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 C933 non-normal (D4) quartic CM field invariants: 106 fields
K |
Quartic invariants |
Cl(OK) |
Igusa invariants |
Kr |
Reflex invariants |
Cl(OKr) |
Igusa invariants |
1) |
[8, 6542, 10698929] |
C933 |
|
---) |
[10698929, 3271, 128] |
C6531 |
2) |
[8, 5726, 8178337] |
C933 |
|
101) |
[8178337, 2863, 4608] |
C933 |
3) |
[13, 9081, 20387909] |
C933 |
|
106) |
[20387909, 16753, 24292957] |
C933 |
4) |
[17, 3326, 2761217] |
C933 |
|
95) |
[2761217, 1663, 1088] |
C933 |
5) |
[37, 3342, 2328113] |
C933 |
|
93) |
[2328113, 1671, 116032] |
C933 |
6) |
[53, 3982, 3960689] |
C933 |
|
98) |
[3960689, 1991, 848] |
C933 |
7) |
[73, 2510, 1196593] |
C933 |
|
---) |
[1196593, 1255, 94608] |
C4665 |
8) |
[97, 1334, 406089] |
C933 |
|
85) |
[45121, 667, 9700] |
C933 |
9) |
[181, 3774, 2402369] |
C933 |
|
94) |
[2402369, 1887, 289600] |
C933 |
10) |
[241, 1547, 591012] |
C933 |
|
73) |
[16417, 1963, 926404] |
C933 |
11) |
[293, 2374, 940169] |
C933 |
|
91) |
[940169, 1187, 117200] |
C933 |
12) |
[449, 430, 17489] |
C933 |
|
77) |
[17489, 215, 7184] |
C933 |
13) |
[617, 1258, 333941] |
C933 |
|
89) |
[333941, 629, 15425] |
C933 |
14) |
[761, 1242, 17317] |
C933 |
|
---) |
[17317, 621, 92081] |
C311 |
15) |
[761, 1067, 275300] |
C933 |
|
---) |
[2753, 1003, 3044] |
C311 |
16) |
[941, 1793, 577637] |
C933 |
|
---) |
[577637, 3586, 904301] |
C3 x C933 |
17) |
[977, 2271, 1136704] |
C933 |
|
81) |
[17761, 3883, 35172] |
C933 |
18) |
[1489, 635, 55764] |
C933 |
|
---) |
[1549, 1270, 180169] |
C311 |
19) |
[1609, 411, 41828] |
C933 |
|
---) |
[10457, 822, 1609] |
C3 x C933 |
20) |
[2381, 1621, 442025] |
C933 |
|
80) |
[17681, 3242, 859541] |
C933 |
21) |
[2633, 2846, 508321] |
C933 |
|
38) |
[4201, 1423, 379152] |
C933 |
22) |
[2729, 2966, 2155625] |
C933 |
|
29) |
[3449, 1483, 10916] |
C933 |
23) |
[2801, 1346, 441725] |
C933 |
|
79) |
[17669, 673, 2801] |
C933 |
24) |
[2897, 771, 26212] |
C933 |
|
54) |
[6553, 1542, 489593] |
C933 |
25) |
[2917, 405, 5273] |
C933 |
|
---) |
[5273, 810, 142933] |
C2177 |
26) |
[3169, 2031, 269888] |
C933 |
|
40) |
[4217, 4062, 3045409] |
C933 |
27) |
[3221, 322, 13037] |
C933 |
|
---) |
[13037, 161, 3221] |
C311 |
28) |
[3313, 4551, 4381952] |
C933 |
|
75) |
[17117, 8173, 5569153] |
C933 |
29) |
[3449, 1483, 10916] |
C933 |
|
22) |
[2729, 2966, 2155625] |
C933 |
30) |
[3457, 5831, 1654416] |
C933 |
|
61) |
[11489, 3431, 2710288] |
C933 |
31) |
[3541, 2153, 74421] |
C933 |
|
58) |
[8269, 4306, 4337725] |
C933 |
32) |
[3673, 2983, 2201616] |
C933 |
|
71) |
[15289, 5966, 91825] |
C933 |
33) |
[3877, 261, 16061] |
C933 |
|
---) |
[16061, 522, 3877] |
C311 |
34) |
[4049, 6707, 1324900] |
C933 |
|
65) |
[13249, 4383, 1619600] |
C933 |
35) |
[4073, 267, 16804] |
C933 |
|
39) |
[4201, 534, 4073] |
C933 |
36) |
[4093, 6649, 4338757] |
C933 |
|
69) |
[15013, 4861, 5603317] |
C933 |
37) |
[4153, 1979, 429876] |
C933 |
|
63) |
[11941, 3958, 2196937] |
C933 |
38) |
[4201, 1423, 379152] |
C933 |
|
21) |
[2633, 2846, 508321] |
C933 |
39) |
[4201, 534, 4073] |
C933 |
|
35) |
[4073, 267, 16804] |
C933 |
40) |
[4217, 4062, 3045409] |
C933 |
|
26) |
[3169, 2031, 269888] |
C933 |
41) |
[4273, 7855, 13800448] |
C933 |
|
66) |
[13477, 4429, 1234897] |
C933 |
42) |
[4597, 2405, 341577] |
C933 |
|
---) |
[4217, 4810, 4417717] |
C311 |
43) |
[4649, 2703, 1630132] |
C933 |
|
---) |
[8317, 5406, 785681] |
C311 |
44) |
[4721, 4983, 3600400] |
C933 |
|
59) |
[9001, 4295, 2719296] |
C933 |
45) |
[4789, 9293, 4061025] |
C933 |
|
82) |
[18049, 6851, 6206544] |
C933 |
46) |
[4817, 3035, 76148] |
C933 |
|
84) |
[19037, 6070, 8906633] |
C933 |
47) |
[4861, 7009, 10433125] |
C933 |
|
74) |
[16693, 8761, 10737949] |
C933 |
48) |
[4937, 5627, 2701076] |
C933 |
|
67) |
[13781, 8477, 597377] |
C933 |
49) |
[5077, 5897, 7626213] |
C933 |
|
76) |
[17293, 7505, 3701133] |
C933 |
50) |
[5081, 307, 22292] |
C933 |
|
---) |
[5573, 614, 5081] |
C311 |
51) |
[5393, 651, 72244] |
C933 |
|
83) |
[18061, 1302, 134825] |
C933 |
52) |
[5581, 1209, 364025] |
C933 |
|
68) |
[14561, 2418, 5581] |
C933 |
53) |
[5749, 9930, 2552069] |
C933 |
|
70) |
[15101, 4965, 5524789] |
C933 |
54) |
[6553, 1542, 489593] |
C933 |
|
24) |
[2897, 771, 26212] |
C933 |
55) |
[6997, 2629, 46881] |
C933 |
|
---) |
[5209, 5258, 6724117] |
C311 |
56) |
[7753, 155, 4068] |
C933 |
|
---) |
[113, 310, 7753] |
C311 |
57) |
[8069, 4185, 4037641] |
C933 |
|
---) |
[4801, 4631, 290484] |
C311 |
58) |
[8269, 4306, 4337725] |
C933 |
|
31) |
[3541, 2153, 74421] |
C933 |
59) |
[9001, 4295, 2719296] |
C933 |
|
44) |
[4721, 4983, 3600400] |
C933 |
60) |
[10301, 3205, 1638341] |
C933 |
|
---) |
[5669, 6410, 3718661] |
C311 |
61) |
[11489, 3431, 2710288] |
C933 |
|
30) |
[3457, 5831, 1654416] |
C933 |
62) |
[11821, 3369, 990509] |
C933 |
|
---) |
[5861, 6738, 7388125] |
C311 |
63) |
[11941, 3958, 2196937] |
C933 |
|
37) |
[4153, 1979, 429876] |
C933 |
64) |
[12821, 4249, 3971813] |
C933 |
|
---) |
[4133, 6373, 3705269] |
C311 |
65) |
[13249, 4383, 1619600] |
C933 |
|
34) |
[4049, 6707, 1324900] |
C933 |
66) |
[13477, 4429, 1234897] |
C933 |
|
41) |
[4273, 7855, 13800448] |
C933 |
67) |
[13781, 8477, 597377] |
C933 |
|
48) |
[4937, 5627, 2701076] |
C933 |
68) |
[14561, 2418, 5581] |
C933 |
|
52) |
[5581, 1209, 364025] |
C933 |
69) |
[15013, 4861, 5603317] |
C933 |
|
36) |
[4093, 6649, 4338757] |
C933 |
70) |
[15101, 4965, 5524789] |
C933 |
|
53) |
[5749, 9930, 2552069] |
C933 |
71) |
[15289, 5966, 91825] |
C933 |
|
32) |
[3673, 2983, 2201616] |
C933 |
72) |
[15773, 541, 37681] |
C933 |
|
---) |
[769, 1082, 141957] |
C311 |
73) |
[16417, 1963, 926404] |
C933 |
|
10) |
[241, 1547, 591012] |
C933 |
74) |
[16693, 8761, 10737949] |
C933 |
|
47) |
[4861, 7009, 10433125] |
C933 |
75) |
[17117, 8173, 5569153] |
C933 |
|
28) |
[3313, 4551, 4381952] |
C933 |
76) |
[17293, 7505, 3701133] |
C933 |
|
49) |
[5077, 5897, 7626213] |
C933 |
77) |
[17489, 215, 7184] |
C933 |
|
12) |
[449, 430, 17489] |
C933 |
78) |
[17609, 1758, 490897] |
C933 |
|
---) |
[4057, 879, 70436] |
C311 |
79) |
[17669, 673, 2801] |
C933 |
|
23) |
[2801, 1346, 441725] |
C933 |
80) |
[17681, 3242, 859541] |
C933 |
|
20) |
[2381, 1621, 442025] |
C933 |
81) |
[17761, 3883, 35172] |
C933 |
|
17) |
[977, 2271, 1136704] |
C933 |
82) |
[18049, 6851, 6206544] |
C933 |
|
45) |
[4789, 9293, 4061025] |
C933 |
83) |
[18061, 1302, 134825] |
C933 |
|
51) |
[5393, 651, 72244] |
C933 |
84) |
[19037, 6070, 8906633] |
C933 |
|
46) |
[4817, 3035, 76148] |
C933 |
85) |
[45121, 667, 9700] |
C933 |
|
8) |
[97, 1334, 406089] |
C933 |
86) |
[45641, 2815, 52724] |
C933 |
|
---) |
[269, 2449, 1141025] |
C311 |
87) |
[100469, 1298, 19325] |
C933 |
|
---) |
[773, 649, 100469] |
C311 |
88) |
[209357, 505, 11417] |
C933 |
|
---) |
[233, 1010, 209357] |
C311 |
89) |
[333941, 629, 15425] |
C933 |
|
13) |
[617, 1258, 333941] |
C933 |
90) |
[807113, 931, 14912] |
C933 |
|
---) |
[233, 1862, 807113] |
C311 |
91) |
[940169, 1187, 117200] |
C933 |
|
11) |
[293, 2374, 940169] |
C933 |
92) |
[1945729, 1727, 259200] |
C933 |
|
---) |
[8, 3454, 1945729] |
C311 |
93) |
[2328113, 1671, 116032] |
C933 |
|
5) |
[37, 3342, 2328113] |
C933 |
94) |
[2402369, 1887, 289600] |
C933 |
|
9) |
[181, 3774, 2402369] |
C933 |
95) |
[2761217, 1663, 1088] |
C933 |
|
4) |
[17, 3326, 2761217] |
C933 |
96) |
[3069769, 1987, 219600] |
C933 |
|
---) |
[61, 3974, 3069769] |
C311 |
97) |
[3342601, 1891, 58320] |
C933 |
|
---) |
[5, 3782, 3342601] |
C311 |
98) |
[3960689, 1991, 848] |
C933 |
|
6) |
[53, 3982, 3960689] |
C933 |
99) |
[4032361, 2323, 340992] |
C933 |
|
---) |
[37, 4646, 4032361] |
C311 |
100) |
[4480361, 2291, 192080] |
C933 |
|
---) |
[5, 4582, 4480361] |
C311 |
101) |
[8178337, 2863, 4608] |
C933 |
|
2) |
[8, 5726, 8178337] |
C933 |
102) |
[10970777, 3515, 346112] |
C933 |
|
---) |
[8, 7030, 10970777] |
C311 |
103) |
[11279969, 3407, 81920] |
C933 |
|
---) |
[5, 6814, 11279969] |
C311 |
104) |
[15163033, 3899, 9792] |
C933 |
|
---) |
[17, 7798, 15163033] |
C311 |
105) |
[15936329, 4579, 1257728] |
C933 |
|
---) |
[17, 9158, 15936329] |
C311 |
106) |
[20387909, 16753, 24292957] |
C933 |
|
3) |
[13, 9081, 20387909] |
C933 |