| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Unit group torsion |
Unit group rank |
Regulator |
| 9.1.155996093442686976.1 |
$x^{9} - 48 x^{6} + 54 x^{5} + 216 x^{4} + 408 x^{3} - 7488 x^{2} - 4491 x - 952$ |
$9$ |
[1,4] |
$2^{27}\cdot 3^{19}$ |
$2$ |
$81.3478294015$ |
$139.59713497350066$ |
|
|
? |
$(C_3^2:C_8):C_2$ (as 9T19) |
$[3]$ |
$2$ |
$4$ |
$181371.059066$ |
| 9.3.213...875.31 |
$x^{9} - 27 x^{7} - 3 x^{6} + 198 x^{5} + 549 x^{4} + 2244 x^{3} + 2592 x^{2} + 1053 x + 149$ |
$9$ |
[3,3] |
$-\,3^{19}\cdot 5^{6}\cdot 7^{6}$ |
$3$ |
$108.801448788$ |
$142.37911979255588$ |
|
|
? |
$(C_3^2:C_8):C_2$ (as 9T19) |
trivial |
$2$ |
$5$ |
$1257376.6678$ |
| 10.0.119015574220800000.1 |
$x^{10} - 4 x^{9} + 9 x^{8} - 36 x^{6} + 108 x^{5} - 27 x^{4} + 459 x^{2} + 72 x + 144$ |
$10$ |
[0,5] |
$-\,2^{15}\cdot 3^{19}\cdot 5^{5}$ |
$3$ |
$50.9988495959$ |
$120.34976961701426$ |
|
|
? |
$(A_6 : C_2) : C_2$ (as 10T35) |
$[2, 2]$ |
$2$ |
$4$ |
$63588.8617778$ |
| 10.0.119015574220800000.3 |
$x^{10} - 2 x^{9} + 12 x^{7} - 24 x^{6} - 276 x^{4} - 744 x^{3} + 864 x^{2} + 2944 x + 7504$ |
$10$ |
[0,5] |
$-\,2^{15}\cdot 3^{19}\cdot 5^{5}$ |
$3$ |
$50.9988495959$ |
$107.21945548028316$ |
|
|
? |
$(A_6 : C_2) : C_2$ (as 10T35) |
$[2]$ |
$2$ |
$4$ |
$112275.571319$ |
| 10.2.405528906976985088.1 |
$x^{10} - 5 x^{9} - 9 x^{8} + 54 x^{7} + 54 x^{6} - 180 x^{5} - 216 x^{4} + 90 x^{2} + 42 x + 6$ |
$10$ |
[2,4] |
$2^{18}\cdot 3^{19}\cdot 11^{3}$ |
$3$ |
$57.6503809871$ |
$178.50755587120256$ |
|
|
? |
$(A_6 : C_2) : C_2$ (as 10T35) |
trivial |
$2$ |
$5$ |
$446513.767964$ |
| 10.0.297...000.1 |
$x^{10} - 2 x^{9} - 12 x^{7} + 33 x^{6} + 21 x^{4} - 60 x^{3} + 216 x^{2} - 154 x + 101$ |
$10$ |
[0,5] |
$-\,2^{15}\cdot 3^{19}\cdot 5^{7}$ |
$3$ |
$70.3646254878$ |
$220.06907340902904$ |
|
|
? |
$(A_6 : C_2) : C_2$ (as 10T35) |
trivial |
$2$ |
$4$ |
$1229530.9813$ |
| 10.2.259...632.1 |
$x^{10} - x^{9} + 108 x^{7} - 918 x^{6} + 1638 x^{5} + 612 x^{4} + 2052 x^{3} - 4311 x^{2} + 5223 x - 8868$ |
$10$ |
[2,4] |
$2^{24}\cdot 3^{19}\cdot 11^{3}$ |
$3$ |
$87.3816375279$ |
$300.21272765559274$ |
|
|
|
$(A_6 : C_2) : C_2$ (as 10T35) |
$[2]$ |
$2$ |
$5$ |
$3648801.08999$ |
| 10.2.259...632.2 |
$x^{10} - 5 x^{9} - 18 x^{8} + 60 x^{7} + 492 x^{6} - 252 x^{5} - 5964 x^{4} - 3300 x^{3} + 11385 x^{2} - 2461 x - 3886$ |
$10$ |
[2,4] |
$2^{24}\cdot 3^{19}\cdot 11^{3}$ |
$3$ |
$87.3816375279$ |
$300.21272765559274$ |
|
|
|
$(A_6 : C_2) : C_2$ (as 10T35) |
trivial |
$2$ |
$5$ |
$15693384.5665$ |
| 10.4.207...056.2 |
$x^{10} - 2 x^{9} - 27 x^{8} + 72 x^{7} - 36 x^{6} + 216 x^{5} + 216 x^{4} - 864 x^{3} - 756 x^{2} - 2232 x - 2556$ |
$10$ |
[4,3] |
$-\,2^{27}\cdot 3^{19}\cdot 11^{3}$ |
$3$ |
$107.579414871$ |
$327.38430095295297$ |
|
|
? |
$(A_6 : C_2) : C_2$ (as 10T35) |
trivial |
$2$ |
$6$ |
$18932580.2488$ |
| 10.2.166...448.1 |
$x^{10} - 2 x^{9} + 9 x^{8} - 144 x^{7} - 900 x^{6} + 1080 x^{5} + 25380 x^{4} - 864 x^{3} + 96552 x^{2} + 289872 x - 430056$ |
$10$ |
[2,4] |
$2^{30}\cdot 3^{19}\cdot 11^{3}$ |
$3$ |
$132.44579561$ |
$462.99131851570104$ |
|
|
? |
$(A_6 : C_2) : C_2$ (as 10T35) |
trivial |
$2$ |
$5$ |
$44796788.2559$ |
| 10.2.445...536.1 |
$x^{10} - 2 x^{9} + 9 x^{8} + 72 x^{7} + 288 x^{6} - 216 x^{5} + 7560 x^{4} + 3672 x^{3} - 18387 x^{2} + 148446 x - 303939$ |
$10$ |
[2,4] |
$2^{27}\cdot 3^{19}\cdot 13^{4}$ |
$3$ |
$146.180254341$ |
$355.9042576357628$ |
|
|
? |
$(A_6 : C_2) : C_2$ (as 10T35) |
trivial |
$2$ |
$5$ |
$111118731.397$ |
| 10.4.941...448.1 |
$x^{10} - x^{9} - 36 x^{8} + 192 x^{7} + 1248 x^{6} - 2448 x^{5} - 25296 x^{4} - 25608 x^{3} + 120789 x^{2} + 299323 x + 182852$ |
$10$ |
[4,3] |
$-\,2^{24}\cdot 3^{19}\cdot 13^{6}$ |
$3$ |
$198.320854476$ |
$500.45111290090057$ |
|
|
|
$(A_6 : C_2) : C_2$ (as 10T35) |
trivial |
$2$ |
$6$ |
$1348921894.05$ |
| 10.2.752...584.1 |
$x^{10} - 4 x^{9} + 72 x^{8} + 48 x^{7} + 384 x^{6} - 4824 x^{5} + 72588 x^{4} - 335208 x^{3} + 343485 x^{2} + 1777276 x - 4817092$ |
$10$ |
[2,4] |
$2^{27}\cdot 3^{19}\cdot 13^{6}$ |
$3$ |
$244.161612038$ |
$545.745808439366$ |
|
|
? |
$(A_6 : C_2) : C_2$ (as 10T35) |
trivial |
$2$ |
$5$ |
$878490673.053$ |
| 10.2.155...000.1 |
$x^{10} - 2 x^{9} + 63 x^{8} - 504 x^{7} + 90 x^{6} - 27324 x^{5} + 107838 x^{4} + 82728 x^{3} + 2111751 x^{2} - 4990950 x - 181575$ |
$10$ |
[2,4] |
$2^{34}\cdot 3^{19}\cdot 5^{7}$ |
$3$ |
$262.610068069$ |
$740.2211797514364$ |
|
|
? |
$(A_6 : C_2) : C_2$ (as 10T35) |
trivial |
$2$ |
$5$ |
$1605409946.69$ |
| 10.4.221...288.1 |
$x^{10} - 18 x^{8} - 96 x^{7} - 90 x^{6} + 5904 x^{5} - 20904 x^{4} + 9216 x^{3} + 60273 x^{2} - 104048 x + 44946$ |
$10$ |
[4,3] |
$-\,2^{30}\cdot 3^{19}\cdot 11^{6}$ |
$3$ |
$271.929285802$ |
$690.4596364059256$ |
|
|
? |
$(A_6 : C_2) : C_2$ (as 10T35) |
trivial |
$2$ |
$6$ |
$2061026923.28$ |
