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, 886, 190469]	C₂ x C₁₀₄		27007)	[190469, 443, 1445]	C₂ x C₁₀₄
2)	[5, 1104, 294124]	C₂ x C₁₀₄		13829)	[556, 552, 2645]	C₂ x C₂ x C₅₂
3)	[5, 1314, 386524]	C₂ x C₁₀₄		---)	[386524, 748, 43245]	C₈ x C₁₀₄
4)	[5, 608, 90611]	C₂ x C₂ x C₅₂		15771)	[1004, 1216, 7220]	C₂ x C₂ x C₅₂
5)	[5, 3174, 2414889]	C₂ x C₁₀₄		27383)	[268321, 1587, 25920]	C₂ x C₁₀₄
6)	[5, 994, 247004]	C₂₀₈		---)	[247004, 748, 78125]	C₁₀₄₀
7)	[5, 763, 145481]	C₄ x C₅₂		19467)	[2969, 581, 48020]	C₂ x C₂ x C₂ x C₂₆
8)	[5, 3806, 3001889]	C₂ x C₁₀₄		23718)	[24809, 1903, 154880]	C₄ x C₅₂
9)	[5, 3597, 3211821]	C₂₀₈		27620)	[356869, 2529, 796005]	C₂ x C₁₀₄
10)	[5, 7381, 13503509]	C₂ x C₂ x C₅₂		19883)	[3629, 5917, 5376845]	C₄ x C₅₂
11)	[5, 695, 119845]	C₂ x C₂ x C₅₂		---)	[119845, 555, 47045]	C₂ x C₄ x C₁₀₄
12)	[5, 2198, 1066681]	C₂ x C₁₀₄		23459)	[21769, 1099, 35280]	C₂ x C₁₀₄
13)	[5, 2854, 2035609]	C₂ x C₁₀₄		---)	[2035609, 1427, 180]	C₈ x C₁₀₄
14)	[5, 2470, 1513705]	C₂ x C₁₀₄		---)	[1513705, 1235, 2880]	C₂ x C₂ x C₂₀₈
15)	[5, 1684, 632084]	C₂ x C₁₀₄		---)	[158021, 842, 19220]	C₂ x C₂₀₈
16)	[5, 2686, 1570369]	C₂₀₈		28400)	[1570369, 1343, 58320]	C₂₀₈
17)	[5, 2901, 1845169]	C₂₀₈		---)	[1845169, 1607, 184320]	C₄₁₆
18)	[5, 2950, 2088505]	C₂ x C₁₀₄		---)	[2088505, 1475, 21780]	C₈ x C₇₂₈
19)	[5, 553, 74551]	C₂₀₈		27465)	[298204, 1106, 7605]	C₂₀₈
20)	[5, 1646, 673949]	C₂ x C₂ x C₅₂		---)	[673949, 823, 845]	C₂ x C₂ x C₁₀₄
21)	[5, 778, 151196]	C₂₀₈		26730)	[151196, 596, 51005]	C₂₀₈
22)	[5, 3645, 3289905]	C₂ x C₂ x C₅₂		---)	[365545, 2535, 784080]	C₂ x C₄ x C₉₃₆
23)	[5, 2589, 1548529]	C₂ x C₁₀₄		---)	[1548529, 1543, 208080]	C₂ x C₂ x C₁₀₄
24)	[5, 3694, 3283409]	C₂ x C₂ x C₅₂		---)	[3283409, 1847, 32000]	C₂ x C₄ x C₁₀₄
25)	[5, 1582, 567361]	C₂ x C₁₀₄		---)	[567361, 791, 14580]	C₂ x C₂₀₈
26)	[5, 750, 139645]	C₂ x C₂ x C₅₂		---)	[139645, 375, 245]	C₂ x C₄ x C₁₀₄
27)	[5, 1175, 317405]	C₂ x C₂ x C₂ x C₂₆		---)	[317405, 695, 41405]	C₂ x C₂ x C₄ x C₁₀₄
28)	[5, 2837, 2007181]	C₂₀₈		28464)	[2007181, 2049, 547805]	C₂₀₈
29)	[5, 3486, 2473569]	C₂ x C₂ x C₅₂		20717)	[5609, 1743, 141120]	C₂ x C₂ x C₂ x C₂₆
30)	[5, 795, 151345]	C₂ x C₁₀₄		---)

Class number: [Non-normal] [Cyclic]

Class number 208 non-normal (D4) quartic CM field invariants: 28630 fields

Class number 208 non-normal (D₄) quartic CM field invariants: 28630 fields