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 84 Igusa CM invariants of non-normal (D4) fields: 197
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[317, 753, 123921] |
[1] |
1 |
[317, 753, 123921] |
42 |
C42 |
2) |
[661, 181, 8025] |
[1] |
1 |
[661, 181, 8025] |
42 |
C42 |
3) |
[344, 610, 51401] |
[1] |
1 |
[344, 610, 51401] |
42 |
C42 |
4) |
[157, 305, 14425] |
[1] |
1 |
[157, 305, 14425] |
42 |
C42 |
5) |
[237, 106, 1861] |
[1] |
1 |
[237, 106, 1861] |
42 |
C42 |
6) |
[9769, 137, 2250] |
[1] |
1 |
[9769, 137, 2250] |
42 |
C42 |
7) |
[437, 85, 1697] |
[1] |
1 |
[437, 85, 1697] |
42 |
C42 |
8) |
[437, 65, 73] |
[2, 2] |
2 |
[437, 65, 73] |
14 |
C14 |
9) |
[901, 461, 2449] |
[1] |
1 |
[901, 461, 2449] |
168 |
C168 |
10) |
[269, 414, 4113] |
[1] |
2 |
[269, 414, 4113] |
84 |
C84 |
11) |
[137, 175, 6800] |
[1] |
1 |
[137, 175, 6800] |
42 |
C42 |
12) |
[137, 671, 43204] |
[1] |
1 |
[137, 671, 43204] |
42 |
C42 |
13) |
[7529, 402, 10285] |
[1] |
1 |
[7529, 402, 10285] |
42 |
C42 |
14) |
[88, 530, 50425] |
[1] |
2 |
[88, 530, 50425] |
84 |
C2 x C42 |
15) |
[104, 162, 6457] |
[1] |
1 |
[104, 162, 6457] |
84 |
C84 |
16) |
[104, 372, 34180] |
[1] |
1 |
[104, 372, 34180] |
84 |
C84 |
17) |
[145, 139, 4504] |
[1] |
1 |
[145, 139, 4504] |
168 |
C168 |
18) |
[145, 122, 3141] |
[1] |
1 |
[145, 122, 3141] |
168 |
C168 |
19) |
[109, 685, 40761] |
[1] |
1 |
[109, 685, 40761] |
42 |
C42 |
20) |
[109, 262, 1465] |
[1] |
1 |
[109, 262, 1465] |
42 |
C42 |
21) |
[2381, 658, 22525] |
[1] |
1 |
[2381, 658, 22525] |
42 |
C42 |
22) |
[1765, 137, 721] |
[1] |
1 |
[1765, 137, 721] |
252 |
C3 x C84 |
23) |
[7489, 200, 2511] |
[1] |
1 |
[7489, 200, 2511] |
42 |
C42 |
24) |
[685, 501, 929] |
[1] |
1 |
[685, 501, 929] |
84 |
C2 x C42 |
25) |
[253, 446, 13297] |
[1] |
1 |
[253, 446, 13297] |
42 |
C42 |
26) |
[209, 827, 170512] |
[1] |
1 |
[209, 827, 170512] |
42 |
C42 |
27) |
[209, 216, 1423] |
[1] |
1 |
[209, 216, 1423] |
42 |
C42 |
28) |
[209, 111, 3028] |
[2] |
1 |
[209, 111, 3028] |
42 |
C42 |
29) |
[209, 111, 3028] |
[1] |
1 |
[209, 111, 3028] |
42 |
C42 |
30) |
[1709, 165, 2961] |
[1] |
2 |
[1709, 165, 2961] |
84 |
C2 x C42 |
31) |
[493, 513, 593] |
[1] |
1 |
[493, 513, 593] |
84 |
C2 x C42 |
32) |
[13, 665, 97657] |
[1] |
1 |
[13, 665, 97657] |
42 |
C42 |
33) |
[13, 705, 122225] |
[1] |
2 |
[13, 705, 122225] |
84 |
C84 |
34) |
[13, 549, 24569] |
[1] |
1 |
[13, 549, 24569] |
42 |
C42 |
35) |
[13, 758, 136153] |
[1] |
1 |
[13, 758, 136153] |
42 |
C42 |
36) |
[13, 701, 121417] |
[1] |
1 |
[13, 701, 121417] |
42 |
C42 |
37) |
[13, 157, 6133] |
[3, 3] |
1 |
[13, 157, 6133] |
21 |
C21 |
38) |
[13, 870, 184025] |
[1] |
2 |
[13, 870, 184025] |
84 |
C2 x C42 |
39) |
[13, 298, 21733] |
[1] |
1 |
[13, 298, 21733] |
42 |
C42 |
40) |
[13, 758, 126793] |
[1] |
1 |
[13, 758, 126793] |
42 |
C42 |
41) |
[13, 49, 571] |
[1] |
1 |
[13, 49, 571] |
42 |
C42 |
42) |
[13, 710, 118537] |
[1] |
1 |
[13, 710, 118537] |
42 |
C42 |
43) |
[13, 693, 116081] |
[1] |
2 |
[13, 693, 116081] |
84 |
C2 x C42 |
44) |
[13, 64, 556] |
[1] |
1 |
[13, 64, 556] |
42 |
C42 |
45) |
[76, 366, 3089] |
[1] |
1 |
[76, 366, 3089] |
42 |
C42 |
46) |
[3497, 498, 48013] |
[1] |
1 |
[3497, 498, 48013] |
84 |
C84 |
47) |
[1285, 341, 3049] |
[1] |
1 |
[1285, 341, 3049] |
84 |
C2 x C42 |
48) |
[8, 1026, 134137] |
[1] |
1 |
[8, 1026, 134137] |
42 |
C42 |
49) |
[8, 458, 29969] |
[1] |
1 |
[8, 458, 29969] |
42 |
C42 |
50) |
[8, 658, 108169] |
[1] |
1 |
[8, 658, 108169] |
42 |
C42 |
51) |
[8, 650, 93457] |
[1] |
2 |
[8, 650, 93457] |
84 |
C2 x C42 |
52) |
[8, 1638, 584233] |
[1] |
2 |
[8, 1638, 584233] |
84 |
C84 |
53) |
[8, 2790, 1318825] |
[1] |
2 |
[8, 2790, 1318825] |
84 |
C2 x C42 |
54) |
[8, 430, 36977] |
[1] |
1 |
[8, 430, 36977] |
42 |
C42 |
55) |
[8, 1030, 251113] |
[1] |
1 |
[8, 1030, 251113] |
42 |
C42 |
56) |
[8, 602, 58849] |
[1] |
2 |
[8, 602, 58849] |
84 |
C2 x C42 |
57) |
[8, 234, 10801] |
[1] |
1 |
[8, 234, 10801] |
42 |
C42 |
58) |
[8, 490, 35825] |
[1] |
1 |
[8, 490, 35825] |
42 |
C42 |
59) |
[5, 809, 161089] |
[1] |
1 |
[5, 809, 161089] |
42 |
C42 |
60) |
[5, 405, 34345] |
[1] |
1 |
[5, 405, 34345] |
42 |
C42 |
61) |
[5, 886, 192329] |
[1] |
1 |
[5, 886, 192329] |
42 |
C42 |
62) |
[5, 1701, 620389] |
[1] |
2 |
[5, 1701, 620389] |
84 |
C2 x C42 |
63) |
[5, 661, 90929] |
[1] |
1 |
[5, 661, 90929] |
42 |
C42 |
64) |
[5, 789, 141849] |
[1] |
1 |
[5, 789, 141849] |
42 |
C42 |
65) |
[5, 598, 75881] |
[1] |
1 |
[5, 598, 75881] |
42 |
C42 |
66) |
[5, 533, 66061] |
[1] |
1 |
[5, 533, 66061] |
42 |
C42 |
67) |
[5, 633, 85321] |
[1] |
1 |
[5, 633, 85321] |
42 |
C42 |
68) |
[5, 473, 47321] |
[1] |
1 |
[5, 473, 47321] |
42 |
C42 |
69) |
[5, 709, 124889] |
[1] |
1 |
[5, 709, 124889] |
42 |
C42 |
70) |
[5, 897, 200601] |
[1] |
2 |
[5, 897, 200601] |
84 |
C2 x C42 |
71) |
[5, 766, 144689] |
[1] |
1 |
[5, 766, 144689] |
42 |
C42 |
72) |
[5, 901, 199169] |
[1] |
1 |
[5, 901, 199169] |
42 |
C42 |
73) |
[5, 949, 224369] |
[1] |
1 |
[5, 949, 224369] |
42 |
C42 |
74) |
[5, 697, 104921] |
[1] |
1 |
[5, 697, 104921] |
42 |
C42 |
75) |
[5, 969, 232429] |
[1] |
1 |
[5, 969, 232429] |
42 |
C42 |
76) |
[5, 601, 89249] |
[1] |
1 |
[5, 601, 89249] |
42 |
C42 |
77) |
[5, 929, 203509] |
[1] |
1 |
[5, 929, 203509] |
42 |
C42 |
78) |
[5, 393, 38161] |
[1] |
1 |
[5, 393, 38161] |
42 |
C42 |
79) |
[5, 461, 52849] |
[1] |
1 |
[5, 461, 52849] |
42 |
C42 |
80) |
[5, 433, 46321] |
[1] |
1 |
[5, 433, 46321] |
42 |
C42 |
81) |
[5, 422, 42521] |
[1] |
1 |
[5, 422, 42521] |
42 |
C42 |
82) |
[5, 501, 58689] |
[1] |
1 |
[5, 501, 58689] |
42 |
C42 |
83) |
[5, 689, 111649] |
[1] |
1 |
[5, 689, 111649] |
42 |
C42 |
84) |
[5, 1301, 369589] |
[1] |
1 |
[5, 1301, 369589] |
42 |
C42 |
85) |
[5, 741, 123489] |
[1] |
1 |
[5, 741, 123489] |
42 |
C42 |
86) |
[5, 886, 194969] |
[1] |
1 |
[5, 886, 194969] |
42 |
C42 |
87) |
[5, 726, 128889] |
[1] |
1 |
[5, 726, 128889] |
42 |
C42 |
88) |
[5, 814, 163649] |
[1] |
1 |
[5, 814, 163649] |
42 |
C42 |
89) |
[5, 1573, 617221] |
[1] |
2 |
[5, 1573, 617221] |
84 |
C2 x C42 |
90) |
[5, 942, 221121] |
[1] |
2 |
[5, 942, 221121] |
84 |
C2 x C42 |
91) |
[5, 1017, 258561] |
[1] |
2 |
[5, 1017, 258561] |
84 |
C84 |
92) |
[29, 309, 20673] |
[1] |
1 |
[29, 309, 20673] |
42 |
C42 |
93) |
[29, 574, 59633] |
[1] |
2 |
[29, 574, 59633] |
84 |
C2 x C42 |
94) |
[29, 470, 38521] |
[1] |
1 |
[29, 470, 38521] |
42 |
C42 |
95) |
[29, 610, 41869] |
[1] |
1 |
[29, 610, 41869] |
42 |
C42 |
96) |
[124, 400, 29956] |
[1] |
1 |
[124, 400, 29956] |
42 |
C42 |
97) |
[93, 157, 5581] |
[1] |
1 |
[93, 157, 5581] |
42 |
C42 |
98) |
[93, 278, 17833] |
[1] |
1 |
[93, 278, 17833] |
42 |
C42 |
99) |
[24, 254, 14593] |
[1] |
1 |
[24, 254, 14593] |
42 |
C42 |
100) |
[24, 770, 145321] |
[1] |
2 |
[24, 770, 145321] |
84 |
C2 x C42 |
101) |
[24, 434, 45913] |
[1] |
2 |
[24, 434, 45913] |
84 |
C2 x C42 |
102) |
[24, 340, 22756] |
[1] |
1 |
[24, 340, 22756] |
42 |
C42 |
103) |
[221, 93, 781] |
[1] |
1 |
[221, 93, 781] |
84 |
C84 |
104) |
[413, 190, 2417] |
[1] |
1 |
[413, 190, 2417] |
42 |
C42 |
105) |
[2273, 309, 9664] |
[1] |
1 |
[2273, 309, 9664] |
42 |
C42 |
106) |
[1141, 146, 765] |
[1] |
1 |
[1141, 146, 765] |
42 |
C42 |
107) |
[141, 365, 17761] |
[1] |
1 |
[141, 365, 17761] |
42 |
C42 |
108) |
[141, 689, 115825] |
[1] |
1 |
[141, 689, 115825] |
42 |
C42 |
109) |
[152, 676, 26692] |
[1] |
1 |
[152, 676, 26692] |
42 |
C42 |
110) |
[149, 485, 2149] |
[1] |
1 |
[149, 485, 2149] |
42 |
C42 |
111) |
[149, 101, 2513] |
[1] |
1 |
[149, 101, 2513] |
42 |
C42 |
112) |
[1453, 273, 833] |
[1] |
2 |
[1453, 273, 833] |
84 |
C2 x C42 |
113) |
[3113, 480, 54487] |
[1] |
1 |
[3113, 480, 54487] |
42 |
C42 |
114) |
[1229, 109, 205] |
[1] |
1 |
[1229, 109, 205] |
126 |
C3 x C42 |
115) |
[185, 165, 5650] |
[1] |
1 |
[185, 165, 5650] |
84 |
C84 |
116) |
[89, 519, 40084] |
[1] |
1 |
[89, 519, 40084] |
42 |
C42 |
117) |
[89, 1787, 710032] |
[1] |
1 |
[89, 1787, 710032] |
42 |
C42 |
118) |
[1721, 726, 21625] |
[1] |
1 |
[1721, 726, 21625] |
42 |
C42 |
119) |
[565, 521, 5569] |
[1] |
1 |
[565, 521, 5569] |
84 |
C2 x C42 |
120) |
[497, 390, 6217] |
[1] |
1 |
[497, 390, 6217] |
42 |
C42 |
121) |
[53, 189, 8917] |
[1] |
1 |
[53, 189, 8917] |
42 |
C42 |
122) |
[7681, 277, 1900] |
[1] |
1 |
[7681, 277, 1900] |
42 |
C42 |
123) |
[184, 106, 1153] |
[1] |
1 |
[184, 106, 1153] |
42 |
C42 |
124) |
[37, 521, 49129] |
[1] |
1 |
[37, 521, 49129] |
42 |
C42 |
125) |
[37, 593, 43873] |
[1] |
1 |
[37, 593, 43873] |
42 |
C42 |
126) |
[37, 166, 1561] |
[2, 2] |
1 |
[37, 166, 1561] |
42 |
C42 |
127) |
[37, 461, 43057] |
[1] |
1 |
[37, 461, 43057] |
42 |
C42 |
128) |
[37, 166, 1561] |
[1] |
1 |
[37, 166, 1561] |
42 |
C42 |
129) |
[37, 677, 84529] |
[1] |
1 |
[37, 677, 84529] |
42 |
C42 |
130) |
[37, 481, 57609] |
[1] |
1 |
[37, 481, 57609] |
42 |
C42 |
131) |
[37, 566, 32137] |
[1] |
1 |
[37, 566, 32137] |
42 |
C42 |
132) |
[37, 438, 10073] |
[1] |
1 |
[37, 438, 10073] |
42 |
C42 |
133) |
[37, 833, 169393] |
[1] |
2 |
[37, 833, 169393] |
84 |
C2 x C42 |
134) |
[37, 477, 17801] |
[1] |
1 |
[37, 477, 17801] |
42 |
C42 |
135) |
[37, 350, 25297] |
[1] |
1 |
[37, 350, 25297] |
42 |
C42 |
136) |
[949, 525, 57281] |
[1] |
1 |
[949, 525, 57281] |
84 |
C84 |
137) |
[789, 485, 1801] |
[1] |
1 |
[789, 485, 1801] |
42 |
C42 |
138) |
[7901, 474, 24565] |
[1] |
1 |
[7901, 474, 24565] |
42 |
C42 |
139) |
[61, 605, 51841] |
[1] |
1 |
[61, 605, 51841] |
42 |
C42 |
140) |
[61, 257, 13081] |
[1] |
1 |
[61, 257, 13081] |
42 |
C42 |
141) |
[61, 510, 17201] |
[1] |
1 |
[61, 510, 17201] |
42 |
C42 |
142) |
[61, 29, 73] |
[13] |
1 |
[61, 29, 73] |
3 |
C3 |
143) |
[197, 445, 2177] |
[1] |
1 |
[197, 445, 2177] |
42 |
C42 |
144) |
[17, 530, 20653] |
[1] |
1 |
[17, 530, 20653] |
42 |
C42 |
145) |
[17, 1494, 122809] |
[1] |
1 |
[17, 1494, 122809] |
42 |
C42 |
146) |
[1757, 141, 1017] |
[1] |
2 |
[1757, 141, 1017] |
84 |
C2 x C42 |
147) |
[1037, 421, 497] |
[1] |
1 |
[1037, 421, 497] |
84 |
C84 |
148) |
[173, 233, 3841] |
[1] |
1 |
[173, 233, 3841] |
42 |
C42 |
149) |
[545, 695, 90100] |
[1] |
1 |
[545, 695, 90100] |
84 |
C84 |
150) |
[2801, 474, 44965] |
[1] |
1 |
[2801, 474, 44965] |
42 |
C42 |
151) |
[77, 390, 26937] |
[1] |
2 |
[77, 390, 26937] |
84 |
C2 x C42 |
152) |
[77, 173, 7309] |
[1] |
1 |
[77, 173, 7309] |
42 |
C42 |
153) |
[77, 582, 40329] |
[1] |
2 |
[77, 582, 40329] |
84 |
C2 x C42 |
154) |
[569, 183, 4816] |
[1] |
1 |
[569, 183, 4816] |
42 |
C42 |
155) |
[701, 561, 39249] |
[1] |
1 |
[701, 561, 39249] |
42 |
C42 |
156) |
[389, 113, 2317] |
[1] |
1 |
[389, 113, 2317] |
42 |
C42 |
157) |
[389, 201, 9225] |
[1] |
1 |
[389, 201, 9225] |
42 |
C42 |
158) |
[1157, 45, 217] |
[1] |
1 |
[1157, 45, 217] |
84 |
C84 |
159) |
[1157, 385, 2057] |
[1] |
2 |
[1157, 385, 2057] |
168 |
C2 x C2 x C42 |
160) |
[12, 422, 43321] |
[1] |
1 |
[12, 422, 43321] |
42 |
C42 |
161) |
[12, 590, 67825] |
[1] |
2 |
[12, 590, 67825] |
84 |
C2 x C42 |
162) |
[12, 610, 77473] |
[1] |
1 |
[12, 610, 77473] |
42 |
C42 |
163) |
[12, 106, 1942] |
[1] |
1 |
[12, 106, 1942] |
42 |
C42 |
164) |
[12, 130, 3142] |
[1] |
1 |
[12, 130, 3142] |
42 |
C42 |
165) |
[12, 290, 15217] |
[1] |
1 |
[12, 290, 15217] |
42 |
C42 |
166) |
[12, 458, 24793] |
[1] |
1 |
[12, 458, 24793] |
42 |
C42 |
167) |
[12, 566, 27817] |
[1] |
1 |
[12, 566, 27817] |
42 |
C42 |
168) |
[12, 422, 30649] |
[1] |
1 |
[12, 422, 30649] |
42 |
C42 |
169) |
[21, 590, 70561] |
[1] |
1 |
[21, 590, 70561] |
42 |
C42 |
170) |
[21, 509, 25033] |
[1] |
1 |
[21, 509, 25033] |
42 |
C42 |
171) |
[21, 845, 170521] |
[1] |
2 |
[21, 845, 170521] |
84 |
C2 x C42 |
172) |
[21, 253, 8017] |
[1] |
1 |
[21, 253, 8017] |
42 |
C42 |
173) |
[21, 701, 119569] |
[1] |
1 |
[21, 701, 119569] |
42 |
C42 |
174) |
[21, 166, 6553] |
[1] |
1 |
[21, 166, 6553] |
42 |
C42 |
175) |
[21, 701, 106969] |
[1] |
1 |
[21, 701, 106969] |
42 |
C42 |
176) |
[21, 166, 6553] |
[2, 2] |
1 |
[21, 166, 6553] |
42 |
C42 |
177) |
[21, 289, 14449] |
[1] |
1 |
[21, 289, 14449] |
42 |
C42 |
178) |
[21, 785, 140401] |
[1] |
1 |
[21, 785, 140401] |
42 |
C42 |
179) |
[21, 869, 183073] |
[1] |
2 |
[21, 869, 183073] |
84 |
C2 x C42 |
180) |
[21, 193, 9181] |
[1] |
1 |
[21, 193, 9181] |
42 |
C42 |
181) |
[21, 533, 65977] |
[1] |
1 |
[21, 533, 65977] |
42 |
C42 |
182) |
[21, 85, 1801] |
[2, 2] |
2 |
[21, 85, 1801] |
14 |
C14 |
183) |
[85, 497, 6481] |
[1] |
1 |
[85, 497, 6481] |
84 |
C2 x C42 |
184) |
[601, 599, 35460] |
[1] |
1 |
[601, 599, 35460] |
42 |
C42 |
185) |
[56, 202, 9697] |
[1] |
1 |
[56, 202, 9697] |
42 |
C42 |
186) |
[41, 1415, 496036] |
[1] |
1 |
[41, 1415, 496036] |
42 |
C42 |
187) |
[41, 919, 162340] |
[1] |
1 |
[41, 919, 162340] |
42 |
C42 |
188) |
[201, 103, 1396] |
[1] |
1 |
[201, 103, 1396] |
42 |
C42 |
189) |
[201, 103, 1396] |
[2] |
1 |
[201, 103, 1396] |
42 |
C42 |
190) |
[365, 89, 1889] |
[1] |
1 |
[365, 89, 1889] |
84 |
C2 x C42 |
191) |
[2073, 226, 4477] |
[1] |
1 |
[2073, 226, 4477] |
42 |
C42 |
192) |
[3089, 1502, 119185] |
[1] |
1 |
[3089, 1502, 119185] |
42 |
C42 |
193) |
[101, 534, 13113] |
[1] |
2 |
[101, 534, 13113] |
84 |
C2 x C42 |
194) |
[101, 341, 27025] |
[1] |
1 |
[101, 341, 27025] |
42 |
C42 |
195) |
[481, 254, 8433] |
[1] |
1 |
[481, 254, 8433] |
84 |
C2 x C42 |
196) |
[381, 521, 8329] |
[1] |
1 |
[381, 521, 8329] |
42 |
C42 |
197) |
[69, 533, 14977] |
[1] |
1 |
[69, 533, 14977] |
42 |
C42 |