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, 5662, 7613153]	C₉₀₅		---)	[7613153, 2831, 100352]	C₂₇₁₅
2)	[17, 2494, 1119809]	C₉₀₅		---)	[1119809, 1247, 108800]	C₅ x C₉₀₅
3)	[17, 2158, 1146833]	C₉₀₅		97)	[1146833, 1079, 4352]	C₉₀₅
4)	[29, 4598, 5018137]	C₉₀₅		105)	[5018137, 2299, 66816]	C₉₀₅
5)	[37, 4998, 6235529]	C₉₀₅		106)	[6235529, 2499, 2368]	C₉₀₅
6)	[73, 942, 217169]	C₉₀₅		88)	[217169, 471, 1168]	C₉₀₅
7)	[101, 3550, 2627041]	C₉₀₅		102)	[2627041, 1775, 130896]	C₉₀₅
8)	[109, 1902, 562577]	C₉₀₅		93)	[562577, 951, 85456]	C₉₀₅
9)	[157, 2742, 1628441]	C₉₀₅		98)	[1628441, 1371, 62800]	C₉₀₅
10)	[173, 3590, 1882313]	C₉₀₅		100)	[1882313, 1795, 334928]	C₉₀₅
11)	[277, 4310, 4005817]	C₉₀₅		104)	[4005817, 2155, 159552]	C₉₀₅
12)	[401, 330, 25621]	C₉₀₅		82)	[25621, 165, 401]	C₉₀₅
13)	[409, 630, 92681]	C₉₀₅		85)	[92681, 315, 1636]	C₉₀₅
14)	[461, 1533, 545917]	C₉₀₅		92)	[545917, 3066, 166421]	C₉₀₅
15)	[797, 1461, 499957]	C₉₀₅		91)	[499957, 2922, 134693]	C₉₀₅
16)	[881, 310, 9929]	C₉₀₅		63)	[9929, 155, 3524]	C₉₀₅
17)	[929, 2543, 635456]	C₉₀₅		62)	[9929, 2075, 1073924]	C₉₀₅
18)	[977, 4379, 3420004]	C₉₀₅		76)	[17449, 2331, 97700]	C₉₀₅
19)	[1033, 1883, 638244]	C₉₀₅		77)	[17729, 3766, 992713]	C₉₀₅
20)	[1301, 1093, 272317]	C₉₀₅		89)	[272317, 2186, 105381]	C₉₀₅
21)	[1553, 866, 181277]	C₉₀₅		87)	[181277, 433, 1553]	C₉₀₅
22)	[1777, 1790, 346113]	C₉₀₅		42)	[4273, 895, 113728]	C₉₀₅
23)	[2113, 886, 162441]	C₉₀₅		78)	[18049, 443, 8452]	C₉₀₅
24)	[2137, 3799, 602944]	C₉₀₅		59)	[9421, 3517, 2053657]	C₉₀₅
25)	[2153, 1175, 150848]	C₉₀₅		---)	[2357, 2237, 260513]	C₁₈₁
26)	[2161, 355, 26644]	C₉₀₅		53)	[6661, 710, 19449]	C₉₀₅
27)	[2417, 3566, 704081]	C₉₀₅		70)	[14369, 1783, 618752]	C₉₀₅
28)	[2473, 4303, 1151296]	C₉₀₅		---)	[17989, 6841, 2473]	C₈₁₄₅
29)	[2593, 4519, 198736]	C₉₀₅		66)	[12421, 5333, 1890297]	C₉₀₅
30)	[2657, 3203, 2548196]	C₉₀₅		67)	[13001, 5843, 3071492]	C₉₀₅
31)	[2689, 1402, 394597]	C₉₀₅		56)	[8053, 701, 24201]	C₉₀₅
32)	[2753, 283, 13828]	C₉₀₅		38)	[3457, 566, 24777]	C₉₀₅
33)	[3121, 2503, 1078596]	C₉₀₅		---)	[3329, 3315, 2446864]	C₁₈₁
34)	[3181, 917, 75825]	C₉₀₅		---)	[337, 683, 114516]	C₁₈₁
35)	[3253, 297, 1721]	C₉₀₅		---)	[1721, 594, 81325]	C₁₈₁
36)	[3329, 1131, 219088]	C₉₀₅		---)	[13693, 2262, 402809]	C₅ x C₂₇₁₅
37)	[3449, 1202, 16301]	C₉₀₅		73)	[16301, 601, 86225]	C₉₀₅
38)	[3457, 566, 24777]	C₉₀₅		32)	[2753, 283, 13828]	C₉₀₅
39)	[3469, 3781, 3427425]	C₉₀₅		72)	[15233, 7039, 13876]	C₉₀₅
40)	[3581, 373, 12401]	C₉₀₅		---)	[12401, 746, 89525]	C₂₇₁₅
41)	[3929, 6771, 2596804]	C₉₀₅		68)	[13249, 6735, 4023296]	C₉₀₅
42)	[4273, 895, 113728]	C₉₀₅		22)	[1777, 1790, 346113]	C₉₀₅
43)	[4561, 5406, 8609]	C₉₀₅		57)	[8609, 2703, 1824400]	C₉₀₅
44)	[5009, 3050, 702709]	C₉₀₅		69)	[14341, 1525, 405729]	C₉₀₅
45)	[5009, 5455, 766016]	C₉₀₅		64)	[11969, 5663, 8014400]	C₉₀₅
46)	[5021, 5317, 6841]	C₉₀₅		54)	[6841, 5443, 180756]	C₉₀₅
47)	[5413, 9146, 19851381]	C₉₀₅		---)	[18229, 4573, 265237]	C₁₇₁₉₅
48)	[5413, 7925, 7255773]	C₉₀₅		74)	[16453, 5621, 3946077]	C₉₀₅
49)	[5641, 3758, 281425]	C₉₀₅		---)	[11257, 1879, 812304]	C₁₅₃₈₅
50)	[5669, 6965, 2829229]	C₉₀₅		---)	[16741, 7961, 1275525]	C₅ x C₉₀₅
51)	[5881, 4114, 4207725]	C₉₀₅		---)	[18701, 2057, 5881]	C₂₇₁₅
52)	[5897, 7763, 14734336]	C₉₀₅		---)	[14389, 7797, 14158697]	C₂₇₁₅
53)	[6661, 710, 19449]	C₉₀₅		26)	[2161, 355, 26644]	C₉₀₅
54)	[6841, 5443, 180756]	C₉₀₅		46)	[5021, 5317, 6841]	C₉₀₅
55)	[6949, 1957, 38457]	C₉₀₅		---)	[4273, 3914, 3676021]	C₁₈₁
56)	[8053, 701, 24201]	C₉₀₅		31)	[2689, 1402, 394597]	C₉₀₅
57)	[8609, 2703, 1824400]	C₉₀₅		43)	[4561, 5406, 8609]	C₉₀₅
58)	[9181, 4513, 1233477]	C₉₀₅		---)	[2797, 3557, 2653309]	C₁₈₁
59)	[9421, 3517, 2053657]	C₉₀₅		24)	[2137, 3799, 602944]	C₉₀₅
60)	[9829, 5058, 6356525]	C₉₀₅		---)	[5189, 2529, 9829]	C₁₈₁
61)	[9829, 4829, 4529925]	C₉₀₅		---)	[2237, 2481, 1189309]	C₁₈₁
62)	[9929, 2075, 1073924]	C₉₀₅		17)	[929, 2543, 635456]	C₉₀₅
63)	[9929, 155, 3524]	C₉₀₅		16)	[881, 310, 9929]	C₉₀₅
64)	[11969, 5663, 8014400]	C₉₀₅		45)	[5009, 5455, 766016]	C₉₀₅
65)	[12101, 125, 881]	C₉₀₅		---)	[881, 250, 12101]	C₁₈₁
66)	[12421, 5333, 1890297]	C₉₀₅		29)	[2593, 4519, 198736]	C₉₀₅
67)	[13001, 5843, 3071492]	C₉₀₅		30)	[2657, 3203, 2548196]	C₉₀₅
68)	[13249, 6735, 4023296]	C₉₀₅		41)	[3929, 6771, 2596804]	C₉₀₅
69)	[14341, 1525, 405729]	C₉₀₅		44)	[5009, 3050, 702709]	C₉₀₅
70)	[14369, 1783, 618752]	C₉₀₅		27)	[2417, 3566, 704081]	C₉₀₅
71)	[15121, 2463, 424100]	C₉₀₅		---)	[4241, 4926, 4369969]	C₁₈₁
72)	[15233, 7039, 13876]	C₉₀₅		39)	[3469, 3781, 3427425]	C₉₀₅
73)	[16301, 601, 86225]	C₉₀₅		37)	[3449, 1202, 16301]	C₉₀₅
74)	[16453, 5621, 3946077]	C₉₀₅		48)	[5413, 7925, 7255773]	C₉₀₅
75)	[17033, 2886, 992137]	C₉₀₅		---)	[3433, 1443, 272528]	C₁₈₁
76)	[17449, 2331, 97700]	C₉₀₅		18)	[977, 4379, 3420004]	C₉₀₅
77)	[17729, 3766, 992713]	C₉₀₅		19)	[1033, 1883, 638244]	C₉₀₅
78)	[18049, 443, 8452]	C₉₀₅		23)	[2113, 886, 162441]	C₉₀₅
79)	[18773, 4361, 807557]	C₉₀₅		---)	[2237, 4961, 3172637]	C₁₈₁
80)	[19477, 6493, 5860413]	C₉₀₅		---)	[3853, 6325, 175293]	C₁₈₁
81)	[21317, 1121, 266197]	C₉₀₅		---)	[277, 2242, 191853]	C₁₈₁
82)	[25621, 165, 401]	C₉₀₅		12)	[401, 330, 25621]	C₉₀₅
83)	[43889, 914, 33293]	C₉₀₅		---)	[197, 457, 43889]	C₁₈₁
84)	[61493, 953, 88693]	C₉₀₅		---)	[733, 1906, 553437]	C₅₄₃
85)	[92681, 315, 1636]	C₉₀₅		13)	[409, 630, 92681]	C₉₀₅
86)	[131893, 653, 73629]	C₉₀₅		---)	[101, 1306, 131893]	C₁₈₁
87)	[181277, 433, 1553]	C₉₀₅		21)	[1553, 866, 181277]	C₉₀₅
88)	[217169, 471, 1168]	C₉₀₅		6)	[73, 942, 217169]	C₉₀₅
89)	[272317, 2186, 105381]	C₉₀₅		20)	[1301, 1093, 272317]	C₉₀₅
90)	[475109, 853, 63125]	C₉₀₅		---)	[101, 1706, 475109]	C₁₈₁
91)	[499957, 2922, 134693]	C₉₀₅		15)	[797, 1461, 499957]	C₉₀₅
92)	[545917, 3066, 166421]	C₉₀₅		14)	[461, 1533, 545917]	C₉₀₅
93)	[562577, 951, 85456]	C₉₀₅		8)	[109, 1902, 562577]	C₉₀₅
94)	[665813, 821, 2057]	C₉₀₅		---)	[17, 1642, 665813]	C₁₈₁
95)	[709913, 1275, 228928]	C₉₀₅		---)	[73, 2550, 709913]	C₁₈₁
96)	[792241, 895, 2196]	C₉₀₅		---)	[61, 1790, 792241]	C₁₈₁
97)	[1146833, 1079, 4352]	C₉₀₅		3)	[17, 2158, 1146833]	C₉₀₅
98)	[1628441, 1371, 62800]	C₉₀₅		9)	[157, 2742, 1628441]	C₉₀₅
99)	[1731721, 1411, 64800]	C₉₀₅		---)	[8, 2822, 1731721]	C₁₈₁
100)	[1882313, 1795, 334928]	C₉₀₅		10)	[173, 3590, 1882313]	C₉₀₅
101)	[2363401, 2051, 460800]	C₉₀₅		---)	[8, 4102, 2363401]	C₁₈₁
102)	[2627041, 1775, 130896]	C₉₀₅		7)	[101, 3550, 2627041]	C₉₀₅
103)	[3652049, 2743, 968000]	C₉₀₅		---)	[5, 3829, 3652049]	C₁₈₁
104)	[4005817, 2155, 159552]	C₉₀₅		11)	[277, 4310, 4005817]	C₉₀₅
105)	[5018137, 2299, 66816]	C₉₀₅		4)	[29, 4598, 5018137]	C₉₀₅
106)	[6235529, 2499, 2368]	C₉₀₅		5)	[37, 4998, 6235529]	C₉₀₅
107)	[9778073, 3131, 6272]	C₉₀₅		---)	[8, 6262, 9778073]	C₁₈₁

Class number: [Non-normal] [Cyclic]

Class group C905 non-normal (D4) quartic CM field invariants: 107 fields

Class group C₉₀₅ non-normal (D₄) quartic CM field invariants: 107 fields