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, 914, 201629]	C₃ x C₉	■	117)	[201629, 457, 1805]	C₃ x C₉	■
2)	[5, 701, 119849]	C₃ x C₉	■	111)	[119849, 587, 56180]	C₃ x C₉	■
3)	[5, 1361, 446549]	C₃ x C₉	■	---)	[446549, 877, 80645]	C₃ x C₃ x C₉	■
4)	[5, 481, 48809]	C₃ x C₉	■	103)	[48809, 467, 42320]	C₃ x C₉	■
5)	[5, 841, 173309]	C₃ x C₉	■	115)	[173309, 697, 78125]	C₃ x C₉	■
6)	[5, 417, 43321]	C₃ x C₉	■	---)	[43321, 299, 11520]	C₃ x C₃ x C₉	■
7)	[5, 586, 81349]	C₃ x C₉	■	105)	[81349, 293, 1125]	C₃ x C₉	■
8)	[8, 694, 107609]	C₃ x C₉	■	109)	[107609, 347, 3200]	C₃ x C₉	■
9)	[8, 754, 99497]	C₃ x C₉	■	108)	[99497, 377, 10658]	C₃ x C₉	■
10)	[8, 950, 220217]	C₃ x C₉	■	---)	[220217, 475, 1352]	C₃ x C₃ x C₃ x C₉	■
11)	[8, 742, 133769]	C₃ x C₉	■	---)	[133769, 371, 968]	C₃ x C₃ x C₉	■
12)	[8, 1090, 159737]	C₃ x C₉	■	---)	[159737, 545, 34322]	C₃ x C₃ x C₉	■
13)	[8, 886, 119417]	C₃ x C₉	■	110)	[119417, 443, 19208]	C₃ x C₉	■
14)	[8, 834, 107641]	C₃ x C₉	■	---)	[107641, 417, 16562]	C₃ x C₉ x C₂₇	■
15)	[8, 502, 58393]	C₃ x C₉	■	104)	[58393, 251, 1152]	C₃ x C₉	■
16)	[8, 914, 199049]	C₃ x C₉	■	116)	[199049, 457, 2450]	C₃ x C₉	■
17)	[13, 881, 92221]	C₃ x C₉	■	106)	[92221, 697, 98397]	C₃ x C₉	■
18)	[13, 422, 27673]	C₃ x C₉	■	---)	[27673, 211, 4212]	C₃ x C₃ x C₉	■
19)	[13, 770, 144013]	C₃ x C₉	■	113)	[144013, 385, 1053]	C₃ x C₉	■
20)	[13, 426, 30341]	C₃ x C₉	■	---)	[30341, 213, 3757]	C₃ x C₄₅	■
21)	[13, 818, 144349]	C₃ x C₉	■	114)	[144349, 409, 5733]	C₃ x C₉	■
22)	[17, 1134, 92737]	C₃ x C₉	■	107)	[92737, 567, 57188]	C₃ x C₉	■
23)	[17, 934, 86441]	C₃ x C₉	■	---)	[86441, 467, 32912]	C₃ x C₃ x C₉	■
24)	[17, 1270, 219353]	C₃ x C₉	■	118)	[219353, 635, 45968]	C₃ x C₉	■
25)	[17, 287, 19636]	C₃ x C₉	■	81)	[4909, 281, 18513]	C₃ x C₉	■
26)	[17, 1486, 138337]	C₃ x C₉	■	112)	[138337, 743, 103428]	C₃ x C₉	■
27)	[29, 621, 22453]	C₃ x C₉	■	101)	[22453, 753, 1421]	C₃ x C₉	■
28)	[29, 277, 10301]	C₃ x C₉	■	---)	[10301, 554, 35525]	C₃ x C₃ x C₉	■
29)	[37, 713, 125973]	C₃ x C₉	■	93)	[13997, 365, 1813]	C₃ x C₉	■
30)	[37, 685, 117297]	C₃ x C₉	■	---)	[13033, 595, 85248]	C₃ x C₁₁₇	■
31)	[41, 271, 16628]	C₃ x C₉	■	78)	[4157, 389, 11849]	C₃ x C₉	■
32)	[53, 250, 5237]	C₃ x C₉	■	82)	[5237, 125, 2597]	C₃ x C₉	■
33)	[61, 885, 14621]	C₃ x C₉	■	95)	[14621, 533, 38125]	C₃ x C₉	■
34)	[73, 999, 98372]	C₃ x C₉	■	---)	[24593, 1071, 280612]	C₃ x C₄₅	■
35)	[73, 939, 219536]	C₃ x C₉	■	92)	[13721, 679, 84388]	C₃ x C₉	■
36)	[73, 471, 53252]	C₃ x C₉	■	---)	[13313, 942, 8833]	C₃ x C₆₃	■
37)	[73, 963, 231824]	C₃ x C₉	■	94)	[14489, 743, 105412]	C₃ x C₉	■
38)	[97, 822, 13721]	C₃ x C₉	■	91)	[13721, 411, 38800]	C₃ x C₉	■
39)	[101, 677, 101225]	C₃ x C₉	■	77)	[4049, 407, 40400]	C₃ x C₉	■
40)	[101, 133, 4397]	C₃ x C₉	■	79)	[4397, 266, 101]	C₃ x C₉	■
41)	[113, 1315, 333968]	C₃ x C₉	■	99)	[20873, 1067, 28928]	C₃ x C₉	■
42)	[149, 329, 26725]	C₃ x C₉	■	58)	[1069, 357, 25181]	C₃ x C₉	■
43)	[173, 117, 2341]	C₃ x C₉	■	67)	[2341, 234, 4325]	C₃ x C₉	■
44)	[197, 113, 2749]	C₃ x C₉	■	72)	[2749, 226, 1773]	C₃ x C₉	■
45)	[197, 125, 1493]	C₃ x C₉	■	61)	[1493, 250, 9653]	C₃ x C₉	■
46)	[197, 673, 104909]	C₃ x C₉	■	65)	[2141, 353, 4925]	C₃ x C₉	■
47)	[229, 66, 173]	C₃ x C₉	■	---)	[173, 33, 229]	C₉	■
48)	[257, 66, 61]	C₃ x C₉	■	---)	[61, 33, 257]	C₉	■
49)	[257, 227, 12304]	C₃ x C₉	■	---)	[769, 454, 2313]	C₉	■
50)	[257, 87, 1828]	C₃ x C₉	■	---)	[457, 174, 257]	C₉	■
51)	[317, 89, 1901]	C₃ x C₉	■	---)	[1901, 178, 317]	C₃ x C₃ x C₉	■
52)	[569, 934, 72425]	C₃ x C₉	■	73)	[2897, 467, 36416]	C₃ x C₉	■
53)	[613, 538, 11061]	C₃ x C₉	■	---)	[1229, 269, 15325]	C₃ x C₃ x C₉	■
54)	[641, 1110, 267001]	C₃ x C₉	■	83)	[5449, 555, 10256]	C₃ x C₉	■
55)	[701, 409, 2389]	C₃ x C₉	■	68)	[2389, 818, 157725]	C₃ x C₉	■
56)	[761, 143, 356]	C₃ x C₉	■	---)	[89, 286, 19025]	C₉	■
57)	[929, 319, 6628]	C₃ x C₉	■	62)	[1657, 638, 75249]	C₃ x C₉	■
58)	[1069, 357, 25181]	C₃ x C₉	■	42)	[149, 329, 26725]	C₃ x C₉	■
59)	[1373, 145, 4913]	C₃ x C₉	■	---)	[17, 151, 5492]	C₉	■
60)	[1489, 151, 5328]	C₃ x C₉	■	---)	[37, 241, 13401]	C₉	■
61)	[1493, 250, 9653]	C₃ x C₉	■	45)	[197, 125, 1493]	C₃ x C₉	■
62)	[1657, 638, 75249]	C₃ x C₉	■	57)	[929, 319, 6628]	C₃ x C₉	■
63)	[1777, 511, 64836]	C₃ x C₉	■	64)	[1801, 1022, 1777]	C₃ x C₉	■
64)	[1801, 1022, 1777]	C₃ x C₉	■	63)	[1777, 511, 64836]	C₃ x C₉	■
65)	[2141, 353, 4925]	C₃ x C₉	■	46)	[197, 673, 104909]	C₃ x C₉	■
66)	[2213, 69, 637]	C₃ x C₉	■	---)	[13, 138, 2213]	C₉	■
67)	[2341, 234, 4325]	C₃ x C₉	■	43)	[173, 117, 2341]	C₃ x C₉	■
68)	[2389, 818, 157725]	C₃ x C₉	■	55)	[701, 409, 2389]	C₃ x C₉	■
69)	[2557, 258, 6413]	C₃ x C₉	■	---)	[53, 129, 2557]	C₉	■
70)	[2609, 95, 1604]	C₃ x C₉	■	---)	[401, 190, 2609]	C₃ x C₄₅	■
71)	[2677, 61, 261]	C₃ x C₉	■	---)	[29, 122, 2677]	C₉	■
72)	[2749, 226, 1773]	C₃ x C₉	■	44)	[197, 113, 2749]	C₃ x C₉	■
73)	[2897, 467, 36416]	C₃ x C₉	■	52)	[569, 934, 72425]	C₃ x C₉	■
74)	[3061, 1717, 699525]	C₃ x C₉	■	75)	[3109, 2897, 76525]	C₃ x C₉	■
75)	[3109, 2897, 76525]	C₃ x C₉	■	74)	[3061, 1717, 699525]	C₃ x C₉	■
76)	[3889, 63, 20]	C₃ x C₉	■	---)	[5, 126, 3889]	C₉	■
77)	[4049, 407, 40400]	C₃ x C₉	■	39)	[101, 677, 101225]	C₃ x C₉	■
78)	[4157, 389, 11849]	C₃ x C₉	■	31)	[41, 271, 16628]	C₃ x C₉	■
79)	[4397, 266, 101]	C₃ x C₉	■	40)	[101, 133, 4397]	C₃ x C₉	■
80)	[4729, 619, 94608]	C₃ x C₉	■	---)	[73, 359, 18916]	C₉	■
81)	[4909, 281, 18513]	C₃ x C₉	■	25)	[17, 287, 19636]	C₃ x C₉	■
82)	[5237, 125, 2597]	C₃ x C₉	■	32)	[53, 250, 5237]	C₃ x C₉	■
83)	[5449, 555, 10256]	C₃ x C₉	■	54)	[641, 1110, 267001]	C₃ x C₉	■
84)	[5477, 241, 2197]	C₃ x C₉	■	---)	[13, 225, 5477]	C₉	■
85)	[5821, 121, 2205]	C₃ x C₉	■	---)	[5, 153, 5821]	C₉	■
86)	[7481, 91, 200]	C₃ x C₉	■	---)	[8, 182, 7481]	C₉	■
87)	[8713, 99, 272]	C₃ x C₉	■	---)	[17, 198, 8713]	C₉	■
88)	[10069, 157, 3645]	C₃ x C₉	■	---)	[5, 201, 10069]	C₉	■
89)	[10457, 283, 17408]	C₃ x C₉	■	---)	[17, 415, 41828]	C₉	■
90)	[12269, 113, 125]	C₃ x C₉	■	---)	[5, 226, 12269]	C₉	■
91)	[13721, 411, 38800]	C₃ x C₉	■	38)	[97, 822, 13721]	C₃ x C₉	■
92)	[13721, 679, 84388]	C₃ x C₉	■	35)	[73, 939, 219536]	C₃ x C₉	■
93)	[13997, 365, 1813]	C₃ x C₉	■	29)	[37, 713, 125973]	C₃ x C₉	■
94)	[14489, 743, 105412]	C₃ x C₉	■	37)	[73, 963, 231824]	C₃ x C₉	■
95)	[14621, 533, 38125]	C₃ x C₉	■	33)	[61, 885, 14621]	C₃ x C₉	■
96)	[14969, 139, 1088]	C₃ x C₉	■	---)	[17, 278, 14969]	C₉	■
97)	[15349, 173, 3645]	C₃ x C₉	■	---)	[5, 249, 15349]	C₉	■
98)	[15881, 137, 722]	C₃ x C₉	■	---)	[8, 274, 15881]	C₉	■
99)	[20873, 1067, 28928]	C₃ x C₉	■	41)	[113, 1315, 333968]	C₃ x C₉	■
100)	[22229, 157, 605]	C₃ x C₉	■	---)	[5, 314, 22229]	C₉	■
101)	[22453, 753, 1421]	C₃ x C₉	■	27)	[29, 621, 22453]	C₃ x C₉	■
102)	[24749, 193, 3125]	C₃ x C₉	■	---)	[5, 329, 24749]	C₉	■
103)	[48809, 467, 42320]	C₃ x C₉	■	4)	[5, 481, 48809]	C₃ x C₉	■
104)	[58393, 251, 1152]	C₃ x C₉	■	15)	[8, 502, 58393]	C₃ x C₉	■
105)	[81349, 293, 1125]	C₃ x C₉	■	7)	[5, 586, 81349]	C₃ x C₉	■
106)	[92221, 697, 98397]	C₃ x C₉	■	17)	[13, 881, 92221]	C₃ x C₉	■
107)	[92737, 567, 57188]	C₃ x C₉	■	22)	[17, 1134, 92737]	C₃ x C₉	■
108)	[99497, 377, 10658]	C₃ x C₉	■	9)	[8, 754, 99497]	C₃ x C₉	■
109)	[107609, 347, 3200]	C₃ x C₉	■	8)	[8, 694, 107609]	C₃ x C₉	■
110)	[119417, 443, 19208]	C₃ x C₉	■	13)	[8, 886, 119417]	C₃ x C₉	■
111)	[119849, 587, 56180]	C₃ x C₉	■	2)	[5, 701, 119849]	C₃ x C₉	■
112)	[138337, 743, 103428]	C₃ x C₉	■	26)	[17, 1486, 138337]	C₃ x C₉	■
113)	[144013, 385, 1053]	C₃ x C₉	■	19)	[13, 770, 144013]	C₃ x C₉	■
114)	[144349, 409, 5733]	C₃ x C₉	■	21)	[13, 818, 144349]	C₃ x C₉	■
115)	[173309, 697, 78125]	C₃ x C₉	■	5)	[5, 841, 173309]	C₃ x C₉	■
116)	[199049, 457, 2450]	C₃ x C₉	■	16)	[8, 914, 199049]	C₃ x C₉	■
117)	[201629, 457, 1805]	C₃ x C₉	■	1)	[5, 914, 201629]	C₃ x C₉	■
118)	[219353, 635, 45968]	C₃ x C₉	■	24)	[17, 1270, 219353]	C₃ x C₉	■

Class number: [Non-normal] [Cyclic]

Class group C3 x C9 non-normal (D4) quartic CM field invariants: 118 fields

Class group C₃ x C₉ non-normal (D₄) quartic CM field invariants: 118 fields