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)	[13, 7209, 12990701]	C₈₉₇		---)	[12990701, 12541, 10090093]	C₁₅₂₄₉
2)	[53, 3958, 3251609]	C₈₉₇		128)	[3251609, 1979, 166208]	C₈₉₇
3)	[53, 6262, 9636953]	C₈₉₇		---)	[9636953, 3131, 41552]	C₃ x C₈₉₇
4)	[73, 1278, 291521]	C₈₉₇		113)	[291521, 639, 29200]	C₈₉₇
5)	[97, 454, 37561]	C₈₉₇		100)	[37561, 227, 3492]	C₈₉₇
6)	[157, 5174, 5878681]	C₈₉₇		131)	[5878681, 2587, 203472]	C₈₉₇
7)	[233, 4006, 3877801]	C₈₉₇		---)	[3877801, 2003, 33552]	C₄₇₅₄₁
8)	[233, 2838, 2009833]	C₈₉₇		101)	[41017, 1419, 932]	C₈₉₇
9)	[257, 2134, 546361]	C₈₉₇		---)	[546361, 1067, 148032]	C₂₉₉
10)	[269, 3014, 1840649]	C₈₉₇		125)	[1840649, 1507, 107600]	C₈₉₇
11)	[293, 1750, 596857]	C₈₉₇		117)	[596857, 875, 42192]	C₈₉₇
12)	[313, 1571, 616932]	C₈₉₇		91)	[17137, 1715, 11268]	C₈₉₇
13)	[421, 966, 226553]	C₈₉₇		110)	[226553, 483, 1684]	C₈₉₇
14)	[509, 1046, 240953]	C₈₉₇		111)	[240953, 523, 8144]	C₈₉₇
15)	[613, 1245, 379997]	C₈₉₇		115)	[379997, 2490, 30037]	C₈₉₇
16)	[641, 926, 50273]	C₈₉₇		103)	[50273, 463, 41024]	C₈₉₇
17)	[733, 894, 12161]	C₈₉₇		---)	[12161, 447, 46912]	C₃₂₈₉
18)	[773, 1246, 375761]	C₈₉₇		114)	[375761, 623, 3092]	C₈₉₇
19)	[857, 2279, 278416]	C₈₉₇		92)	[17401, 4131, 85700]	C₈₉₇
20)	[953, 1135, 236048]	C₈₉₇		83)	[14753, 2270, 344033]	C₈₉₇
21)	[1013, 910, 142193]	C₈₉₇		107)	[142193, 455, 16208]	C₈₉₇
22)	[1373, 613, 35933]	C₈₉₇		---)	[35933, 1226, 232037]	C₁₄₉₅
23)	[1409, 563, 70436]	C₈₉₇		---)	[17609, 1126, 35225]	C₃ x C₈₉₇
24)	[1433, 970, 183637]	C₈₉₇		108)	[183637, 485, 12897]	C₈₉₇
25)	[1609, 4543, 2253456]	C₈₉₇		86)	[15649, 3427, 2838276]	C₈₉₇
26)	[1697, 674, 106781]	C₈₉₇		---)	[106781, 337, 1697]	C₄₄₈₅
27)	[2341, 2773, 152001]	C₈₉₇		89)	[16889, 5546, 7081525]	C₈₉₇
28)	[2381, 5197, 6489697]	C₈₉₇		94)	[17977, 6123, 9152564]	C₈₉₇
29)	[2557, 1621, 426141]	C₈₉₇		56)	[5261, 3242, 923077]	C₈₉₇
30)	[2657, 3467, 23204]	C₈₉₇		60)	[5801, 2519, 1062800]	C₈₉₇
31)	[2729, 3618, 2999581]	C₈₉₇		93)	[17749, 1809, 68225]	C₈₉₇
32)	[2729, 3043, 1168100]	C₈₉₇		73)	[11681, 5959, 43664]	C₈₉₇
33)	[2753, 3630, 475153]	C₈₉₇		70)	[9697, 1815, 704768]	C₈₉₇
34)	[2753, 1383, 48016]	C₈₉₇		37)	[3001, 2766, 1720625]	C₈₉₇
35)	[2789, 6265, 7999009]	C₈₉₇		---)	[15121, 5107, 6425856]	C₄₄₈₅
36)	[2917, 261, 16301]	C₈₉₇		---)	[16301, 522, 2917]	C₂₉₉
37)	[3001, 2766, 1720625]	C₈₉₇		34)	[2753, 1383, 48016]	C₈₉₇
38)	[3061, 3781, 3573225]	C₈₉₇		---)	[15881, 7562, 3061]	C₃ x C₈₉₇
39)	[3313, 4802, 980829]	C₈₉₇		74)	[12109, 2401, 1195993]	C₈₉₇
40)	[3433, 4955, 4242132]	C₈₉₇		77)	[13093, 4645, 415393]	C₈₉₇
41)	[3433, 3306, 2059541]	C₈₉₇		90)	[17021, 1653, 168217]	C₈₉₇
42)	[3529, 330, 13109]	C₈₉₇		78)	[13109, 165, 3529]	C₈₉₇
43)	[3673, 4931, 54052]	C₈₉₇		80)	[13513, 6127, 4760208]	C₈₉₇
44)	[3709, 3593, 1179117]	C₈₉₇		82)	[14557, 7186, 8193181]	C₈₉₇
45)	[3889, 387, 13136]	C₈₉₇		---)	[821, 774, 97225]	C₂₉₉
46)	[4273, 5162, 4593429]	C₈₉₇		66)	[6301, 2581, 517033]	C₈₉₇
47)	[4289, 2735, 67604]	C₈₉₇		---)	[16901, 5470, 7209809]	C₆₂₇₉
48)	[4337, 2154, 726229]	C₈₉₇		84)	[14821, 1077, 108425]	C₈₉₇
49)	[4561, 2450, 1482381]	C₈₉₇		96)	[18301, 1225, 4561]	C₈₉₇
50)	[4657, 3095, 437652]	C₈₉₇		75)	[12157, 6190, 7828417]	C₈₉₇
51)	[5021, 3690, 9829]	C₈₉₇		---)	[9829, 1845, 848549]	C₄₄₈₅
52)	[5021, 6374, 9835625]	C₈₉₇		---)	[15737, 3187, 80336]	C₃ x C₈₉₇
53)	[5081, 586, 65525]	C₈₉₇		---)	[2621, 293, 5081]	C₂₉₉
54)	[5261, 362, 11717]	C₈₉₇		---)	[11717, 181, 5261]	C₂₉₉
55)	[5261, 1021, 248773]	C₈₉₇		---)	[5077, 2042, 47349]	C₂₉₉
56)	[5261, 3242, 923077]	C₈₉₇		29)	[2557, 1621, 426141]	C₈₉₇
57)	[5297, 583, 20084]	C₈₉₇		---)	[5021, 1166, 259553]	C₂₉₉
58)	[5569, 2210, 129501]	C₈₉₇		---)	[14389, 1105, 272881]	C₃ x C₈₉₇
59)	[5689, 3011, 899748]	C₈₉₇		---)	[2777, 3699, 2753476]	C₃ x C₈₉₇
60)	[5801, 2519, 1062800]	C₈₉₇		30)	[2657, 3467, 23204]	C₈₉₇
61)	[5813, 7685, 5230033]	C₈₉₇		---)	[18097, 6975, 4557392]	C₃ x C₈₉₇
62)	[5881, 8547, 18261332]	C₈₉₇		87)	[15797, 7417, 10873969]	C₈₉₇
63)	[5881, 7842, 671741]	C₈₉₇		81)	[13709, 3921, 3675625]	C₈₉₇
64)	[6053, 2413, 1409]	C₈₉₇		---)	[1409, 1943, 605300]	C₂₉₉
65)	[6053, 2417, 357313]	C₈₉₇		---)	[2953, 3807, 1549568]	C₂₉₉
66)	[6301, 2581, 517033]	C₈₉₇		46)	[4273, 5162, 4593429]	C₈₉₇
67)	[8069, 2857, 570037]	C₈₉₇		---)	[3373, 5714, 5882301]	C₂₉₉
68)	[8837, 2218, 346181]	C₈₉₇		---)	[2861, 1109, 220925]	C₂₉₉
69)	[9413, 5314, 2503757]	C₈₉₇		---)	[4733, 2657, 1138973]	C₂₉₉
70)	[9697, 1815, 704768]	C₈₉₇		33)	[2753, 3630, 475153]	C₈₉₇
71)	[10733, 4222, 163121]	C₈₉₇		---)	[3329, 2111, 1073300]	C₂₉₉
72)	[11197, 593, 85113]	C₈₉₇		---)	[193, 1186, 11197]	C₂₉₉
73)	[11681, 5959, 43664]	C₈₉₇		32)	[2729, 3043, 1168100]	C₈₉₇
74)	[12109, 2401, 1195993]	C₈₉₇		39)	[3313, 4802, 980829]	C₈₉₇
75)	[12157, 6190, 7828417]	C₈₉₇		50)	[4657, 3095, 437652]	C₈₉₇
76)	[12821, 3082, 1913125]	C₈₉₇		---)	[3061, 1541, 115389]	C₂₉₉
77)	[13093, 4645, 415393]	C₈₉₇		40)	[3433, 4955, 4242132]	C₈₉₇
78)	[13109, 165, 3529]	C₈₉₇		42)	[3529, 330, 13109]	C₈₉₇
79)	[13457, 514, 12221]	C₈₉₇		---)	[101, 257, 13457]	C₆₉
80)	[13513, 6127, 4760208]	C₈₉₇		43)	[3673, 4931, 54052]	C₈₉₇
81)	[13709, 3921, 3675625]	C₈₉₇		63)	[5881, 7842, 671741]	C₈₉₇
82)	[14557, 7186, 8193181]	C₈₉₇		44)	[3709, 3593, 1179117]	C₈₉₇
83)	[14753, 2270, 344033]	C₈₉₇		20)	[953, 1135, 236048]	C₈₉₇
84)	[14821, 1077, 108425]	C₈₉₇		48)	[4337, 2154, 726229]	C₈₉₇
85)	[15193, 4607, 106308]	C₈₉₇		---)	[2953, 5015, 4922532]	C₂₉₉
86)	[15649, 3427, 2838276]	C₈₉₇		25)	[1609, 4543, 2253456]	C₈₉₇
87)	[15797, 7417, 10873969]	C₈₉₇		62)	[5881, 8547, 18261332]	C₈₉₇
88)	[16141, 5689, 1307925]	C₈₉₇		---)	[5813, 8269, 15511501]	C₂₉₉
89)	[16889, 5546, 7081525]	C₈₉₇		27)	[2341, 2773, 152001]	C₈₉₇
90)	[17021, 1653, 168217]	C₈₉₇		41)	[3433, 3306, 2059541]	C₈₉₇
91)	[17137, 1715, 11268]	C₈₉₇		12)	[313, 1571, 616932]	C₈₉₇
92)	[17401, 4131, 85700]	C₈₉₇		19)	[857, 2279, 278416]	C₈₉₇
93)	[17749, 1809, 68225]	C₈₉₇		31)	[2729, 3618, 2999581]	C₈₉₇
94)	[17977, 6123, 9152564]	C₈₉₇		28)	[2381, 5197, 6489697]	C₈₉₇
95)	[18097, 1750, 476073]	C₈₉₇		---)	[313, 875, 72388]	C₂₉₉
96)	[18301, 1225, 4561]	C₈₉₇		49)	[4561, 2450, 1482381]	C₈₉₇
97)	[19949, 7226, 11058869]	C₈₉₇		---)	[5981, 3613, 498725]	C₂₉₉
98)	[24197, 1246, 977]	C₈₉₇		---)	[977, 623, 96788]	C₂₉₉
99)	[24917, 165, 577]	C₈₉₇		---)	[577, 330, 24917]	C₂₀₉₃
100)	[37561, 227, 3492]	C₈₉₇		5)	[97, 454, 37561]	C₈₉₇
101)	[41017, 1419, 932]	C₈₉₇		8)	[233, 2838, 2009833]	C₈₉₇
102)	[43321, 1194, 183125]	C₈₉₇		---)	[293, 597, 43321]	C₂₉₉
103)	[50273, 463, 41024]	C₈₉₇		16)	[641, 926, 50273]	C₈₉₇
104)	[118033, 535, 42048]	C₈₉₇		---)	[73, 1070, 118033]	C₂₉₉
105)	[121997, 353, 653]	C₈₉₇		---)	[653, 706, 121997]	C₂₉₉
106)	[124513, 1771, 5904]	C₈₉₇		---)	[41, 1527, 498052]	C₆₉
107)	[142193, 455, 16208]	C₈₉₇		21)	[1013, 910, 142193]	C₈₉₇
108)	[183637, 485, 12897]	C₈₉₇		24)	[1433, 970, 183637]	C₈₉₇
109)	[217517, 2098, 230333]	C₈₉₇		---)	[797, 1049, 217517]	C₂₉₉
110)	[226553, 483, 1684]	C₈₉₇		13)	[421, 966, 226553]	C₈₉₇
111)	[240953, 523, 8144]	C₈₉₇		14)	[509, 1046, 240953]	C₈₉₇
112)	[263849, 523, 2420]	C₈₉₇		---)	[5, 1046, 263849]	C₆₉
113)	[291521, 639, 29200]	C₈₉₇		4)	[73, 1278, 291521]	C₈₉₇
114)	[375761, 623, 3092]	C₈₉₇		18)	[773, 1246, 375761]	C₈₉₇
115)	[379997, 2490, 30037]	C₈₉₇		15)	[613, 1245, 379997]	C₈₉₇
116)	[380929, 727, 36900]	C₈₉₇		---)	[41, 1454, 380929]	C₆₉
117)	[596857, 875, 42192]	C₈₉₇		11)	[293, 1750, 596857]	C₈₉₇
118)	[708857, 1067, 107408]	C₈₉₇		---)	[137, 2134, 708857]	C₂₉₉
119)	[760637, 1049, 84941]	C₈₉₇		---)	[101, 2098, 760637]	C₂₉₉
120)	[1014521, 3071, 75088]	C₈₉₇		---)	[13, 2169, 1014521]	C₂₉₉
121)	[1050817, 1375, 209952]	C₈₉₇		---)	[8, 2750, 1050817]	C₂₉₉
122)	[1112513, 1695, 440128]	C₈₉₇		---)	[13, 3390, 1112513]	C₂₉₉
123)	[1393313, 1191, 6292]	C₈₉₇		---)	[13, 2382, 1393313]	C₂₉₉
124)	[1780081, 2759, 1458000]	C₈₉₇		---)	[5, 2877, 1780081]	C₂₉₉
125)	[1840649, 1507, 107600]	C₈₉₇		10)	[269, 3014, 1840649]	C₈₉₇
126)	[2464361, 1579, 7220]	C₈₉₇		---)	[5, 3158, 2464361]	C₂₉₉
127)	[2692121, 2011, 338000]	C₈₉₇		---)	[5, 3433, 2692121]	C₂₉₉
128)	[3251609, 1979, 166208]	C₈₉₇		2)	[53, 3958, 3251609]	C₈₉₇
129)	[5359769, 2387, 84500]	C₈₉₇		---)	[5, 4774, 5359769]	C₂₉₉
130)	[5523809, 2383, 38720]	C₈₉₇		---)	[5, 4766, 5523809]	C₂₉₉
131)	[5878681, 2587, 203472]	C₈₉₇		6)	[157, 5174, 5878681]	C₈₉₇
132)	[8258137, 2875, 1872]	C₈₉₇		---)	[13, 5750, 8258137]	C₂₉₉
133)	[8425433, 2971, 100352]	C₈₉₇		---)	[8, 5942, 8425433]	C₂₉₉
134)	[9131849, 3043, 32000]	C₈₉₇		---)	[5, 6086, 9131849]	C₂₉₉
135)	[9626137, 3163, 94608]	C₈₉₇		---)	[73, 6326, 9626137]	C₂₉₉
136)	[9701177, 3115, 512]	C₈₉₇		---)	[8, 6230, 9701177]	C₂₉₉

Class number: [Non-normal] [Cyclic]

Class group C897 non-normal (D4) quartic CM field invariants: 136 fields

Class group C₈₉₇ non-normal (D₄) quartic CM field invariants: 136 fields