| 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 |
| 15.1.196421600341796875.1 |
$x^{15} - x^{10} + 1$ |
$15$ |
[1,7] |
$-\,5^{15}\cdot 23^{5}$ |
$2$ |
$14.2193348993$ |
$34.72138363576141$ |
|
|
✓ |
$C_5^2:(C_4\times S_3)$ (as 15T27) |
trivial |
$2$ |
$7$ |
$358.947276162$ |
| 15.1.873692352294921875.1 |
$x^{15} + x^{5} - 1$ |
$15$ |
[1,7] |
$-\,5^{15}\cdot 31^{5}$ |
$2$ |
$15.706903262$ |
$40.310107120236324$ |
|
|
✓ |
$C_5^2:(C_4\times S_3)$ (as 15T27) |
trivial |
$2$ |
$7$ |
$890.572745674$ |
| 15.1.503...000.1 |
$x^{15} - x^{10} + x^{5} + 1$ |
$15$ |
[1,7] |
$-\,2^{10}\cdot 5^{15}\cdot 11^{5}$ |
$3$ |
$17.651741676630316$ |
$38.11677176459088$ |
|
|
✓ |
$C_5^2:(C_4\times S_3)$ (as 15T27) |
trivial |
$2$ |
$7$ |
$2893.5472483909075$ |
| 15.3.615...000.1 |
$x^{15} - 7 x^{10} + 9 x^{5} + 1$ |
$15$ |
[3,6] |
$2^{10}\cdot 5^{9}\cdot 79^{5}$ |
$3$ |
$17.8900284058$ |
$59.438938453253584$ |
|
|
? |
$C_5^2:(C_4\times S_3)$ (as 15T27) |
trivial |
$2$ |
$8$ |
$8138.95877003$ |
| 15.5.103...875.1 |
$x^{15} - 15 x^{13} + 90 x^{11} - 3 x^{10} - 275 x^{9} + 30 x^{8} + 450 x^{7} - 105 x^{6} - 373 x^{5} + 150 x^{4} + 115 x^{3} - 75 x^{2} + 10 x + 1$ |
$15$ |
[5,5] |
$-\,5^{15}\cdot 23^{7}$ |
$2$ |
$21.5994650145$ |
$34.72138363576141$ |
|
|
✓ |
$C_5^2:(C_4\times S_3)$ (as 15T27) |
trivial |
$2$ |
$9$ |
$21869.311632$ |
| 15.5.608...000.1 |
$x^{15} - 15 x^{13} + 90 x^{11} - x^{10} - 275 x^{9} + 10 x^{8} + 450 x^{7} - 35 x^{6} - 376 x^{5} + 50 x^{4} + 130 x^{3} - 25 x^{2} - 5 x - 1$ |
$15$ |
[5,5] |
$-\,2^{10}\cdot 5^{15}\cdot 11^{7}$ |
$3$ |
$24.3018827503$ |
$38.11677176459088$ |
|
|
✓ |
$C_5^2:(C_4\times S_3)$ (as 15T27) |
trivial |
$2$ |
$9$ |
$93323.0722574$ |
| 15.3.216...000.1 |
$x^{15} - x^{10} - 5 x^{5} + 1$ |
$15$ |
[3,6] |
$2^{10}\cdot 5^{15}\cdot 37^{5}$ |
$3$ |
$26.4478623635$ |
$69.90699452642565$ |
|
|
? |
$C_5^2:(C_4\times S_3)$ (as 15T27) |
trivial |
$2$ |
$8$ |
$120917.551662$ |
| 15.15.246...000.1 |
$x^{15} - 30 x^{13} + 360 x^{11} - 26 x^{10} - 2200 x^{9} + 520 x^{8} + 7200 x^{7} - 3640 x^{6} - 11790 x^{5} + 10400 x^{4} + 5900 x^{3} - 10400 x^{2} + 4200 x - 496$ |
$15$ |
[15,0] |
$2^{18}\cdot 5^{15}\cdot 79^{5}$ |
$3$ |
$49.2888134008$ |
$169.81992506527055$ |
|
|
? |
$C_5^2:(C_4\times S_3)$ (as 15T27) |
trivial |
$2$ |
$14$ |
$303823085.333$ |
| 15.15.153...000.1 |
$x^{15} - 50 x^{13} + 890 x^{11} - 174 x^{10} - 7300 x^{9} + 2960 x^{8} + 28900 x^{7} - 14660 x^{6} - 55334 x^{5} + 26400 x^{4} + 47920 x^{3} - 12800 x^{2} - 16000 x - 2176$ |
$15$ |
[15,0] |
$2^{18}\cdot 5^{15}\cdot 79^{7}$ |
$3$ |
$88.2602815277$ |
$169.81992506527055$ |
|
|
? |
$C_5^2:(C_4\times S_3)$ (as 15T27) |
trivial |
$2$ |
$14$ |
$18287336542.5$ |
