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 70 Igusa CM invariants of non-normal (D4) fields: 122
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[157, 293, 4153] |
[1] |
1 |
[157, 293, 4153] |
35 |
C35 |
2) |
[157, 165, 5825] |
[1] |
2 |
[157, 165, 5825] |
70 |
C70 |
3) |
[1361, 567, 63700] |
[1] |
2 |
[1361, 567, 63700] |
70 |
C70 |
4) |
[1361, 951, 13444] |
[1] |
1 |
[1361, 951, 13444] |
35 |
C35 |
5) |
[229, 274, 10525] |
[1] |
1 |
[229, 274, 10525] |
105 |
C105 |
6) |
[1049, 906, 100309] |
[1] |
1 |
[1049, 906, 100309] |
35 |
C35 |
7) |
[109, 150, 3881] |
[1] |
1 |
[109, 150, 3881] |
35 |
C35 |
8) |
[109, 194, 8973] |
[1] |
1 |
[109, 194, 8973] |
35 |
C35 |
9) |
[1381, 245, 14661] |
[1] |
1 |
[1381, 245, 14661] |
35 |
C35 |
10) |
[13, 225, 12497] |
[1] |
1 |
[13, 225, 12497] |
35 |
C35 |
11) |
[13, 593, 52081] |
[1] |
1 |
[13, 593, 52081] |
35 |
C35 |
12) |
[13, 298, 17989] |
[1] |
1 |
[13, 298, 17989] |
35 |
C35 |
13) |
[13, 249, 15497] |
[1] |
1 |
[13, 249, 15497] |
35 |
C35 |
14) |
[13, 157, 3793] |
[1] |
1 |
[13, 157, 3793] |
35 |
C35 |
15) |
[13, 653, 104233] |
[1] |
1 |
[13, 653, 104233] |
35 |
C35 |
16) |
[13, 237, 13649] |
[1] |
1 |
[13, 237, 13649] |
35 |
C35 |
17) |
[13, 313, 13933] |
[1] |
1 |
[13, 313, 13933] |
35 |
C35 |
18) |
[13, 641, 66889] |
[1] |
1 |
[13, 641, 66889] |
35 |
C35 |
19) |
[13, 590, 79537] |
[1] |
1 |
[13, 590, 79537] |
35 |
C35 |
20) |
[977, 750, 124993] |
[1] |
1 |
[977, 750, 124993] |
35 |
C35 |
21) |
[8, 850, 142537] |
[1] |
1 |
[8, 850, 142537] |
35 |
C35 |
22) |
[8, 1410, 472825] |
[1] |
2 |
[8, 1410, 472825] |
70 |
C70 |
23) |
[8, 586, 51001] |
[1] |
2 |
[8, 586, 51001] |
70 |
C70 |
24) |
[8, 522, 48121] |
[1] |
2 |
[8, 522, 48121] |
70 |
C70 |
25) |
[8, 234, 13681] |
[1] |
1 |
[8, 234, 13681] |
35 |
C35 |
26) |
[8, 386, 35449] |
[1] |
1 |
[8, 386, 35449] |
35 |
C35 |
27) |
[8, 902, 184969] |
[1] |
1 |
[8, 902, 184969] |
35 |
C35 |
28) |
[8, 998, 192553] |
[1] |
1 |
[8, 998, 192553] |
35 |
C35 |
29) |
[8, 1090, 288313] |
[1] |
1 |
[8, 1090, 288313] |
35 |
C35 |
30) |
[8, 598, 70969] |
[1] |
1 |
[8, 598, 70969] |
35 |
C35 |
31) |
[8, 510, 35257] |
[1] |
2 |
[8, 510, 35257] |
70 |
C70 |
32) |
[8, 334, 26737] |
[1] |
1 |
[8, 334, 26737] |
35 |
C35 |
33) |
[8, 1206, 263257] |
[1] |
1 |
[8, 1206, 263257] |
35 |
C35 |
34) |
[8, 646, 101737] |
[1] |
1 |
[8, 646, 101737] |
35 |
C35 |
35) |
[5, 228, 10996] |
[1] |
2 |
[5, 228, 10996] |
70 |
C70 |
36) |
[5, 353, 31121] |
[1] |
1 |
[5, 353, 31121] |
35 |
C35 |
37) |
[5, 351, 29269] |
[1] |
2 |
[5, 351, 29269] |
70 |
C70 |
38) |
[5, 761, 132529] |
[1] |
1 |
[5, 761, 132529] |
35 |
C35 |
39) |
[5, 553, 70501] |
[1] |
1 |
[5, 553, 70501] |
35 |
C35 |
40) |
[5, 337, 26681] |
[1] |
1 |
[5, 337, 26681] |
35 |
C35 |
41) |
[5, 622, 92801] |
[1] |
1 |
[5, 622, 92801] |
35 |
C35 |
42) |
[5, 393, 33961] |
[1] |
1 |
[5, 393, 33961] |
35 |
C35 |
43) |
[5, 749, 138349] |
[1] |
1 |
[5, 749, 138349] |
35 |
C35 |
44) |
[5, 318, 24001] |
[1] |
1 |
[5, 318, 24001] |
35 |
C35 |
45) |
[5, 537, 68581] |
[1] |
1 |
[5, 537, 68581] |
35 |
C35 |
46) |
[5, 1129, 312709] |
[1] |
1 |
[5, 1129, 312709] |
35 |
C35 |
47) |
[5, 677, 109621] |
[1] |
1 |
[5, 677, 109621] |
35 |
C35 |
48) |
[5, 493, 56701] |
[1] |
1 |
[5, 493, 56701] |
35 |
C35 |
49) |
[5, 1041, 218389] |
[1] |
1 |
[5, 1041, 218389] |
35 |
C35 |
50) |
[5, 681, 114229] |
[1] |
1 |
[5, 681, 114229] |
35 |
C35 |
51) |
[5, 1161, 293269] |
[1] |
1 |
[5, 1161, 293269] |
35 |
C35 |
52) |
[5, 534, 66169] |
[1] |
1 |
[5, 534, 66169] |
35 |
C35 |
53) |
[5, 319, 22189] |
[1] |
2 |
[5, 319, 22189] |
70 |
C70 |
54) |
[5, 921, 212029] |
[1] |
1 |
[5, 921, 212029] |
35 |
C35 |
55) |
[5, 273, 16921] |
[1] |
1 |
[5, 273, 16921] |
35 |
C35 |
56) |
[5, 874, 189349] |
[1] |
1 |
[5, 874, 189349] |
35 |
C35 |
57) |
[5, 382, 35201] |
[1] |
1 |
[5, 382, 35201] |
35 |
C35 |
58) |
[5, 303, 22501] |
[1] |
2 |
[5, 303, 22501] |
70 |
C70 |
59) |
[5, 966, 232569] |
[1] |
2 |
[5, 966, 232569] |
70 |
C70 |
60) |
[5, 581, 74929] |
[1] |
1 |
[5, 581, 74929] |
35 |
C35 |
61) |
[5, 614, 76249] |
[1] |
1 |
[5, 614, 76249] |
35 |
C35 |
62) |
[5, 562, 64381] |
[1] |
1 |
[5, 562, 64381] |
35 |
C35 |
63) |
[5, 262, 15541] |
[1] |
2 |
[5, 262, 15541] |
70 |
C70 |
64) |
[5, 589, 86629] |
[1] |
1 |
[5, 589, 86629] |
35 |
C35 |
65) |
[5, 398, 39521] |
[1] |
1 |
[5, 398, 39521] |
35 |
C35 |
66) |
[5, 781, 141209] |
[1] |
1 |
[5, 781, 141209] |
35 |
C35 |
67) |
[5, 342, 25321] |
[1] |
1 |
[5, 342, 25321] |
35 |
C35 |
68) |
[5, 597, 87201] |
[1] |
2 |
[5, 597, 87201] |
70 |
C70 |
69) |
[5, 762, 137941] |
[1] |
1 |
[5, 762, 137941] |
35 |
C35 |
70) |
[5, 646, 97849] |
[1] |
1 |
[5, 646, 97849] |
35 |
C35 |
71) |
[5, 601, 90089] |
[1] |
1 |
[5, 601, 90089] |
35 |
C35 |
72) |
[5, 502, 57881] |
[1] |
1 |
[5, 502, 57881] |
35 |
C35 |
73) |
[5, 429, 44809] |
[1] |
1 |
[5, 429, 44809] |
35 |
C35 |
74) |
[5, 1197, 340501] |
[1] |
2 |
[5, 1197, 340501] |
70 |
C70 |
75) |
[5, 829, 158029] |
[1] |
1 |
[5, 829, 158029] |
35 |
C35 |
76) |
[5, 457, 49681] |
[1] |
1 |
[5, 457, 49681] |
35 |
C35 |
77) |
[29, 325, 16481] |
[1] |
1 |
[29, 325, 16481] |
35 |
C35 |
78) |
[29, 525, 48541] |
[1] |
1 |
[29, 525, 48541] |
35 |
C35 |
79) |
[29, 149, 4673] |
[1] |
1 |
[29, 149, 4673] |
35 |
C35 |
80) |
[29, 178, 1396] |
[1] |
2 |
[29, 178, 1396] |
70 |
C70 |
81) |
[1613, 205, 425] |
[1] |
2 |
[1613, 205, 425] |
70 |
C70 |
82) |
[953, 191, 6976] |
[1] |
1 |
[953, 191, 6976] |
35 |
C35 |
83) |
[1549, 237, 4361] |
[1] |
1 |
[1549, 237, 4361] |
35 |
C35 |
84) |
[877, 545, 56497] |
[1] |
1 |
[877, 545, 56497] |
35 |
C35 |
85) |
[428, 222, 1621] |
[1] |
2 |
[428, 222, 1621] |
70 |
C70 |
86) |
[113, 726, 16057] |
[1] |
1 |
[113, 726, 16057] |
35 |
C35 |
87) |
[89, 426, 2293] |
[1] |
1 |
[89, 426, 2293] |
35 |
C35 |
88) |
[53, 330, 21925] |
[1] |
2 |
[53, 330, 21925] |
70 |
C70 |
89) |
[53, 362, 30853] |
[1] |
1 |
[53, 362, 30853] |
35 |
C35 |
90) |
[53, 337, 12161] |
[1] |
1 |
[53, 337, 12161] |
35 |
C35 |
91) |
[53, 357, 28881] |
[1] |
2 |
[53, 357, 28881] |
70 |
C70 |
92) |
[37, 153, 4289] |
[1] |
1 |
[37, 153, 4289] |
35 |
C35 |
93) |
[37, 117, 2969] |
[1] |
1 |
[37, 117, 2969] |
35 |
C35 |
94) |
[37, 845, 176425] |
[1] |
2 |
[37, 845, 176425] |
70 |
C70 |
95) |
[293, 966, 3577] |
[1] |
2 |
[293, 966, 3577] |
70 |
C70 |
96) |
[61, 141, 2393] |
[1] |
1 |
[61, 141, 2393] |
35 |
C35 |
97) |
[61, 225, 12641] |
[1] |
1 |
[61, 225, 12641] |
35 |
C35 |
98) |
[17, 758, 104473] |
[1] |
1 |
[17, 758, 104473] |
35 |
C35 |
99) |
[17, 1175, 338692] |
[1] |
1 |
[17, 1175, 338692] |
35 |
C35 |
100) |
[17, 966, 124489] |
[1] |
1 |
[17, 966, 124489] |
35 |
C35 |
101) |
[17, 1206, 85081] |
[1] |
1 |
[17, 1206, 85081] |
35 |
C35 |
102) |
[17, 1807, 811684] |
[1] |
1 |
[17, 1807, 811684] |
35 |
C35 |
103) |
[17, 1350, 428425] |
[1] |
2 |
[17, 1350, 428425] |
70 |
C70 |
104) |
[17, 178, 7309] |
[1] |
1 |
[17, 178, 7309] |
35 |
C35 |
105) |
[17, 1543, 563044] |
[1] |
1 |
[17, 1543, 563044] |
35 |
C35 |
106) |
[373, 69, 1097] |
[1] |
1 |
[373, 69, 1097] |
35 |
C35 |
107) |
[173, 802, 5101] |
[1] |
1 |
[173, 802, 5101] |
35 |
C35 |
108) |
[773, 1337, 361669] |
[1] |
2 |
[773, 1337, 361669] |
70 |
C70 |
109) |
[181, 161, 6073] |
[1] |
1 |
[181, 161, 6073] |
35 |
C35 |
110) |
[1013, 53, 449] |
[1] |
1 |
[1013, 53, 449] |
35 |
C35 |
111) |
[44, 300, 13876] |
[1] |
2 |
[44, 300, 13876] |
70 |
C70 |
112) |
[44, 238, 4261] |
[1] |
2 |
[44, 238, 4261] |
70 |
C70 |
113) |
[389, 286, 14225] |
[1] |
1 |
[389, 286, 14225] |
35 |
C35 |
114) |
[389, 301, 769] |
[1] |
1 |
[389, 301, 769] |
35 |
C35 |
115) |
[613, 350, 20817] |
[1] |
1 |
[613, 350, 20817] |
35 |
C35 |
116) |
[1097, 975, 7012] |
[1] |
1 |
[1097, 975, 7012] |
35 |
C35 |
117) |
[41, 354, 3613] |
[1] |
1 |
[41, 354, 3613] |
35 |
C35 |
118) |
[41, 1319, 377284] |
[1] |
1 |
[41, 1319, 377284] |
35 |
C35 |
119) |
[41, 582, 19081] |
[1] |
1 |
[41, 582, 19081] |
35 |
C35 |
120) |
[41, 630, 96601] |
[1] |
1 |
[41, 630, 96601] |
35 |
C35 |
121) |
[101, 201, 9873] |
[1] |
2 |
[101, 201, 9873] |
70 |
C70 |
122) |
[1949, 49, 113] |
[1] |
1 |
[1949, 49, 113] |
35 |
C35 |