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, 5414, 7186729]	C₇ x C₅₆		96)	[7186729, 2707, 35280]	C₇ x C₅₆
2)	[8, 6822, 11630313]	C₇ x C₅₆		---)	[1292257, 3411, 1152]	C₁₄ x C₂₈
3)	[12, 1990, 986137]	C₇ x C₅₆		94)	[986137, 995, 972]	C₇ x C₅₆
4)	[13, 2334, 1361681]	C₇ x C₅₆		95)	[1361681, 1167, 52]	C₇ x C₅₆
5)	[13, 5390, 7195633]	C₇ x C₅₆		97)	[7195633, 2695, 16848]	C₇ x C₅₆
6)	[21, 529, 68443]	C₇ x C₅₆		---)	[273772, 1058, 6069]	C₁₄ x C₈₄
7)	[37, 459, 47777]	C₇ x C₅₆		---)	[47777, 918, 19573]	C₁₄ x C₂₈
8)	[57, 2802, 1960749]	C₇ x C₅₆		---)	[217861, 1401, 513]	C₁₄ x C₂₅₂
9)	[61, 274, 13828]	C₇ x C₅₆		---)	[3457, 548, 19764]	C₁₄ x C₂₈
10)	[85, 5254, 4268169]	C₇ x C₅₆		---)	[474241, 2627, 658240]	C₇ x C₂₈
11)	[133, 933, 215993]	C₇ x C₅₆		---)	[215993, 1866, 6517]	C₁₄ x C₂₈
12)	[253, 422, 24028]	C₇ x C₅₆		---)	[24028, 844, 81972]	C₁₄ x C₂₈
13)	[293, 854, 177641]	C₇ x C₅₆		---)	[177641, 427, 1172]	C₇ x C₁₁₂
14)	[293, 397, 12959]	C₇ x C₅₆		64)	[51836, 794, 105773]	C₇ x C₅₆
15)	[293, 1273, 14783]	C₇ x C₅₆		---)	[59132, 2546, 1561397]	C₇ x C₁₆₈
16)	[301, 1361, 39799]	C₇ x C₅₆		---)	[159196, 2722, 1693125]	C₁₄ x C₂₈
17)	[505, 458, 1941]	C₇ x C₅₆		---)	[1941, 229, 12625]	C₇ x C₁₄
18)	[557, 929, 215621]	C₇ x C₅₆		82)	[215621, 1858, 557]	C₇ x C₅₆
19)	[577, 3947, 1920064]	C₇ x C₅₆		---)	[30001, 2227, 332352]	C₅₆
20)	[577, 1182, 266193]	C₇ x C₅₆		---)	[29577, 591, 20772]	C₅₆
21)	[1009, 478, 40977]	C₇ x C₅₆		---)	[4553, 239, 4036]	C₁₁₂
22)	[1009, 271, 18108]	C₇ x C₅₆		---)	[2012, 542, 1009]	C₅₆
23)	[1009, 893, 15472]	C₇ x C₅₆		---)	[3868, 1786, 735561]	C₅₆
24)	[1021, 2699, 1635073]	C₇ x C₅₆		---)	[13513, 2701, 36756]	C₁₄ x C₂₈
25)	[1133, 502, 44873]	C₇ x C₅₆		---)	[44873, 251, 4532]	C₁₄ x C₂₈
26)	[1293, 4789, 15661]	C₇ x C₅₆		---)	[15661, 2609, 570213]	C₇ x C₁₆₈
27)	[1601, 223, 12032]	C₇ x C₅₆		---)	[188, 446, 1601]	C₅₆
28)	[1601, 409, 22208]	C₇ x C₅₆		---)	[1388, 818, 78449]	C₅₆
29)	[1761, 678, 2217]	C₇ x C₅₆		---)	[2217, 339, 28176]	C₂ x C₂₈
30)	[1761, 1599, 406308]	C₇ x C₅₆		---)	[2073, 1563, 112704]	C₂ x C₂₈
31)	[2029, 1021, 247929]	C₇ x C₅₆	■	---)	[2049, 2042, 50725]	C₅₆
32)	[2029, 57, 305]	C₇ x C₅₆		---)	[305, 114, 2029]	C₂ x C₅₆
33)	[2029, 149, 985]	C₇ x C₅₆		---)	[985, 298, 18261]	C₃₃₆
34)	[2029, 285, 7625]	C₇ x C₅₆		---)	[305, 570, 50725]	C₂ x C₅₆
35)	[2029, 337, 3537]	C₇ x C₅₆		---)	[393, 674, 99421]	C₅₆
36)	[2029, 137, 127]	C₇ x C₅₆		---)	[508, 274, 18261]	C₅₆
37)	[2129, 2223, 59692]	C₇ x C₅₆		66)	[59692, 4446, 4702961]	C₇ x C₅₆
38)	[2137, 3684, 467411]	C₇ x C₅₆		---)	[38156, 7368, 11702212]	C₇ x C₇ x C₅₆
39)	[2757, 377, 1759]	C₇ x C₅₆		---)	[7036, 754, 135093]	C₁₄ x C₂₈
40)	[2913, 446, 3121]	C₇ x C₅₆		---)	[3121, 223, 11652]	C₂₈₀
41)	[5233, 1852, 726651]	C₇ x C₅₆		59)	[35884, 3704, 523300]	C₇ x C₅₆
42)	[5273, 436, 67]	C₇ x C₅₆		---)	[268, 872, 189828]	C₅₆
43)	[5849, 6829, 2532908]	C₇ x C₅₆		63)	[51692, 13658, 36503609]	C₇ x C₅₆
44)	[8097, 1019, 14656]	C₇ x C₅₆		---)	[229, 1093, 202425]	C₁₆₈	■
45)	[8465, 111, 964]	C₇ x C₅₆	■	---)	[241, 222, 8465]	C₂₈	■
46)	[9029, 1362, 427645]	C₇ x C₅₆		---)	[445, 681, 9029]	C₂ x C₁₁₂
47)	[9173, 103, 359]	C₇ x C₅₆		---)	[1436, 206, 9173]	C₇ x C₁₆₈
48)	[9208, 598, 52569]	C₇ x C₅₆		---)	[649, 299, 9208]	C₂ x C₂₈
49)	[10713, 830, 817]	C₇ x C₅₆		---)	[817, 415, 42852]	C₂ x C₁₄₀
50)	[14201, 791, 124468]	C₇ x C₅₆		---)	[37, 441, 14201]	C₅₆
51)	[17413, 215, 7203]	C₇ x C₅₆		---)	[12, 430, 17413]	C₂ x C₂₈
52)	[18053, 908, 43639]	C₇ x C₅₆		---)	[604, 1816, 649908]	C₁₄ x C₂₈
53)	[18808, 268, 13254]	C₇ x C₅₆		---)	[24, 212, 4702]	C₂ x C₂₈
54)	[21832, 1414, 150537]	C₇ x C₅₆		---)	[417, 707, 87328]	C₇ x C₁₄
55)	[24604, 314, 45]	C₇ x C₅₆		---)	[5, 157, 6151]	C₅₆
56)	[25084, 3790, 3189681]	C₇ x C₅₆		---)	[2929, 1895, 100336]	C₁₄ x C₅₆
57)	[28869, 802, 45325]	C₇ x C₅₆		---)	[37, 401, 28869]	C₅₆
58)	[33793, 898, 66429]	C₇ x C₅₆		---)	[61, 449, 33793]	C₅₆	■
59)	[35884, 3704, 523300]	C₇ x C₅₆		41)	[5233, 1852, 726651]	C₇ x C₅₆
60)	[42577, 229, 2466]	C₇ x C₅₆		---)	[1096, 458, 42577]	C₁₄ x C₁₁₂
61)	[44857, 379, 24696]	C₇ x C₅₆		---)	[56, 758, 44857]	C₂ x C₂₈
62)	[49553, 1567, 6848]	C₇ x C₅₆		---)	[428, 3134, 2428097]	C₁₄ x C₂₈
63)	[51692, 13658, 36503609]	C₇ x C₅₆		43)	[5849, 6829, 2532908]	C₇ x C₅₆
64)	[51836, 794, 105773]	C₇ x C₅₆		14)	[293, 397, 12959]	C₇ x C₅₆
65)	[52009, 1382, 9400]	C₇ x C₅₆		---)	[376, 2764, 1872324]	C₅₆
66)	[59692, 4446, 4702961]	C₇ x C₅₆		37)	[2129, 2223, 59692]	C₇ x C₅₆
67)	[64681, 397, 23232]	C₇ x C₅₆		---)	[12, 794, 64681]	C₂ x C₂₈
68)	[67217, 313, 7688]	C₇ x C₅₆		---)	[8, 626, 67217]	C₅₆
69)	[70897, 267, 98]	C₇ x C₅₆		---)	[8, 534, 70897]	C₂ x C₂₈
70)	[85121, 323, 4802]	C₇ x C₅₆		---)	[8, 646, 85121]	C₅₆
71)	[85317, 309, 2541]	C₇ x C₅₆		---)	[21, 618, 85317]	C₂ x C₂₈
72)	[93817, 395, 15552]	C₇ x C₅₆		---)	[12, 790, 93817]	C₂ x C₂₈
73)	[99001, 1387, 456192]	C₇ x C₅₆		---)	[88, 2774, 99001]	C₂ x C₂₈
74)	[99001, 315, 56]	C₇ x C₅₆		---)	[56, 630, 99001]	C₂ x C₂₈
75)	[140009, 403, 5600]	C₇ x C₅₆		---)	[56, 806, 140009]	C₅₆
76)	[144649, 387, 1280]	C₇ x C₅₆		---)	[5, 774, 144649]	C₅₆
77)	[150229, 1193, 17797]	C₇ x C₅₆	■	---)	[13, 821, 150229]	C₂₈	■
78)	[160057, 1271, 43732]	C₇ x C₅₆		---)	[13, 821, 160057]	C₅₆	■
79)	[173276, 872, 16820]	C₇ x C₅₆		---)	[5, 436, 43319]	C₅₆
80)	[194156, 1432, 318500]	C₇ x C₅₆		---)	[65, 716, 48539]	C₂ x C₅₆
81)	[208337, 1826, 221]	C₇ x C₅₆		---)	[221, 913, 208337]	C₁₄ x C₅₆
82)	[215621, 1858, 557]	C₇ x C₅₆		18)	[557, 929, 215621]	C₇ x C₅₆
83)	[254521, 1024, 7623]	C₇ x C₅₆		---)	[28, 2048, 1018084]	C₂ x C₂₈
84)	[296201, 3947, 266240]	C₇ x C₅₆		---)	[65, 2471, 1184804]	C₁₁₂
85)	[297793, 613, 19494]	C₇ x C₅₆		---)	[24, 1226, 297793]	C₅₆
86)	[303449, 563, 3380]	C₇ x C₅₆		---)	[5, 1126, 303449]	C₅₆
87)	[353593, 811, 76032]	C₇ x C₅₆		---)	[33, 1622, 353593]	C₂ x C₂₈
88)	[368392, 1314, 63257]	C₇ x C₅₆		---)	[17, 657, 92098]	C₇ x C₁₄
89)	[417577, 1075, 184512]	C₇ x C₅₆		---)	[12, 2150, 417577]	C₅₆
90)	[419449, 781, 47628]	C₇ x C₅₆		---)	[12, 1562, 419449]	C₅₆
91)	[534349, 737, 2205]	C₇ x C₅₆		---)	[5, 1474, 534349]	C₅₆
92)	[554069, 1133, 182405]	C₇ x C₅₆		---)	[5, 1489, 554069]	C₅₆
93)	[812069, 1733, 547805]	C₇ x C₅₆		---)	[5, 1889, 812069]	C₅₆
94)	[986137, 995, 972]	C₇ x C₅₆		3)	[12, 1990, 986137]	C₇ x C₅₆
95)	[1361681, 1167, 52]	C₇ x C₅₆		4)	[13, 2334, 1361681]	C₇ x C₅₆
96)	[7186729, 2707, 35280]	C₇ x C₅₆		1)	[5, 5414, 7186729]	C₇ x C₅₆
97)	[7195633, 2695, 16848]	C₇ x C₅₆		5)	[13, 5390, 7195633]	C₇ x C₅₆

Class number: [Non-normal] [Cyclic]

Class group C7 x C56 non-normal (D4) quartic CM field invariants: 97 fields

Class group C₇ x C₅₆ non-normal (D₄) quartic CM field invariants: 97 fields