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, 6589, 10808129]	C₁₁ x C₃₃		12)	[10808129, 4703, 2827520]	C₁₁ x C₃₃
2)	[5, 6094, 8772209]	C₁₁ x C₃₃		11)	[8772209, 3047, 128000]	C₁₁ x C₃₃
3)	[1297, 1363, 456336]	C₁₁ x C₃₃		---)	[3169, 1547, 20752]	C₃₃
4)	[3373, 2113, 670113]	C₁₁ x C₃₃		6)	[8273, 4226, 1784317]	C₁₁ x C₃₃
5)	[3581, 1509, 546889]	C₁₁ x C₃₃		7)	[11161, 3018, 89525]	C₁₁ x C₃₃
6)	[8273, 4226, 1784317]	C₁₁ x C₃₃		4)	[3373, 2113, 670113]	C₁₁ x C₃₃
7)	[11161, 3018, 89525]	C₁₁ x C₃₃		5)	[3581, 1509, 546889]	C₁₁ x C₃₃
8)	[41389, 3165, 755621]	C₁₁ x C₃₃		---)	[269, 2097, 1034725]	C₁₁ x C₁₁
9)	[109169, 487, 32000]	C₁₁ x C₃₃		---)	[5, 661, 109169]	C₃₃	■
10)	[309989, 1237, 305045]	C₁₁ x C₃₃		---)	[5, 1241, 309989]	C₃₃
11)	[8772209, 3047, 128000]	C₁₁ x C₃₃		2)	[5, 6094, 8772209]	C₁₁ x C₃₃
12)	[10808129, 4703, 2827520]	C₁₁ x C₃₃		1)	[5, 6589, 10808129]	C₁₁ x C₃₃

Class number: [Non-normal] [Cyclic]

Class group C11 x C33 non-normal (D4) quartic CM field invariants: 12 fields

Class group C₁₁ x C₃₃ non-normal (D₄) quartic CM field invariants: 12 fields