An Igusa CM invariant is specified by a sequence of three polynomials
[ H1(x), G2(x)/N2, G3(x)/N3],
such that
H1(x), G2(x), and G3(x) are in Z[x],
H1(i1) = 0, |
i2 = G2(i1)/N1N2, |
i3 = G3(i1)/N1N3, |
where N1 = H1'(i1),
and N2 and N3 are integers, and
i1 = I4I6/I10, |
i2 = I23I4/I10, |
i3 = I22I6/I10,
|
in terms of the Igusa-Clebsch invariants
[
I2,
I4,
I6,
I10
].
Degree:
[Non-normal]
[Cyclic]
Degree 336 Igusa CM invariants of non-normal (D4) fields: 145
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[3541, 277, 18297] |
[1] |
1 |
[3541, 277, 18297] |
168 |
C168 |
2) |
[317, 313, 18073] |
[1] |
1 |
[317, 313, 18073] |
168 |
C2 x C84 |
3) |
[165, 761, 129889] |
[1] |
1 |
[165, 761, 129889] |
336 |
C2 x C168 |
4) |
[165, 277, 15841] |
[1] |
1 |
[165, 277, 15841] |
336 |
C4 x C84 |
5) |
[165, 417, 42441] |
[1] |
1 |
[165, 417, 42441] |
336 |
C2 x C2 x C84 |
6) |
[165, 662, 99001] |
[1] |
1 |
[165, 662, 99001] |
336 |
C4 x C84 |
7) |
[165, 629, 73129] |
[1] |
1 |
[165, 629, 73129] |
336 |
C4 x C84 |
8) |
[1829, 109, 2513] |
[1] |
1 |
[1829, 109, 2513] |
168 |
C168 |
9) |
[437, 405, 35653] |
[1] |
1 |
[437, 405, 35653] |
168 |
C2 x C84 |
10) |
[60, 806, 150649] |
[1] |
1 |
[60, 806, 150649] |
336 |
C2 x C2 x C84 |
11) |
[60, 482, 42721] |
[1] |
1 |
[60, 482, 42721] |
336 |
C2 x C2 x C84 |
12) |
[60, 794, 151609] |
[1] |
1 |
[60, 794, 151609] |
336 |
C2 x C2 x C84 |
13) |
[60, 746, 136969] |
[1] |
1 |
[60, 746, 136969] |
336 |
C2 x C2 x C84 |
14) |
[229, 689, 93433] |
[1] |
1 |
[229, 689, 93433] |
504 |
C3 x C168 |
15) |
[88, 334, 27537] |
[1] |
1 |
[88, 334, 27537] |
168 |
C2 x C84 |
16) |
[120, 626, 77689] |
[1] |
1 |
[120, 626, 77689] |
336 |
C2 x C2 x C84 |
17) |
[429, 725, 113281] |
[1] |
1 |
[429, 725, 113281] |
336 |
C2 x C168 |
18) |
[357, 581, 37177] |
[1] |
1 |
[357, 581, 37177] |
336 |
C2 x C2 x C84 |
19) |
[104, 286, 16705] |
[1] |
1 |
[104, 286, 16705] |
336 |
C4 x C84 |
20) |
[104, 458, 52337] |
[1] |
1 |
[104, 458, 52337] |
336 |
C2 x C2 x C84 |
21) |
[161, 182, 5705] |
[1] |
1 |
[161, 182, 5705] |
168 |
C2 x C84 |
22) |
[312, 338, 25753] |
[1] |
1 |
[312, 338, 25753] |
336 |
C4 x C84 |
23) |
[813, 241, 14317] |
[1] |
1 |
[813, 241, 14317] |
168 |
C168 |
24) |
[348, 326, 25177] |
[1] |
1 |
[348, 326, 25177] |
336 |
C2 x C168 |
25) |
[1384, 314, 12193] |
[1] |
1 |
[1384, 314, 12193] |
1008 |
C2 x C6 x C84 |
26) |
[1501, 261, 7649] |
[1] |
1 |
[1501, 261, 7649] |
168 |
C168 |
27) |
[209, 478, 3617] |
[1] |
1 |
[209, 478, 3617] |
168 |
C168 |
28) |
[1005, 461, 22729] |
[1] |
1 |
[1005, 461, 22729] |
336 |
C2 x C2 x C84 |
29) |
[13, 990, 244817] |
[1] |
1 |
[13, 990, 244817] |
168 |
C168 |
30) |
[13, 918, 210473] |
[1] |
1 |
[13, 918, 210473] |
168 |
C168 |
31) |
[220, 626, 66289] |
[1] |
1 |
[220, 626, 66289] |
336 |
C2 x C2 x C2 x C42 |
32) |
[76, 698, 110857] |
[1] |
1 |
[76, 698, 110857] |
168 |
C2 x C84 |
33) |
[8, 958, 228641] |
[1] |
1 |
[8, 958, 228641] |
168 |
C2 x C84 |
34) |
[8, 938, 218161] |
[1] |
1 |
[8, 938, 218161] |
168 |
C2 x C84 |
35) |
[280, 446, 39649] |
[1] |
1 |
[280, 446, 39649] |
336 |
C2 x C2 x C2 x C42 |
36) |
[1784, 130, 2441] |
[1] |
1 |
[1784, 130, 2441] |
168 |
C168 |
37) |
[29, 853, 176617] |
[1] |
1 |
[29, 853, 176617] |
168 |
C2 x C84 |
38) |
[92, 286, 18977] |
[1] |
1 |
[92, 286, 18977] |
168 |
C2 x C84 |
39) |
[1693, 129, 3737] |
[1] |
1 |
[1693, 129, 3737] |
168 |
C168 |
40) |
[780, 506, 14089] |
[1] |
1 |
[780, 506, 14089] |
672 |
C2 x C2 x C2 x C84 |
41) |
[589, 725, 130081] |
[1] |
1 |
[589, 725, 130081] |
168 |
C168 |
42) |
[24, 1010, 255001] |
[1] |
1 |
[24, 1010, 255001] |
168 |
C2 x C84 |
43) |
[24, 706, 119209] |
[1] |
1 |
[24, 706, 119209] |
168 |
C2 x C2 x C42 |
44) |
[24, 914, 208633] |
[1] |
1 |
[24, 914, 208633] |
168 |
C2 x C2 x C42 |
45) |
[221, 649, 76073] |
[1] |
1 |
[221, 649, 76073] |
336 |
C2 x C2 x C84 |
46) |
[221, 361, 28105] |
[1] |
1 |
[221, 361, 28105] |
336 |
C2 x C2 x C84 |
47) |
[221, 497, 57277] |
[1] |
1 |
[221, 497, 57277] |
336 |
C4 x C84 |
48) |
[413, 553, 21833] |
[1] |
1 |
[413, 553, 21833] |
168 |
C168 |
49) |
[285, 365, 32665] |
[1] |
1 |
[285, 365, 32665] |
336 |
C4 x C84 |
50) |
[285, 569, 36409] |
[1] |
1 |
[285, 569, 36409] |
336 |
C2 x C168 |
51) |
[781, 489, 3353] |
[1] |
1 |
[781, 489, 3353] |
168 |
C2 x C84 |
52) |
[893, 493, 23033] |
[1] |
1 |
[893, 493, 23033] |
168 |
C2 x C84 |
53) |
[141, 809, 153433] |
[1] |
1 |
[141, 809, 153433] |
168 |
C2 x C84 |
54) |
[141, 385, 34201] |
[1] |
1 |
[141, 385, 34201] |
168 |
C2 x C84 |
55) |
[141, 941, 220489] |
[1] |
1 |
[141, 941, 220489] |
168 |
C168 |
56) |
[952, 450, 3977] |
[1] |
1 |
[952, 450, 3977] |
336 |
C4 x C84 |
57) |
[1093, 417, 10409] |
[1] |
1 |
[1093, 417, 10409] |
840 |
C840 |
58) |
[40, 654, 90929] |
[1] |
1 |
[40, 654, 90929] |
336 |
C2 x C2 x C84 |
59) |
[40, 606, 64769] |
[1] |
1 |
[40, 606, 64769] |
336 |
C2 x C2 x C84 |
60) |
[728, 146, 4601] |
[1] |
1 |
[728, 146, 4601] |
336 |
C2 x C2 x C84 |
61) |
[149, 342, 26857] |
[1] |
1 |
[149, 342, 26857] |
168 |
C168 |
62) |
[149, 694, 110873] |
[1] |
1 |
[149, 694, 110873] |
168 |
C2 x C84 |
63) |
[1541, 241, 4889] |
[1] |
1 |
[1541, 241, 4889] |
168 |
C168 |
64) |
[140, 230, 12665] |
[1] |
1 |
[140, 230, 12665] |
336 |
C4 x C84 |
65) |
[140, 410, 39785] |
[1] |
1 |
[140, 410, 39785] |
336 |
C4 x C84 |
66) |
[140, 646, 76889] |
[1] |
1 |
[140, 646, 76889] |
336 |
C2 x C168 |
67) |
[140, 386, 32209] |
[1] |
1 |
[140, 386, 32209] |
336 |
C2 x C2 x C2 x C42 |
68) |
[1704, 170, 5521] |
[1] |
1 |
[1704, 170, 5521] |
336 |
C2 x C168 |
69) |
[248, 290, 8873] |
[1] |
1 |
[248, 290, 8873] |
168 |
C168 |
70) |
[168, 602, 62209] |
[1] |
1 |
[168, 602, 62209] |
336 |
C2 x C2 x C84 |
71) |
[89, 763, 33380] |
[1] |
1 |
[89, 763, 33380] |
168 |
C168 |
72) |
[744, 138, 4017] |
[1] |
1 |
[744, 138, 4017] |
336 |
C4 x C84 |
73) |
[533, 377, 34333] |
[1] |
1 |
[533, 377, 34333] |
336 |
C4 x C84 |
74) |
[53, 790, 142457] |
[1] |
1 |
[53, 790, 142457] |
168 |
C2 x C84 |
75) |
[53, 517, 54089] |
[1] |
1 |
[53, 517, 54089] |
168 |
C168 |
76) |
[53, 1382, 374873] |
[1] |
1 |
[53, 1382, 374873] |
168 |
C168 |
77) |
[53, 701, 102697] |
[1] |
1 |
[53, 701, 102697] |
168 |
C2 x C84 |
78) |
[568, 578, 37513] |
[1] |
1 |
[568, 578, 37513] |
504 |
C2 x C6 x C42 |
79) |
[341, 317, 20945] |
[1] |
1 |
[341, 317, 20945] |
168 |
C2 x C84 |
80) |
[332, 474, 54841] |
[1] |
1 |
[332, 474, 54841] |
168 |
C168 |
81) |
[332, 274, 6817] |
[1] |
1 |
[332, 274, 6817] |
168 |
C2 x C84 |
82) |
[184, 394, 23905] |
[1] |
1 |
[184, 394, 23905] |
168 |
C2 x C84 |
83) |
[37, 981, 240137] |
[1] |
1 |
[37, 981, 240137] |
168 |
C168 |
84) |
[37, 549, 69569] |
[1] |
1 |
[37, 549, 69569] |
168 |
C168 |
85) |
[37, 741, 132377] |
[1] |
1 |
[37, 741, 132377] |
168 |
C168 |
86) |
[949, 465, 13961] |
[1] |
1 |
[949, 465, 13961] |
336 |
C2 x C2 x C84 |
87) |
[293, 461, 47197] |
[1] |
1 |
[293, 461, 47197] |
168 |
C168 |
88) |
[28, 950, 224617] |
[1] |
1 |
[28, 950, 224617] |
168 |
C168 |
89) |
[28, 702, 101249] |
[1] |
1 |
[28, 702, 101249] |
168 |
C2 x C84 |
90) |
[28, 938, 218953] |
[1] |
1 |
[28, 938, 218953] |
168 |
C2 x C2 x C42 |
91) |
[445, 537, 13241] |
[1] |
1 |
[445, 537, 13241] |
672 |
C2 x C336 |
92) |
[581, 217, 10465] |
[1] |
1 |
[581, 217, 10465] |
168 |
C2 x C2 x C42 |
93) |
[316, 374, 23593] |
[1] |
1 |
[316, 374, 23593] |
504 |
C3 x C168 |
94) |
[508, 762, 143129] |
[1] |
1 |
[508, 762, 143129] |
168 |
C2 x C84 |
95) |
[501, 593, 42697] |
[1] |
1 |
[501, 593, 42697] |
168 |
C168 |
96) |
[617, 806, 152537] |
[1] |
1 |
[617, 806, 152537] |
168 |
C168 |
97) |
[1677, 185, 8137] |
[1] |
1 |
[1677, 185, 8137] |
672 |
C2 x C2 x C168 |
98) |
[197, 401, 38969] |
[1] |
1 |
[197, 401, 38969] |
168 |
C2 x C84 |
99) |
[597, 545, 20377] |
[1] |
1 |
[597, 545, 20377] |
168 |
C2 x C84 |
100) |
[492, 234, 5817] |
[1] |
1 |
[492, 234, 5817] |
336 |
C4 x C84 |
101) |
[1661, 193, 8897] |
[1] |
1 |
[1661, 193, 8897] |
168 |
C2 x C84 |
102) |
[664, 530, 16441] |
[1] |
1 |
[664, 530, 16441] |
168 |
C2 x C84 |
103) |
[664, 178, 7257] |
[1] |
1 |
[664, 178, 7257] |
168 |
C2 x C84 |
104) |
[17, 478, 39713] |
[1] |
1 |
[17, 478, 39713] |
168 |
C168 |
105) |
[17, 446, 48641] |
[1] |
1 |
[17, 446, 48641] |
168 |
C168 |
106) |
[373, 270, 12257] |
[1] |
1 |
[373, 270, 12257] |
168 |
C2 x C84 |
107) |
[645, 697, 120001] |
[1] |
1 |
[645, 697, 120001] |
336 |
C4 x C84 |
108) |
[997, 145, 3013] |
[1] |
1 |
[997, 145, 3013] |
168 |
C168 |
109) |
[2789, 593, 3545] |
[1] |
1 |
[2789, 593, 3545] |
168 |
C168 |
110) |
[181, 361, 27105] |
[1] |
1 |
[181, 361, 27105] |
168 |
C2 x C2 x C42 |
111) |
[869, 505, 27041] |
[1] |
1 |
[869, 505, 27041] |
168 |
C2 x C84 |
112) |
[133, 630, 65177] |
[1] |
1 |
[133, 630, 65177] |
168 |
C168 |
113) |
[133, 917, 207529] |
[1] |
1 |
[133, 917, 207529] |
168 |
C2 x C84 |
114) |
[3389, 349, 22825] |
[1] |
1 |
[3389, 349, 22825] |
168 |
C168 |
115) |
[77, 805, 155057] |
[1] |
1 |
[77, 805, 155057] |
168 |
C2 x C84 |
116) |
[77, 677, 114409] |
[1] |
1 |
[77, 677, 114409] |
168 |
C168 |
117) |
[77, 901, 199697] |
[1] |
1 |
[77, 901, 199697] |
168 |
C168 |
118) |
[620, 514, 4049] |
[1] |
1 |
[620, 514, 4049] |
336 |
C2 x C2 x C84 |
119) |
[44, 418, 42097] |
[1] |
1 |
[44, 418, 42097] |
168 |
C2 x C84 |
120) |
[44, 458, 51737] |
[1] |
1 |
[44, 458, 51737] |
168 |
C2 x C84 |
121) |
[44, 694, 99113] |
[1] |
1 |
[44, 694, 99113] |
168 |
C2 x C84 |
122) |
[389, 313, 23617] |
[1] |
1 |
[389, 313, 23617] |
168 |
C2 x C84 |
123) |
[613, 189, 8777] |
[1] |
1 |
[613, 189, 8777] |
168 |
C168 |
124) |
[12, 766, 131137] |
[1] |
1 |
[12, 766, 131137] |
168 |
C2 x C84 |
125) |
[21, 901, 201769] |
[1] |
1 |
[21, 901, 201769] |
168 |
C168 |
126) |
[21, 649, 101473] |
[1] |
1 |
[21, 649, 101473] |
168 |
C2 x C84 |
127) |
[21, 917, 209041] |
[1] |
1 |
[21, 917, 209041] |
168 |
C168 |
128) |
[277, 349, 27057] |
[1] |
1 |
[277, 349, 27057] |
168 |
C2 x C84 |
129) |
[741, 141, 4785] |
[1] |
1 |
[741, 141, 4785] |
336 |
C2 x C2 x C84 |
130) |
[56, 322, 24521] |
[1] |
1 |
[56, 322, 24521] |
168 |
C2 x C2 x C42 |
131) |
[56, 574, 81473] |
[1] |
1 |
[56, 574, 81473] |
168 |
C2 x C2 x C42 |
132) |
[56, 574, 44513] |
[1] |
1 |
[56, 574, 44513] |
168 |
C2 x C84 |
133) |
[56, 466, 53785] |
[1] |
1 |
[56, 466, 53785] |
168 |
C2 x C84 |
134) |
[56, 946, 222329] |
[1] |
1 |
[56, 946, 222329] |
168 |
C168 |
135) |
[1036, 434, 9793] |
[1] |
1 |
[1036, 434, 9793] |
336 |
C2 x C2 x C2 x C42 |
136) |
[485, 269, 17969] |
[1] |
1 |
[485, 269, 17969] |
336 |
C4 x C84 |
137) |
[41, 422, 43865] |
[1] |
1 |
[41, 422, 43865] |
168 |
C2 x C84 |
138) |
[812, 490, 8057] |
[1] |
1 |
[812, 490, 8057] |
336 |
C2 x C2 x C2 x C42 |
139) |
[101, 661, 93449] |
[1] |
1 |
[101, 661, 93449] |
168 |
C2 x C84 |
140) |
[101, 545, 63121] |
[1] |
1 |
[101, 545, 63121] |
168 |
C2 x C84 |
141) |
[101, 421, 42265] |
[1] |
1 |
[101, 421, 42265] |
168 |
C2 x C84 |
142) |
[717, 521, 16057] |
[1] |
1 |
[717, 521, 16057] |
168 |
C168 |
143) |
[69, 713, 126937] |
[1] |
1 |
[69, 713, 126937] |
168 |
C2 x C84 |
144) |
[69, 905, 201841] |
[1] |
1 |
[69, 905, 201841] |
168 |
C2 x C84 |
145) |
[444, 514, 2113] |
[1] |
1 |
[444, 514, 2113] |
336 |
C2 x C2 x C84 |