| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Narrow class group |
Unit group torsion |
Unit group rank |
Regulator |
| 13.1.101439097511492601.1 |
$x^{13} - 4 x^{12} + 10 x^{11} - 25 x^{10} + 52 x^{9} - 75 x^{8} + 90 x^{7} - 113 x^{6} + 114 x^{5} - 65 x^{4} + 10 x^{3} + 37 x^{2} - 19 x - 10$ |
$13$ |
[1,6] |
$3^{6}\cdot 7^{8}\cdot 17^{6}$ |
$3$ |
$20.3315104648$ |
$26.132669826287227$ |
|
|
? |
$C_{13}:C_6$ (as 13T5) |
trivial |
trivial |
$2$ |
$6$ |
$4878.48838792$ |
| 13.1.234...625.1 |
$x^{13} - 2 x^{12} + 9 x^{11} - 23 x^{10} + 58 x^{9} - 93 x^{8} + 156 x^{7} - 183 x^{6} + 105 x^{5} + 7 x^{4} + 7 x^{3} - 42 x^{2} + 7 x + 7$ |
$13$ |
[1,6] |
$3^{12}\cdot 5^{6}\cdot 7^{10}$ |
$3$ |
$25.8878852921$ |
$31.199884665023223$ |
|
|
? |
$C_{13}:C_6$ (as 13T5) |
trivial |
trivial |
$2$ |
$6$ |
$30169.0835469$ |
| 13.13.567...184.1 |
$x^{13} - 117 x^{11} - 26 x^{10} + 3692 x^{9} + 2938 x^{8} - 38987 x^{7} - 54314 x^{6} + 137670 x^{5} + 290524 x^{4} - 5824 x^{3} - 298948 x^{2} - 169403 x - 13406$ |
$13$ |
[13,0] |
$2^{12}\cdot 3^{6}\cdot 13^{20}$ |
$3$ |
$162.870584734$ |
$204.39719270911772$ |
|
|
? |
$C_{13}:C_6$ (as 13T5) |
trivial |
trivial |
$2$ |
$12$ |
$95460081074.3$ |
| 13.13.170...729.1 |
$x^{13} - 78 x^{11} + 1989 x^{9} - 1326 x^{8} - 21255 x^{7} + 33813 x^{6} + 68328 x^{5} - 216723 x^{4} + 191178 x^{3} - 51948 x^{2} - 5850 x + 1875$ |
$13$ |
[13,0] |
$3^{12}\cdot 13^{22}$ |
$2$ |
$211.618934626$ |
$249.4371574945215$ |
|
|
? |
$C_{13}:C_6$ (as 13T5) |
trivial |
trivial |
$2$ |
$12$ |
$394704115709$ |
