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 170 Igusa CM invariants of non-normal (D4) fields: 34
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[229, 29, 153] |
[17] |
1 |
[229, 29, 153] |
15 |
C15 |
2) |
[137, 1303, 409348] |
[1] |
1 |
[137, 1303, 409348] |
85 |
C85 |
3) |
[109, 541, 17989] |
[1] |
1 |
[109, 541, 17989] |
85 |
C85 |
4) |
[8, 1778, 789673] |
[1] |
1 |
[8, 1778, 789673] |
85 |
C85 |
5) |
[8, 1826, 831769] |
[1] |
1 |
[8, 1826, 831769] |
85 |
C85 |
6) |
[8, 1698, 719833] |
[1] |
1 |
[8, 1698, 719833] |
85 |
C85 |
7) |
[8, 1542, 593641] |
[1] |
1 |
[8, 1542, 593641] |
85 |
C85 |
8) |
[8, 1666, 685177] |
[1] |
1 |
[8, 1666, 685177] |
85 |
C85 |
9) |
[8, 1218, 337081] |
[1] |
1 |
[8, 1218, 337081] |
85 |
C85 |
10) |
[8, 414, 42337] |
[1] |
1 |
[8, 414, 42337] |
85 |
C85 |
11) |
[5, 1217, 367021] |
[1] |
1 |
[5, 1217, 367021] |
85 |
C85 |
12) |
[5, 1577, 620821] |
[1] |
1 |
[5, 1577, 620821] |
85 |
C85 |
13) |
[5, 1461, 479029] |
[1] |
1 |
[5, 1461, 479029] |
85 |
C85 |
14) |
[5, 1566, 581089] |
[1] |
1 |
[5, 1566, 581089] |
85 |
C85 |
15) |
[5, 1734, 743689] |
[1] |
1 |
[5, 1734, 743689] |
85 |
C85 |
16) |
[5, 1257, 393301] |
[1] |
1 |
[5, 1257, 393301] |
85 |
C85 |
17) |
[5, 1437, 480541] |
[1] |
1 |
[5, 1437, 480541] |
85 |
C85 |
18) |
[5, 993, 222361] |
[1] |
1 |
[5, 993, 222361] |
85 |
C85 |
19) |
[29, 1269, 289309] |
[1] |
1 |
[29, 1269, 289309] |
85 |
C85 |
20) |
[29, 990, 77521] |
[1] |
1 |
[29, 990, 77521] |
85 |
C85 |
21) |
[29, 769, 147253] |
[1] |
1 |
[29, 769, 147253] |
85 |
C85 |
22) |
[313, 535, 70852] |
[1] |
1 |
[313, 535, 70852] |
85 |
C85 |
23) |
[89, 1230, 376801] |
[1] |
1 |
[89, 1230, 376801] |
85 |
C85 |
24) |
[53, 862, 63649] |
[1] |
1 |
[53, 862, 63649] |
85 |
C85 |
25) |
[617, 1023, 72676] |
[1] |
1 |
[617, 1023, 72676] |
85 |
C85 |
26) |
[17, 1398, 471193] |
[1] |
1 |
[17, 1398, 471193] |
85 |
C85 |
27) |
[17, 1838, 842113] |
[1] |
1 |
[17, 1838, 842113] |
85 |
C85 |
28) |
[17, 1518, 562753] |
[1] |
1 |
[17, 1518, 562753] |
85 |
C85 |
29) |
[769, 1015, 48196] |
[1] |
1 |
[769, 1015, 48196] |
85 |
C85 |
30) |
[233, 871, 163972] |
[1] |
1 |
[233, 871, 163972] |
85 |
C85 |
31) |
[41, 1174, 320953] |
[1] |
1 |
[41, 1174, 320953] |
85 |
C85 |
32) |
[41, 1790, 795121] |
[1] |
1 |
[41, 1790, 795121] |
85 |
C85 |
33) |
[2213, 833, 168493] |
[1] |
1 |
[2213, 833, 168493] |
255 |
C255 |
34) |
[353, 343, 9556] |
[1] |
1 |
[353, 343, 9556] |
85 |
C85 |