901, 197, 5477]	C₂₂₃₃
50)	[5569, 2627, 1111300]	C₉₅₇		61)	[11113, 5254, 2455929]	C₉₅₇
51)	[5653, 3561, 557081]	C₉₅₇		64)	[11369, 7122, 10452397]	C₉₅₇
52)	[5869, 4142, 3913425]	C₉₅₇		77)	[17393, 2071, 93904]	C₉₅₇
53)	[7309, 541, 56725]	C₉₅₇		24)	[2269, 1082, 65781]	C₉₅₇
54)	[8837, 3386, 3061]	C₉₅₇		---)	[3061, 1693, 715797]	C₃₁₉
55)	[9137, 2335, 154688]	C₉₅₇		26)	[2417, 4670, 4833473]	C₉₅₇
56)	[9413, 6745, 810017]	C₉₅₇		---)	[4793, 4703, 150608]	C₃₁₉
57)	[10169, 1394, 119725]	C₉₅₇		43)	[4789, 697, 91521]	C₉₅₇
58)	[10289, 5111, 5787200]	C₉₅₇		33)	[3617, 3691, 41156]	C₉₅₇
59)	[10457, 1043, 269348]	C₉₅₇		---)	[233, 1187, 41828]	C₃₁₉
60)	[10513, 3851, 109476]	C₉₅₇		31)	[3041, 4631, 4205200]	C₉₅₇
61)	[11113, 5254, 2455929]	C₉₅₇		50)	[5569, 2627, 1111300]	C₉₅₇
62)	[11197, 1437, 43169]	C₉₅₇		---)	[881, 2874, 1892293]	C₃₁₉
63)	[11197, 2249, 1261701]	C₉₅₇		---)	[2861, 4498, 11197]	C₃₁₉
64)	[11369, 7122, 10452397]	C₉₅₇		51)	[5653, 3561, 557081]	C₉₅₇
65)	[12281, 1134, 124993]	C₉₅₇		---)	[1033, 567, 49124]	C₈₇
66)	[12457, 4330, 651157]	C₉₅₇		35)	[3853, 2165, 1009017]	C₉₅₇
67)	[12713, 3551, 3123796]	C₉₅₇		40)	[4621, 7102, 114417]	C₉₅₇
68)	[12821, 7810, 11095021]	C₉₅₇		---)	[4621, 3905, 1038501]	C₃₁₉
69)	[12829, 5473, 3995737]	C₉₅₇		25)	[2377, 2923, 205264]	C₉₅₇
70)	[13537, 7027, 11935188]	C₉₅₇		---)	[4093, 4429, 1096497]	C₃₁₉
71)	[14929, 2187, 1102436]	C₉₅₇		18)	[521, 1815, 238864]	C₉₅₇
72)	[15289, 911, 111924]	C₉₅₇		32)	[3109, 1822, 382225]	C₉₅₇
73)	[15641, 1315, 240704]	C₉₅₇		---)	[3761, 2630, 766409]	C₃₁₉
74)	[16477, 2661, 1271801]	C₉₅₇		---)	[929, 4167, 4218112]	C₃₁₉
75)	[16661, 874, 124325]	C₉₅₇		---)	[4973, 437, 16661]	C₃₁₉
76)	[17321, 5834, 125525]	C₉₅₇		44)	[5021, 2917, 2095841]	C₉₅₇
77)	[17393, 2071, 93904]	C₉₅₇		52)	[5869, 4142, 3913425]	C₉₅₇
78)	[17657, 2950, 1893113]	C₉₅₇		20)	[857, 1475, 70628]	C₉₅₇
79)	[17713, 5302, 6744393]	C₉₅₇		28)	[2593, 2651, 70852]	C₉₅₇
80)	[18289, 899, 160900]	C₉₅₇		23)	[1609, 1798, 164601]	C₉₅₇
81)	[18397, 3325, 2722513]	C₉₅₇		30)	[2833, 6650, 165573]	C₉₅₇
82)	[18481, 6714, 11195525]	C₉₅₇		34)	[3701, 3357, 18481]	C₉₅₇
83)	[18661, 4210, 773469]	C₉₅₇		---)	[1061, 2105, 914389]	C₃₁₉
84)	[23081, 1990, 620729]	C₉₅₇		17)	[281, 995, 92324]	C₉₅₇
85)	[34157, 1937, 519569]	C₉₅₇		---)	[281, 2483, 546512]	C₃₁₉
86)	[34157, 874, 54341]	C₉₅₇		---)	[1109, 437, 34157]	C₃₁₉
87)	[48481, 1370, 275301]	C₉₅₇		---)	[181, 685, 48481]	C₃₁₉
88)	[56857, 273, 4418]	C₉₅₇		---)	[8, 546, 56857]	C₃₃
89)	[59093, 1458, 295069]	C₉₅₇		---)	[1021, 729, 59093]	C₃₁₉
90)	[63317, 389, 22001]	C₉₅₇		---)	[449, 778, 63317]	C₃₁₉
91)	[70621, 917, 51325]	C₉₅₇		---)	[2053, 1834, 635589]	C₃₁₉
92)	[117281, 397, 10082]	C₉₅₇		---)	[8, 794, 117281]	C₈₇
93)	[155777, 415, 4112]	C₉₅₇		---)	[257, 830, 155777]	C₃ x C₉₅₇
94)	[157013, 1802, 183749]	C₉₅₇		---)	[509, 901, 157013]	C₃₁₉
95)	[224057, 523, 12368]	C₉₅₇		19)	[773, 1046, 224057]	C₉₅₇
96)	[231821, 489, 1825]	C₉₅₇		---)	[73, 978, 231821]	C₃₁₉
97)	[243197, 497, 953]	C₉₅₇		21)	[953, 994, 243197]	C₉₅₇
98)	[250409, 947, 161600]	C₉₅₇		---)	[101, 1894, 250409]	C₃₁₉
99)	[284593, 1447, 452304]	C₉₅₇		---)	[349, 2894, 284593]	C₃₁₉
100)	[329801, 739, 54080]	C₉₅₇		---)	[5, 1177, 329801]	C₈₇
101)	[346877, 665, 23837]	C₉₅₇		---)	[197, 1330, 346877]	C₃₁₉
102)	[371573, 669, 18997]	C₉₅₇		---)	[157, 1338, 371573]	C₃₁₉
103)	[814097, 2843, 188944]	C₉₅₇		---)	[241, 5686, 7326873]	C₃₁₉
104)	[826289, 967, 27200]	C₉₅₇		8)	[17, 1934, 826289]	C₉₅₇
105)	[1028113, 1175, 88128]	C₉₅₇		9)	[17, 2350, 1028113]	C₉₅₇
106)	[1089457, 1365, 193442]	C₉₅₇		---)	[8, 2730, 1089457]	C₃₁₉
107)	[1137161, 1667, 410432]	C₉₅₇		10)	[53, 3334, 1137161]	C₉₅₇
108)	[1327577, 1179, 15616]	C₉₅₇		11)	[61, 2358, 1327577]	C₉₅₇
109)	[1407037, 1217, 18513]	C₉₅₇		---)	[17, 2434, 1407037]	C₃₁₉
110)	[2364361, 1571, 25920]	C₉₅₇		---)	[5, 3142, 2364361]	C₃₁₉
111)	[3262681, 1819, 11520]	C₉₅₇		---)	[5, 3638, 3262681]	C₃₁₉
112)	[5270129, 3047, 1003520]	C₉₅₇		---)	[5, 4661, 5270129]	C₃₁₉
113)	[10789913, 3291, 10192]	C₉₅₇		6)	[13, 6582, 10789913]	C₉₅₇
114)	[10896497, 3303, 3328]	C₉₅₇		7)	[13, 6606, 10896497]	C₉₅₇
115)	[12432569, 3563, 65600]	C₉₅₇		---)	[41, 7126, 12432569]	C₃₁₉
116)	[16409417, 4067, 32768]	C₉₅₇		---)	[8, 8134, 16409417]	C₃₁₉
117)	[19675361, 5231, 1922000]	C₉₅₇		4)	[5, 9493, 19675361]	C₉₅₇
118)	[20271577, 4507, 10368]	C₉₅₇		---)	[8, 9014, 20271577]	C₃₁₉

Class number: [Non-normal] [Cyclic]

Class group C957 non-normal (D4) quartic CM field invariants: 118 fields

Class group C₉₅₇ non-normal (D₄) quartic CM field invariants: 118 fields