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).
Class number:
[Non-normal]
[Cyclic]
Class number 2 non-normal (D4) quartic CM field invariants: 205 fields
K |
Quartic invariants |
Cl(OK) |
Igusa invariants |
Kr |
Reflex invariants |
Cl(OKr) |
Igusa invariants |
1) |
[5, 29, 209] |
C2 |
■ |
162) |
[209, 23, 80] |
C2 |
■ |
2) |
[5, 61, 869] |
C2 |
■ |
201) |
[869, 37, 125] |
C2 |
■ |
3) |
[5, 69, 1189] |
C2 |
■ |
---) |
[1189, 53, 405] |
C2 x C2 |
■ |
4) |
[5, 9, 19] |
C2 |
■ |
128) |
[76, 18, 5] |
C2 |
■ |
5) |
[5, 25, 145] |
C2 |
■ |
---) |
[145, 15, 20] |
C8 |
■ |
6) |
[5, 45, 445] |
C2 |
■ |
---) |
[445, 25, 45] |
C8 |
■ |
7) |
[5, 66, 909] |
C2 |
■ |
140) |
[101, 33, 45] |
C2 |
■ |
8) |
[5, 16, 59] |
C2 |
■ |
167) |
[236, 32, 20] |
C2 |
■ |
9) |
[5, 14, 44] |
C2 |
■ |
112) |
[44, 8, 5] |
C2 |
■ |
10) |
[5, 49, 589] |
C2 |
■ |
196) |
[589, 33, 125] |
C2 |
■ |
11) |
[5, 37, 341] |
C2 |
■ |
180) |
[341, 29, 125] |
C2 |
■ |
12) |
[5, 11, 29] |
C2 |
■ |
89) |
[29, 7, 5] |
C2 |
■ |
13) |
[5, 33, 261] |
C2 |
■ |
90) |
[29, 21, 45] |
C2 |
■ |
14) |
[5, 74, 1349] |
C2 |
■ |
205) |
[1349, 37, 5] |
C2 |
■ |
15) |
[5, 7, 11] |
C2 |
■ |
113) |
[44, 14, 5] |
C2 |
■ |
16) |
[8, 38, 329] |
C2 |
■ |
176) |
[329, 19, 8] |
C2 |
■ |
17) |
[8, 50, 553] |
C2 |
■ |
195) |
[553, 25, 18] |
C2 |
■ |
18) |
[8, 10, 23] |
C2 |
■ |
135) |
[92, 10, 2] |
C2 |
■ |
19) |
[8, 6, 7] |
C2 |
■ |
79) |
[28, 6, 2] |
C2 |
■ |
20) |
[8, 8, 14] |
C2 |
■ |
116) |
[56, 8, 2] |
C2 |
■ |
21) |
[8, 14, 41] |
C2 |
■ |
109) |
[41, 7, 2] |
C2 |
■ |
22) |
[8, 70, 713] |
C2 |
■ |
199) |
[713, 35, 128] |
C2 |
■ |
23) |
[8, 54, 697] |
C2 |
■ |
---) |
[697, 27, 8] |
C2 x C6 |
■ |
24) |
[8, 34, 217] |
C2 |
■ |
165) |
[217, 17, 18] |
C2 |
■ |
25) |
[8, 86, 1337] |
C2 |
■ |
204) |
[1337, 43, 128] |
C2 |
■ |
26) |
[8, 66, 1017] |
C2 |
■ |
143) |
[113, 33, 18] |
C2 |
■ |
27) |
[8, 50, 425] |
C2 |
■ |
54) |
[17, 25, 50] |
C2 |
■ |
28) |
[8, 26, 137] |
C2 |
■ |
148) |
[137, 13, 8] |
C2 |
■ |
29) |
[12, 30, 177] |
C2 |
■ |
155) |
[177, 15, 12] |
C2 |
■ |
30) |
[12, 10, 13] |
C2 |
■ |
47) |
[13, 5, 3] |
C2 |
■ |
31) |
[12, 98, 673] |
C2 |
■ |
198) |
[673, 49, 432] |
C2 |
■ |
32) |
[12, 26, 61] |
C2 |
■ |
124) |
[61, 13, 27] |
C2 |
■ |
33) |
[12, 14, 22] |
C2 |
■ |
132) |
[88, 10, 3] |
C2 |
■ |
34) |
[12, 62, 913] |
C2 |
■ |
202) |
[913, 31, 12] |
C2 |
■ |
35) |
[12, 14, 37] |
C2 |
■ |
103) |
[37, 7, 3] |
C2 |
■ |
36) |
[12, 8, 13] |
C2 |
■ |
49) |
[13, 10, 12] |
C2 |
■ |
37) |
[12, 26, 157] |
C2 |
■ |
152) |
[157, 13, 3] |
C2 |
■ |
38) |
[12, 66, 321] |
C2 |
■ |
---) |
[321, 33, 192] |
C6 |
■ |
39) |
[12, 6, 6] |
C2 |
■ |
75) |
[24, 6, 3] |
C2 |
■ |
40) |
[12, 18, 33] |
C2 |
■ |
98) |
[33, 9, 12] |
C2 |
■ |
41) |
[12, 42, 393] |
C2 |
■ |
183) |
[393, 21, 12] |
C2 |
■ |
42) |
[12, 74, 937] |
C2 |
■ |
203) |
[937, 37, 108] |
C2 |
■ |
43) |
[12, 54, 537] |
C2 |
■ |
193) |
[537, 27, 48] |
C2 |
■ |
44) |
[12, 34, 97] |
C2 |
■ |
138) |
[97, 17, 48] |
C2 |
■ |
45) |
[12, 50, 433] |
C2 |
■ |
189) |
[433, 25, 48] |
C2 |
■ |
46) |
[13, 74, 901] |
C2 |
■ |
---) |
[901, 37, 117] |
C8 |
■ |
47) |
[13, 5, 3] |
C2 |
■ |
30) |
[12, 10, 13] |
C2 |
■ |
48) |
[13, 17, 43] |
C2 |
■ |
153) |
[172, 34, 117] |
C2 |
■ |
49) |
[13, 10, 12] |
C2 |
■ |
36) |
[12, 8, 13] |
C2 |
■ |
50) |
[13, 61, 381] |
C2 |
■ |
181) |
[381, 41, 325] |
C2 |
■ |
51) |
[13, 49, 597] |
C2 |
■ |
197) |
[597, 89, 637] |
C2 |
■ |
52) |
[13, 34, 237] |
C2 |
■ |
168) |
[237, 17, 13] |
C2 |
■ |
53) |
[13, 17, 69] |
C2 |
■ |
125) |
[69, 33, 117] |
C2 |
■ |
54) |
[17, 25, 50] |
C2 |
■ |
27) |
[8, 50, 425] |
C2 |
■ |
55) |
[17, 31, 236] |
C2 |
■ |
166) |
[236, 62, 17] |
C2 |
■ |
56) |
[17, 62, 689] |
C2 |
■ |
---) |
[689, 31, 68] |
C8 |
■ |
57) |
[17, 37, 134] |
C2 |
■ |
192) |
[536, 74, 833] |
C2 |
■ |
58) |
[17, 17, 34] |
C2 |
■ |
---) |
[136, 34, 153] |
C4 |
■ |
59) |
[17, 20, 83] |
C2 |
■ |
178) |
[332, 40, 68] |
C2 |
■ |
60) |
[17, 28, 43] |
C2 |
■ |
154) |
[172, 56, 612] |
C2 |
■ |
61) |
[17, 13, 38] |
C2 |
■ |
151) |
[152, 26, 17] |
C2 |
■ |
62) |
[21, 65, 421] |
C2 |
■ |
187) |
[421, 85, 1701] |
C2 |
■ |
63) |
[21, 53, 445] |
C2 |
■ |
---) |
[445, 106, 1029] |
C8 |
■ |
64) |
[21, 37, 85] |
C2 |
■ |
---) |
[85, 29, 189] |
C4 |
■ |
65) |
[21, 29, 205] |
C2 |
■ |
---) |
[205, 58, 21] |
C4 |
■ |
66) |
[21, 50, 541] |
C2 |
■ |
194) |
[541, 25, 21] |
C2 |
■ |
67) |
[21, 53, 277] |
C2 |
■ |
173) |
[277, 57, 189] |
C2 |
■ |
68) |
[21, 26, 85] |
C2 |
■ |
---) |
[85, 13, 21] |
C4 |
■ |
69) |
[21, 13, 37] |
C2 |
■ |
101) |
[37, 26, 21] |
C2 |
■ |
70) |
[24, 92, 2020] |
C2 |
■ |
---) |
[505, 46, 24] |
C8 |
■ |
71) |
[24, 26, 145] |
C2 |
■ |
---) |
[145, 13, 6] |
C8 |
■ |
72) |
[24, 38, 265] |
C2 |
■ |
---) |
[265, 19, 24] |
C4 |
■ |
73) |
[24, 8, 10] |
C2 |
■ |
---) |
[40, 16, 24] |
C4 |
■ |
74) |
[24, 74, 769] |
C2 |
■ |
200) |
[769, 37, 150] |
C2 |
■ |
75) |
[24, 6, 3] |
C2 |
■ |
39) |
[12, 6, 6] |
C2 |
■ |
76) |
[24, 20, 76] |
C2 |
■ |
129) |
[76, 10, 6] |
C2 |
■ |
77) |
[24, 68, 772] |
C2 |
■ |
159) |
[193, 34, 96] |
C2 |
■ |
78) |
[24, 86, 313] |
C2 |
■ |
175) |
[313, 43, 384] |
C2 |
■ |
79) |
[28, 6, 2] |
C2 |
■ |
19) |
[8, 6, 7] |
C2 |
■ |
80) |
[28, 34, 177] |
C2 |
■ |
157) |
[177, 17, 28] |
C2 |
■ |
81) |
[28, 128, 1828] |
C2 |
■ |
190) |
[457, 64, 567] |
C2 |
■ |
82) |
[28, 46, 417] |
C2 |
■ |
186) |
[417, 23, 28] |
C2 |
■ |
83) |
[28, 32, 228] |
C2 |
■ |
120) |
[57, 16, 7] |
C2 |
■ |
84) |
[28, 58, 393] |
C2 |
■ |
182) |
[393, 29, 112] |
C2 |
■ |
85) |
[28, 64, 996] |
C2 |
■ |
171) |
[249, 32, 7] |
C2 |
■ |
86) |
[28, 30, 113] |
C2 |
■ |
144) |
[113, 15, 28] |
C2 |
■ |
87) |
[28, 80, 1348] |
C2 |
■ |
179) |
[337, 40, 63] |
C2 |
■ |
88) |
[29, 17, 65] |
C2 |
■ |
---) |
[65, 34, 29] |
C2 x C2 |
■ |
89) |
[29, 7, 5] |
C2 |
■ |
12) |
[5, 11, 29] |
C2 |
■ |
90) |
[29, 21, 45] |
C2 |
■ |
13) |
[5, 33, 261] |
C2 |
■ |
91) |
[33, 35, 232] |
C2 |
■ |
---) |
[232, 70, 297] |
C4 |
■ |
92) |
[33, 50, 328] |
C2 |
■ |
---) |
[328, 100, 1188] |
C8 |
■ |
93) |
[33, 23, 124] |
C2 |
■ |
146) |
[124, 46, 33] |
C2 |
■ |
94) |
[33, 62, 433] |
C2 |
■ |
188) |
[433, 31, 132] |
C2 |
■ |
95) |
[33, 26, 37] |
C2 |
■ |
100) |
[37, 13, 33] |
C2 |
■ |
96) |
[33, 41, 412] |
C2 |
■ |
185) |
[412, 82, 33] |
C2 |
■ |
97) |
[33, 71, 1252] |
C2 |
■ |
174) |
[313, 87, 1188] |
C2 |
■ |
98) |
[33, 9, 12] |
C2 |
■ |
40) |
[12, 18, 33] |
C2 |
■ |
99) |
[33, 20, 67] |
C2 |
■ |
172) |
[268, 40, 132] |
C2 |
■ |
100) |
[37, 13, 33] |
C2 |
■ |
95) |
[33, 26, 37] |
C2 |
■ |
101) |
[37, 26, 21] |
C2 |
■ |
69) |
[21, 13, 37] |
C2 |
■ |
102) |
[37, 34, 141] |
C2 |
■ |
150) |
[141, 17, 37] |
C2 |
■ |
103) |
[37, 7, 3] |
C2 |
■ |
35) |
[12, 14, 37] |
C2 |
■ |
104) |
[37, 73, 213] |
C2 |
■ |
163) |
[213, 57, 333] |
C2 |
■ |
105) |
[37, 53, 693] |
C2 |
■ |
131) |
[77, 29, 37] |
C2 |
■ |
106) |
[41, 35, 296] |
C2 |
■ |
---) |
[296, 70, 41] |
C2 x C2 |
■ |
107) |
[41, 16, 23] |
C2 |
■ |
136) |
[92, 32, 164] |
C2 |
■ |
108) |
[41, 9, 10] |
C2 |
■ |
---) |
[40, 18, 41] |
C2 x C2 |
■ |
109) |
[41, 7, 2] |
C2 |
■ |
21) |
[8, 14, 41] |
C2 |
■ |
110) |
[41, 62, 305] |
C2 |
■ |
---) |
[305, 31, 164] |
C4 |
■ |
111) |
[41, 39, 124] |
C2 |
■ |
145) |
[124, 78, 1025] |
C2 |
■ |
112) |
[44, 8, 5] |
C2 |
■ |
9) |
[5, 14, 44] |
C2 |
■ |
113) |
[44, 14, 5] |
C2 |
■ |
15) |
[5, 7, 11] |
C2 |
■ |
114) |
[44, 104, 1604] |
C2 |
■ |
---) |
[401, 52, 275] |
C10 |
■ |
115) |
[53, 34, 77] |
C2 |
■ |
130) |
[77, 17, 53] |
C2 |
■ |
116) |
[56, 8, 2] |
C2 |
■ |
20) |
[8, 8, 14] |
C2 |
■ |
117) |
[56, 44, 260] |
C2 |
■ |
---) |
[65, 22, 56] |
C4 |
■ |
118) |
[56, 26, 113] |
C2 |
■ |
142) |
[113, 13, 14] |
C2 |
■ |
119) |
[57, 17, 58] |
C2 |
■ |
---) |
[232, 34, 57] |
C4 |
■ |
120) |
[57, 16, 7] |
C2 |
■ |
83) |
[28, 32, 228] |
C2 |
■ |
121) |
[57, 167, 1828] |
C2 |
■ |
191) |
[457, 111, 2052] |
C2 |
■ |
122) |
[61, 98, 205] |
C2 |
■ |
---) |
[205, 49, 549] |
C4 |
■ |
123) |
[61, 25, 141] |
C2 |
■ |
149) |
[141, 50, 61] |
C2 |
■ |
124) |
[61, 13, 27] |
C2 |
■ |
32) |
[12, 26, 61] |
C2 |
■ |
125) |
[69, 33, 117] |
C2 |
■ |
53) |
[13, 17, 69] |
C2 |
■ |
126) |
[69, 77, 85] |
C2 |
■ |
---) |
[85, 49, 69] |
C4 |
■ |
127) |
[73, 29, 46] |
C2 |
■ |
158) |
[184, 58, 657] |
C2 |
■ |
128) |
[76, 18, 5] |
C2 |
■ |
4) |
[5, 9, 19] |
C2 |
■ |
129) |
[76, 10, 6] |
C2 |
■ |
76) |
[24, 20, 76] |
C2 |
■ |
130) |
[77, 17, 53] |
C2 |
■ |
115) |
[53, 34, 77] |
C2 |
■ |
131) |
[77, 29, 37] |
C2 |
■ |
105) |
[37, 53, 693] |
C2 |
■ |
132) |
[88, 10, 3] |
C2 |
■ |
33) |
[12, 14, 22] |
C2 |
■ |
133) |
[88, 70, 873] |
C2 |
■ |
139) |
[97, 35, 88] |
C2 |
■ |
134) |
[89, 27, 160] |
C2 |
■ |
---) |
[40, 54, 89] |
C2 x C2 |
■ |
135) |
[92, 10, 2] |
C2 |
■ |
18) |
[8, 10, 23] |
C2 |
■ |
136) |
[92, 32, 164] |
C2 |
■ |
107) |
[41, 16, 23] |
C2 |
■ |
137) |
[93, 69, 981] |
C2 |
■ |
141) |
[109, 97, 2325] |
C2 |
■ |
138) |
[97, 17, 48] |
C2 |
■ |
44) |
[12, 34, 97] |
C2 |
■ |
139) |
[97, 35, 88] |
C2 |
■ |
133) |
[88, 70, 873] |
C2 |
■ |
140) |
[101, 33, 45] |
C2 |
■ |
7) |
[5, 66, 909] |
C2 |
■ |
141) |
[109, 97, 2325] |
C2 |
■ |
137) |
[93, 69, 981] |
C2 |
■ |
142) |
[113, 13, 14] |
C2 |
■ |
118) |
[56, 26, 113] |
C2 |
■ |
143) |
[113, 33, 18] |
C2 |
■ |
26) |
[8, 66, 1017] |
C2 |
■ |
144) |
[113, 15, 28] |
C2 |
■ |
86) |
[28, 30, 113] |
C2 |
■ |
145) |
[124, 78, 1025] |
C2 |
■ |
111) |
[41, 39, 124] |
C2 |
■ |
146) |
[124, 46, 33] |
C2 |
■ |
93) |
[33, 23, 124] |
C2 |
■ |
147) |
[129, 26, 40] |
C2 |
■ |
---) |
[40, 52, 516] |
C4 |
■ |
148) |
[137, 13, 8] |
C2 |
■ |
28) |
[8, 26, 137] |
C2 |
■ |
149) |
[141, 50, 61] |
C2 |
■ |
123) |
[61, 25, 141] |
C2 |
■ |
150) |
[141, 17, 37] |
C2 |
■ |
102) |
[37, 34, 141] |
C2 |
■ |
151) |
[152, 26, 17] |
C2 |
■ |
61) |
[17, 13, 38] |
C2 |
■ |
152) |
[157, 13, 3] |
C2 |
■ |
37) |
[12, 26, 157] |
C2 |
■ |
153) |
[172, 34, 117] |
C2 |
■ |
48) |
[13, 17, 43] |
C2 |
■ |
154) |
[172, 56, 612] |
C2 |
■ |
60) |
[17, 28, 43] |
C2 |
■ |
155) |
[177, 15, 12] |
C2 |
■ |
29) |
[12, 30, 177] |
C2 |
■ |
156) |
[177, 110, 193] |
C2 |
■ |
160) |
[193, 55, 708] |
C2 |
■ |
157) |
[177, 17, 28] |
C2 |
■ |
80) |
[28, 34, 177] |
C2 |
■ |
158) |
[184, 58, 657] |
C2 |
■ |
127) |
[73, 29, 46] |
C2 |
■ |
159) |
[193, 34, 96] |
C2 |
■ |
77) |
[24, 68, 772] |
C2 |
■ |
160) |
[193, 55, 708] |
C2 |
■ |
156) |
[177, 110, 193] |
C2 |
■ |
161) |
[193, 142, 1953] |
C2 |
■ |
164) |
[217, 71, 772] |
C2 |
■ |
162) |
[209, 23, 80] |
C2 |
■ |
1) |
[5, 29, 209] |
C2 |
■ |
163) |
[213, 57, 333] |
C2 |
■ |
104) |
[37, 73, 213] |
C2 |
■ |
164) |
[217, 71, 772] |
C2 |
■ |
161) |
[193, 142, 1953] |
C2 |
■ |
165) |
[217, 17, 18] |
C2 |
■ |
24) |
[8, 34, 217] |
C2 |
■ |
166) |
[236, 62, 17] |
C2 |
■ |
55) |
[17, 31, 236] |
C2 |
■ |
167) |
[236, 32, 20] |
C2 |
■ |
8) |
[5, 16, 59] |
C2 |
■ |
168) |
[237, 17, 13] |
C2 |
■ |
52) |
[13, 34, 237] |
C2 |
■ |
169) |
[241, 107, 2320] |
C2 |
■ |
---) |
[145, 191, 964] |
C8 |
■ |
170) |
[249, 17, 10] |
C2 |
■ |
---) |
[40, 34, 249] |
C4 |
■ |
171) |
[249, 32, 7] |
C2 |
■ |
85) |
[28, 64, 996] |
C2 |
■ |
172) |
[268, 40, 132] |
C2 |
■ |
99) |
[33, 20, 67] |
C2 |
■ |
173) |
[277, 57, 189] |
C2 |
■ |
67) |
[21, 53, 277] |
C2 |
■ |
174) |
[313, 87, 1188] |
C2 |
■ |
97) |
[33, 71, 1252] |
C2 |
■ |
175) |
[313, 43, 384] |
C2 |
■ |
78) |
[24, 86, 313] |
C2 |
■ |
176) |
[329, 19, 8] |
C2 |
■ |
16) |
[8, 38, 329] |
C2 |
■ |
177) |
[329, 67, 1040] |
C2 |
■ |
---) |
[65, 134, 329] |
C4 |
■ |
178) |
[332, 40, 68] |
C2 |
■ |
59) |
[17, 20, 83] |
C2 |
■ |
179) |
[337, 40, 63] |
C2 |
■ |
87) |
[28, 80, 1348] |
C2 |
■ |
180) |
[341, 29, 125] |
C2 |
■ |
11) |
[5, 37, 341] |
C2 |
■ |
181) |
[381, 41, 325] |
C2 |
■ |
50) |
[13, 61, 381] |
C2 |
■ |
182) |
[393, 29, 112] |
C2 |
■ |
84) |
[28, 58, 393] |
C2 |
■ |
183) |
[393, 21, 12] |
C2 |
■ |
41) |
[12, 42, 393] |
C2 |
■ |
184) |
[409, 43, 360] |
C2 |
■ |
---) |
[40, 86, 409] |
C2 x C2 |
■ |
185) |
[412, 82, 33] |
C2 |
■ |
96) |
[33, 41, 412] |
C2 |
■ |
186) |
[417, 23, 28] |
C2 |
■ |
82) |
[28, 46, 417] |
C2 |
■ |
187) |
[421, 85, 1701] |
C2 |
■ |
62) |
[21, 65, 421] |
C2 |
■ |
188) |
[433, 31, 132] |
C2 |
■ |
94) |
[33, 62, 433] |
C2 |
■ |
189) |
[433, 25, 48] |
C2 |
■ |
45) |
[12, 50, 433] |
C2 |
■ |
190) |
[457, 64, 567] |
C2 |
■ |
81) |
[28, 128, 1828] |
C2 |
■ |
191) |
[457, 111, 2052] |
C2 |
■ |
121) |
[57, 167, 1828] |
C2 |
■ |
192) |
[536, 74, 833] |
C2 |
■ |
57) |
[17, 37, 134] |
C2 |
■ |
193) |
[537, 27, 48] |
C2 |
■ |
43) |
[12, 54, 537] |
C2 |
■ |
194) |
[541, 25, 21] |
C2 |
■ |
66) |
[21, 50, 541] |
C2 |
■ |
195) |
[553, 25, 18] |
C2 |
■ |
17) |
[8, 50, 553] |
C2 |
■ |
196) |
[589, 33, 125] |
C2 |
■ |
10) |
[5, 49, 589] |
C2 |
■ |
197) |
[597, 89, 637] |
C2 |
■ |
51) |
[13, 49, 597] |
C2 |
■ |
198) |
[673, 49, 432] |
C2 |
■ |
31) |
[12, 98, 673] |
C2 |
■ |
199) |
[713, 35, 128] |
C2 |
■ |
22) |
[8, 70, 713] |
C2 |
■ |
200) |
[769, 37, 150] |
C2 |
■ |
74) |
[24, 74, 769] |
C2 |
■ |
201) |
[869, 37, 125] |
C2 |
■ |
2) |
[5, 61, 869] |
C2 |
■ |
202) |
[913, 31, 12] |
C2 |
■ |
34) |
[12, 62, 913] |
C2 |
■ |
203) |
[937, 37, 108] |
C2 |
■ |
42) |
[12, 74, 937] |
C2 |
■ |
204) |
[1337, 43, 128] |
C2 |
■ |
25) |
[8, 86, 1337] |
C2 |
■ |
205) |
[1349, 37, 5] |
C2 |
■ |
14) |
[5, 74, 1349] |
C2 |
■ |