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 group C775 non-normal (D4) quartic CM field invariants: 120 fields
K |
Quartic invariants |
Cl(OK) |
Igusa invariants |
Kr |
Reflex invariants |
Cl(OKr) |
Igusa invariants |
1) |
[8, 5246, 6855041] |
C775 |
|
118) |
[6855041, 2623, 6272] |
C775 |
2) |
[8, 4798, 5754689] |
C775 |
|
117) |
[5754689, 2399, 128] |
C775 |
3) |
[13, 5406, 7143137] |
C775 |
|
120) |
[7143137, 2703, 40768] |
C775 |
4) |
[13, 5310, 6995777] |
C775 |
|
119) |
[6995777, 2655, 13312] |
C775 |
5) |
[17, 2398, 1044833] |
C775 |
|
112) |
[1044833, 1199, 98192] |
C775 |
6) |
[17, 1822, 477409] |
C775 |
|
106) |
[477409, 911, 88128] |
C775 |
7) |
[17, 1966, 939089] |
C775 |
|
111) |
[939089, 983, 6800] |
C775 |
8) |
[17, 2558, 1422593] |
C775 |
|
115) |
[1422593, 1279, 53312] |
C775 |
9) |
[37, 3678, 2775713] |
C775 |
|
---) |
[2775713, 1839, 151552] |
C5 x C775 |
10) |
[41, 1366, 465833] |
C775 |
|
105) |
[465833, 683, 164] |
C775 |
11) |
[53, 4478, 3371393] |
C775 |
|
116) |
[3371393, 2239, 410432] |
C775 |
12) |
[53, 5102, 6168401] |
C775 |
|
---) |
[6168401, 2551, 84800] |
C2325 |
13) |
[53, 2486, 1422937] |
C775 |
|
---) |
[1422937, 1243, 30528] |
C2325 |
14) |
[73, 6198, 9487001] |
C775 |
|
---) |
[9487001, 3099, 29200] |
C2325 |
15) |
[109, 2166, 1061273] |
C775 |
|
113) |
[1061273, 1083, 27904] |
C775 |
16) |
[113, 1342, 95873] |
C775 |
|
98) |
[95873, 671, 88592] |
C775 |
17) |
[113, 5510, 7127177] |
C775 |
|
---) |
[7127177, 2755, 115712] |
C5425 |
18) |
[157, 3390, 1174913] |
C775 |
|
114) |
[1174913, 1695, 424528] |
C775 |
19) |
[157, 1686, 670457] |
C775 |
|
108) |
[670457, 843, 10048] |
C775 |
20) |
[269, 1294, 401393] |
C775 |
|
103) |
[401393, 647, 4304] |
C775 |
21) |
[277, 697, 120829] |
C775 |
|
---) |
[120829, 1394, 2493] |
C5 x C775 |
22) |
[277, 1593, 622709] |
C775 |
|
107) |
[622709, 3186, 46813] |
C775 |
23) |
[293, 1846, 776921] |
C775 |
|
110) |
[776921, 923, 18752] |
C775 |
24) |
[317, 1294, 413537] |
C775 |
|
104) |
[413537, 647, 1268] |
C775 |
25) |
[317, 1562, 608693] |
C775 |
|
---) |
[608693, 781, 317] |
C8525 |
26) |
[457, 2295, 1220672] |
C775 |
|
94) |
[19073, 2683, 1756708] |
C775 |
27) |
[461, 1713, 733477] |
C775 |
|
109) |
[733477, 3426, 461] |
C775 |
28) |
[569, 1462, 452425] |
C775 |
|
---) |
[18097, 731, 20484] |
C2325 |
29) |
[593, 1042, 269069] |
C775 |
|
100) |
[269069, 521, 593] |
C775 |
30) |
[677, 1190, 310697] |
C775 |
|
101) |
[310697, 595, 10832] |
C775 |
31) |
[937, 1226, 342037] |
C775 |
|
102) |
[342037, 613, 8433] |
C775 |
32) |
[1153, 4415, 652788] |
C775 |
|
91) |
[18133, 2545, 1578457] |
C775 |
33) |
[1201, 1526, 409225] |
C775 |
|
---) |
[16369, 763, 43236] |
C2325 |
34) |
[1549, 633, 81197] |
C775 |
|
97) |
[81197, 1266, 75901] |
C775 |
35) |
[2017, 783, 128564] |
C775 |
|
96) |
[32141, 1566, 98833] |
C775 |
36) |
[2053, 2614, 525721] |
C775 |
|
76) |
[10729, 1307, 295632] |
C775 |
37) |
[2389, 3489, 362225] |
C775 |
|
81) |
[14489, 6335, 611584] |
C775 |
38) |
[2437, 2341, 443401] |
C775 |
|
---) |
[9049, 4682, 3706677] |
C5425 |
39) |
[2441, 6994, 11438125] |
C775 |
|
92) |
[18301, 3497, 197721] |
C775 |
40) |
[3109, 2989, 1486593] |
C775 |
|
---) |
[18353, 5978, 2987749] |
C5 x C775 |
41) |
[3209, 2050, 10909] |
C775 |
|
---) |
[10909, 1025, 259929] |
C5 x C775 |
42) |
[3257, 635, 34852] |
C775 |
|
---) |
[8713, 1270, 263817] |
C2325 |
43) |
[3301, 3753, 3223337] |
C775 |
|
93) |
[19073, 7506, 1191661] |
C775 |
44) |
[3313, 2399, 1000656] |
C775 |
|
---) |
[6949, 4798, 1752577] |
C5 x C775 |
45) |
[3413, 5013, 4397713] |
C775 |
|
83) |
[15217, 6327, 873728] |
C775 |
46) |
[3581, 5093, 16481] |
C775 |
|
---) |
[16481, 6167, 6932816] |
C2325 |
47) |
[3593, 3751, 3193232] |
C775 |
|
52) |
[4073, 2675, 1739012] |
C775 |
48) |
[3613, 6229, 847357] |
C775 |
|
90) |
[17293, 7145, 5495373] |
C775 |
49) |
[3709, 4273, 884377] |
C775 |
|
65) |
[5233, 2863, 59344] |
C775 |
50) |
[3733, 3918, 911009] |
C775 |
|
72) |
[7529, 1959, 731668] |
C775 |
51) |
[4021, 6894, 4097153] |
C775 |
|
80) |
[14177, 3447, 1946164] |
C775 |
52) |
[4073, 2675, 1739012] |
C775 |
|
47) |
[3593, 3751, 3193232] |
C775 |
53) |
[4129, 354, 14813] |
C775 |
|
82) |
[14813, 177, 4129] |
C775 |
54) |
[4513, 1879, 556596] |
C775 |
|
84) |
[15461, 3758, 1304257] |
C775 |
55) |
[4621, 6210, 4299149] |
C775 |
|
78) |
[11909, 3105, 1335469] |
C775 |
56) |
[4721, 867, 158416] |
C775 |
|
74) |
[9901, 1734, 118025] |
C775 |
57) |
[4789, 4213, 547477] |
C775 |
|
77) |
[11173, 7381, 2533381] |
C775 |
58) |
[4789, 1518, 499457] |
C775 |
|
75) |
[10193, 759, 19156] |
C775 |
59) |
[4813, 833, 172269] |
C775 |
|
95) |
[19141, 1666, 4813] |
C775 |
60) |
[4957, 1214, 51201] |
C775 |
|
70) |
[5689, 607, 79312] |
C775 |
61) |
[4973, 4317, 4508689] |
C775 |
|
85) |
[15601, 8634, 601733] |
C775 |
62) |
[4993, 3331, 465876] |
C775 |
|
79) |
[12941, 6662, 9232057] |
C775 |
63) |
[5009, 4759, 371264] |
C775 |
|
71) |
[5801, 3115, 2424356] |
C775 |
64) |
[5189, 2109, 425725] |
C775 |
|
89) |
[17029, 4218, 2744981] |
C775 |
65) |
[5233, 2863, 59344] |
C775 |
|
49) |
[3709, 4273, 884377] |
C775 |
66) |
[5393, 2479, 68116] |
C775 |
|
88) |
[17029, 4958, 5872977] |
C775 |
67) |
[5441, 1351, 63188] |
C775 |
|
86) |
[15797, 2702, 1572449] |
C775 |
68) |
[5573, 4233, 2772841] |
C775 |
|
73) |
[7681, 5307, 356672] |
C775 |
69) |
[5669, 9137, 4645097] |
C775 |
|
87) |
[16073, 5159, 6553364] |
C775 |
70) |
[5689, 607, 79312] |
C775 |
|
60) |
[4957, 1214, 51201] |
C775 |
71) |
[5801, 3115, 2424356] |
C775 |
|
63) |
[5009, 4759, 371264] |
C775 |
72) |
[7529, 1959, 731668] |
C775 |
|
50) |
[3733, 3918, 911009] |
C775 |
73) |
[7681, 5307, 356672] |
C775 |
|
68) |
[5573, 4233, 2772841] |
C775 |
74) |
[9901, 1734, 118025] |
C775 |
|
56) |
[4721, 867, 158416] |
C775 |
75) |
[10193, 759, 19156] |
C775 |
|
58) |
[4789, 1518, 499457] |
C775 |
76) |
[10729, 1307, 295632] |
C775 |
|
36) |
[2053, 2614, 525721] |
C775 |
77) |
[11173, 7381, 2533381] |
C775 |
|
57) |
[4789, 4213, 547477] |
C775 |
78) |
[11909, 3105, 1335469] |
C775 |
|
55) |
[4621, 6210, 4299149] |
C775 |
79) |
[12941, 6662, 9232057] |
C775 |
|
62) |
[4993, 3331, 465876] |
C775 |
80) |
[14177, 3447, 1946164] |
C775 |
|
51) |
[4021, 6894, 4097153] |
C775 |
81) |
[14489, 6335, 611584] |
C775 |
|
37) |
[2389, 3489, 362225] |
C775 |
82) |
[14813, 177, 4129] |
C775 |
|
53) |
[4129, 354, 14813] |
C775 |
83) |
[15217, 6327, 873728] |
C775 |
|
45) |
[3413, 5013, 4397713] |
C775 |
84) |
[15461, 3758, 1304257] |
C775 |
|
54) |
[4513, 1879, 556596] |
C775 |
85) |
[15601, 8634, 601733] |
C775 |
|
61) |
[4973, 4317, 4508689] |
C775 |
86) |
[15797, 2702, 1572449] |
C775 |
|
67) |
[5441, 1351, 63188] |
C775 |
87) |
[16073, 5159, 6553364] |
C775 |
|
69) |
[5669, 9137, 4645097] |
C775 |
88) |
[17029, 4958, 5872977] |
C775 |
|
66) |
[5393, 2479, 68116] |
C775 |
89) |
[17029, 4218, 2744981] |
C775 |
|
64) |
[5189, 2109, 425725] |
C775 |
90) |
[17293, 7145, 5495373] |
C775 |
|
48) |
[3613, 6229, 847357] |
C775 |
91) |
[18133, 2545, 1578457] |
C775 |
|
32) |
[1153, 4415, 652788] |
C775 |
92) |
[18301, 3497, 197721] |
C775 |
|
39) |
[2441, 6994, 11438125] |
C775 |
93) |
[19073, 7506, 1191661] |
C775 |
|
43) |
[3301, 3753, 3223337] |
C775 |
94) |
[19073, 2683, 1756708] |
C775 |
|
26) |
[457, 2295, 1220672] |
C775 |
95) |
[19141, 1666, 4813] |
C775 |
|
59) |
[4813, 833, 172269] |
C775 |
96) |
[32141, 1566, 98833] |
C775 |
|
35) |
[2017, 783, 128564] |
C775 |
97) |
[81197, 1266, 75901] |
C775 |
|
34) |
[1549, 633, 81197] |
C775 |
98) |
[95873, 671, 88592] |
C775 |
|
16) |
[113, 1342, 95873] |
C775 |
99) |
[133417, 377, 2178] |
C775 |
■ |
---) |
[8, 754, 133417] |
C31 |
■ |
100) |
[269069, 521, 593] |
C775 |
|
29) |
[593, 1042, 269069] |
C775 |
101) |
[310697, 595, 10832] |
C775 |
|
30) |
[677, 1190, 310697] |
C775 |
102) |
[342037, 613, 8433] |
C775 |
|
31) |
[937, 1226, 342037] |
C775 |
103) |
[401393, 647, 4304] |
C775 |
|
20) |
[269, 1294, 401393] |
C775 |
104) |
[413537, 647, 1268] |
C775 |
|
24) |
[317, 1294, 413537] |
C775 |
105) |
[465833, 683, 164] |
C775 |
|
10) |
[41, 1366, 465833] |
C775 |
106) |
[477409, 911, 88128] |
C775 |
|
6) |
[17, 1822, 477409] |
C775 |
107) |
[622709, 3186, 46813] |
C775 |
|
22) |
[277, 1593, 622709] |
C775 |
108) |
[670457, 843, 10048] |
C775 |
|
19) |
[157, 1686, 670457] |
C775 |
109) |
[733477, 3426, 461] |
C775 |
|
27) |
[461, 1713, 733477] |
C775 |
110) |
[776921, 923, 18752] |
C775 |
|
23) |
[293, 1846, 776921] |
C775 |
111) |
[939089, 983, 6800] |
C775 |
|
7) |
[17, 1966, 939089] |
C775 |
112) |
[1044833, 1199, 98192] |
C775 |
|
5) |
[17, 2398, 1044833] |
C775 |
113) |
[1061273, 1083, 27904] |
C775 |
|
15) |
[109, 2166, 1061273] |
C775 |
114) |
[1174913, 1695, 424528] |
C775 |
|
18) |
[157, 3390, 1174913] |
C775 |
115) |
[1422593, 1279, 53312] |
C775 |
|
8) |
[17, 2558, 1422593] |
C775 |
116) |
[3371393, 2239, 410432] |
C775 |
|
11) |
[53, 4478, 3371393] |
C775 |
117) |
[5754689, 2399, 128] |
C775 |
|
2) |
[8, 4798, 5754689] |
C775 |
118) |
[6855041, 2623, 6272] |
C775 |
|
1) |
[8, 5246, 6855041] |
C775 |
119) |
[6995777, 2655, 13312] |
C775 |
|
4) |
[13, 5310, 6995777] |
C775 |
120) |
[7143137, 2703, 40768] |
C775 |
|
3) |
[13, 5406, 7143137] |
C775 |