| 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 |
| 15.3.1788527348449625.1 |
$x^{15} - 2 x^{14} + 4 x^{13} - 9 x^{12} + 13 x^{11} - 15 x^{10} + 18 x^{9} - 23 x^{8} + 33 x^{7} - 44 x^{6} + 48 x^{5} - 44 x^{4} + 30 x^{3} - 16 x^{2} + 6 x - 1$ |
$15$ |
[3,6] |
$5^{3}\cdot 7^{10}\cdot 37^{3}$ |
$3$ |
$10.3952045383$ |
$49.77193869732466$ |
|
|
? |
$S_5 \times C_3$ (as 15T24) |
trivial |
$2$ |
$8$ |
$26.5068203244$ |
| 15.3.4864965285308625.1 |
$x^{15} - 3 x^{14} + 6 x^{13} - 12 x^{12} + 14 x^{11} - 17 x^{10} + 24 x^{9} - 28 x^{8} + 31 x^{7} - 21 x^{6} + 18 x^{5} - 15 x^{4} + 16 x^{3} - 11 x^{2} + 5 x - 1$ |
$15$ |
[3,6] |
$3^{9}\cdot 5^{3}\cdot 7^{11}$ |
$3$ |
$11.1123347675$ |
$40.77320330425099$ |
|
|
? |
$S_5 \times C_3$ (as 15T24) |
trivial |
$2$ |
$8$ |
$50.4138149085$ |
| 15.9.137...247.1 |
$x^{15} - 4 x^{14} - 5 x^{13} + 39 x^{12} - 17 x^{11} - 126 x^{10} + 132 x^{9} + 157 x^{8} - 232 x^{7} - 95 x^{6} + 178 x^{5} + 49 x^{4} - 76 x^{3} - 19 x^{2} + 18 x - 1$ |
$15$ |
[9,3] |
$-\,7^{12}\cdot 463^{3}$ |
$2$ |
$16.1880534698$ |
$108.9027538962374$ |
|
|
? |
$S_5 \times C_3$ (as 15T24) |
trivial |
$2$ |
$11$ |
$3175.51632285$ |
| 15.9.313...727.1 |
$x^{15} - 3 x^{13} - 9 x^{12} - 9 x^{11} + 21 x^{10} + 3 x^{9} + 99 x^{7} + 63 x^{6} - 36 x^{5} - 9 x^{4} - 27 x^{2} - 18 x - 3$ |
$15$ |
[9,3] |
$-\,3^{24}\cdot 223^{3}$ |
$2$ |
$17.1023181075$ |
$86.6056925809443$ |
|
|
? |
$S_5 \times C_3$ (as 15T24) |
trivial |
$2$ |
$11$ |
$6161.99584614$ |
| 15.9.369...824.1 |
$x^{15} - 5 x^{14} + 14 x^{13} - 35 x^{12} + 70 x^{11} - 112 x^{10} + 154 x^{9} - 206 x^{8} + 267 x^{7} - 175 x^{6} - 70 x^{5} + 133 x^{4} - 21 x^{3} - 21 x^{2} + 4 x + 1$ |
$15$ |
[9,3] |
$-\,2^{12}\cdot 7^{14}\cdot 11^{3}$ |
$3$ |
$17.292616263055855$ |
$45.77793254465407$ |
|
|
? |
$S_5 \times C_3$ (as 15T24) |
trivial |
$2$ |
$11$ |
$6210.486465420129$ |
| 15.15.585...473.1 |
$x^{15} - x^{14} - 21 x^{13} + 10 x^{12} + 165 x^{11} - 14 x^{10} - 597 x^{9} - 103 x^{8} + 994 x^{7} + 271 x^{6} - 683 x^{5} - 92 x^{4} + 197 x^{3} - 24 x^{2} - 7 x + 1$ |
$15$ |
[15,0] |
$3^{6}\cdot 7^{10}\cdot 13^{3}\cdot 109^{3}$ |
$4$ |
$24.2393609186$ |
$238.58560980444312$ |
|
|
? |
$S_5 \times C_3$ (as 15T24) |
trivial |
$2$ |
$14$ |
$246980.524869$ |
| 15.15.100...672.1 |
$x^{15} - 5 x^{14} - 9 x^{13} + 71 x^{12} + 3 x^{11} - 367 x^{10} + 187 x^{9} + 827 x^{8} - 660 x^{7} - 740 x^{6} + 816 x^{5} + 86 x^{4} - 327 x^{3} + 127 x^{2} - 19 x + 1$ |
$15$ |
[15,0] |
$2^{12}\cdot 7^{11}\cdot 499^{3}$ |
$3$ |
$25.1294317673$ |
$253.8050745604599$ |
|
|
? |
$S_5 \times C_3$ (as 15T24) |
trivial |
$2$ |
$14$ |
$377551.758655$ |
| 15.9.134...128.1 |
$x^{15} - 3 x^{14} - 8 x^{13} + 43 x^{12} - 98 x^{11} + 206 x^{10} - 138 x^{9} - 450 x^{8} + 935 x^{7} - 737 x^{6} - 670 x^{5} + 1953 x^{4} + 601 x^{3} - 913 x^{2} - 428 x - 43$ |
$15$ |
[9,3] |
$-\,2^{18}\cdot 3^{12}\cdot 7^{13}$ |
$3$ |
$29.87798465767787$ |
$40.54293644764779$ |
|
|
? |
$S_5 \times C_3$ (as 15T24) |
trivial |
$2$ |
$11$ |
$654074.2800450686$ |
| 15.3.319...896.1 |
$x^{15} - 3 x^{14} - 4 x^{13} + 5 x^{12} - 48 x^{11} - 28 x^{10} - 78 x^{9} + 18 x^{8} - 65 x^{7} - 67 x^{6} - 198 x^{5} - 279 x^{4} - 203 x^{3} - 57 x^{2} - 4 x + 1$ |
$15$ |
[3,6] |
$2^{24}\cdot 3^{9}\cdot 7^{13}$ |
$3$ |
$31.647473671903036$ |
$60.918023157039514$ |
|
|
? |
$S_5 \times C_3$ (as 15T24) |
trivial |
$2$ |
$8$ |
$268487.3246402653$ |
| 15.3.581...808.1 |
$x^{15} - 6 x^{14} - 9 x^{13} + 95 x^{12} + 21 x^{11} - 648 x^{10} + 343 x^{9} + 2313 x^{8} - 2322 x^{7} - 3770 x^{6} + 5754 x^{5} + 6498 x^{4} - 13405 x^{3} + 1362 x^{2} + 13041 x - 9629$ |
$15$ |
[3,6] |
$2^{18}\cdot 3^{23}\cdot 11^{9}$ |
$3$ |
$52.198440709420495$ |
$97.28177676525554$ |
|
|
? |
$S_5 \times C_3$ (as 15T24) |
trivial |
$2$ |
$8$ |
$14440406.83035929$ |
| 15.15.108...117.1 |
$x^{15} - 5 x^{14} - 42 x^{13} + 203 x^{12} + 595 x^{11} - 3150 x^{10} - 3122 x^{9} + 22950 x^{8} + 1310 x^{7} - 79947 x^{6} + 32585 x^{5} + 128275 x^{4} - 86317 x^{3} - 70917 x^{2} + 65258 x - 10429$ |
$15$ |
[15,0] |
$7^{13}\cdot 11^{9}\cdot 41^{6}$ |
$3$ |
$100.54661520780213$ |
$230.2022931787676$ |
|
|
|
$S_5 \times C_3$ (as 15T24) |
trivial |
$2$ |
$14$ |
$22895742068.330822$ |
