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, 853, 153401]	C₅₆		19618)	[153401, 451, 12500]	C₅₆
2)	[5, 1889, 812069]	C₅₆		---)	[812069, 1733, 547805]	C₇ x C₅₆
3)	[5, 1385, 469205]	C₂ x C₂ x C₁₄		---)	[469205, 925, 96605]	C₂ x C₄ x C₁₁₂
4)	[5, 1098, 270981]	C₅₆		18473)	[30109, 549, 7605]	C₂ x C₂₈
5)	[5, 861, 184129]	C₂ x C₂₈		---)	[184129, 607, 46080]	C₄ x C₅₆
6)	[5, 1309, 361669]	C₂ x C₂ x C₁₄		6263)	[61, 693, 29645]	C₂ x C₂₈
7)	[5, 1021, 260509]	C₅₆		---)	[260509, 777, 85805]	C₂₈₀
8)	[5, 279, 18409]	C₂ x C₂₈		---)

Class number: [Non-normal] [Cyclic]

Class number 56 non-normal (D4) quartic CM field invariants: 19971 fields

Class number 56 non-normal (D₄) quartic CM field invariants: 19971 fields