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)	[229, 1274, 199669]	C₃ x C₃ x C₃₉		---)	[199669, 637, 51525]	C₃ x C₃₉
2)	[2213, 461, 8317]	C₃ x C₃ x C₃₉		---)	[8317, 922, 179253]	C₃ x C₃₉
3)	[3229, 293, 14197]	C₃ x C₃ x C₃₉		7)	[14197, 586, 29061]	C₃ x C₃ x C₃₉
4)	[5081, 5803, 491072]	C₃ x C₃ x C₃₉		5)	[7673, 6199, 995876]	C₃ x C₃ x C₃₉
5)	[7673, 6199, 995876]	C₃ x C₃ x C₃₉		4)	[5081, 5803, 491072]	C₃ x C₃ x C₃₉
6)	[9293, 394, 1637]	C₃ x C₃ x C₃₉		---)	[1637, 197, 9293]	C₃ x C₃₉
7)	[14197, 586, 29061]	C₃ x C₃ x C₃₉		3)	[3229, 293, 14197]	C₃ x C₃ x C₃₉
8)	[28349, 1398, 35017]	C₃ x C₃ x C₃₉		---)	[97, 699, 113396]	C₃ x C₃₉
9)	[88169, 363, 10900]	C₃ x C₃ x C₃₉		---)	[109, 726, 88169]	C₃ x C₃₉
10)	[859297, 943, 7488]	C₃ x C₃ x C₃₉		---)	[13, 1886, 859297]	C₃ x C₃₉

Class number: [Non-normal] [Cyclic]

Class group C3 x C3 x C39 non-normal (D4) quartic CM field invariants: 10 fields

Class group C₃ x C₃ x C₃₉ non-normal (D₄) quartic CM field invariants: 10 fields