| 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 |
| 15.3.19664802801826816.1 |
$x^{15} - 5 x^{14} + 14 x^{13} - 23 x^{12} + 19 x^{11} + 7 x^{10} - 41 x^{9} + 47 x^{8} - 10 x^{7} - 39 x^{6} + 50 x^{5} - 18 x^{4} - 16 x^{3} + 21 x^{2} - 9 x + 1$ |
$15$ |
[3,6] |
$2^{10}\cdot 79^{7}$ |
$2$ |
$12.1968019833$ |
$17.776388834631177$ |
|
|
? |
$D_5\times S_3$ (as 15T7) |
trivial |
$2$ |
$8$ |
$103.698212623$ |
| 15.1.69378727128301847.1 |
$x^{15} - 2 x^{14} + 2 x^{13} - 2 x^{12} + 2 x^{11} - 4 x^{10} + 3 x^{9} + 2 x^{8} + x^{7} - 5 x^{6} + 3 x^{5} + 3 x^{4} + 6 x^{3} + 2 x^{2} - 1$ |
$15$ |
[1,7] |
$-\,23^{5}\cdot 47^{6}$ |
$2$ |
$13.266257472$ |
$32.87856444554719$ |
|
|
? |
$D_5\times S_3$ (as 15T7) |
trivial |
$2$ |
$7$ |
$185.949282778$ |
| 15.1.96318312824155136.1 |
$x^{15} - 6 x^{14} + 19 x^{13} - 39 x^{12} + 58 x^{11} - 67 x^{10} + 68 x^{9} - 69 x^{8} + 65 x^{7} - 52 x^{6} + 33 x^{5} - 20 x^{4} + 12 x^{3} - 4 x^{2} + 3 x - 1$ |
$15$ |
[1,7] |
$-\,2^{10}\cdot 11^{7}\cdot 13^{6}$ |
$3$ |
$13.5596118481$ |
$18.982555683309183$ |
|
|
? |
$D_5\times S_3$ (as 15T7) |
trivial |
$2$ |
$7$ |
$226.323474369$ |
| 15.3.126064044311049216.1 |
$x^{15} - 4 x^{14} + 3 x^{13} + 15 x^{12} - 40 x^{11} + 23 x^{10} + 52 x^{9} - 111 x^{8} + 83 x^{7} - 67 x^{5} + 86 x^{4} - 62 x^{3} + 26 x^{2} - 7 x + 1$ |
$15$ |
[3,6] |
$2^{10}\cdot 3^{5}\cdot 47^{7}$ |
$3$ |
$13.8050955127$ |
$18.849343120394256$ |
|
|
? |
$D_5\times S_3$ (as 15T7) |
trivial |
$2$ |
$8$ |
$280.863045663$ |
| 15.5.405...643.1 |
$x^{15} - 3 x^{14} - x^{13} - 4 x^{12} + 10 x^{11} + 25 x^{10} + 36 x^{9} - 46 x^{8} - 111 x^{7} - 151 x^{6} + 138 x^{5} + 181 x^{4} - 15 x^{3} - 52 x^{2} - 24 x + 3$ |
$15$ |
[5,5] |
$-\,3^{5}\cdot 401^{7}$ |
$2$ |
$23.6505434997$ |
$34.68429039204925$ |
|
|
|
$D_5\times S_3$ (as 15T7) |
trivial |
$2$ |
$9$ |
$77823.7688685$ |
| 15.5.145...951.1 |
$x^{15} - 4 x^{14} + x^{13} + 10 x^{12} - 18 x^{11} + 78 x^{10} - 154 x^{9} + 13 x^{8} + 122 x^{7} + 108 x^{6} - 197 x^{5} - 61 x^{4} + 98 x^{3} + 38 x^{2} - 21 x - 7$ |
$15$ |
[5,5] |
$-\,7^{6}\cdot 199^{7}$ |
$2$ |
$25.7535627774$ |
$37.322915213043046$ |
|
|
|
$D_5\times S_3$ (as 15T7) |
trivial |
$2$ |
$9$ |
$145057.542197$ |
| 15.15.205...617.1 |
$x^{15} - 2 x^{14} - 31 x^{13} + 56 x^{12} + 340 x^{11} - 528 x^{10} - 1654 x^{9} + 2135 x^{8} + 3636 x^{7} - 3826 x^{6} - 3451 x^{5} + 2550 x^{4} + 1492 x^{3} - 478 x^{2} - 258 x - 25$ |
$15$ |
[15,0] |
$11^{5}\cdot 19^{6}\cdot 43^{7}$ |
$3$ |
$41.7751112097$ |
$94.79978902930111$ |
|
|
? |
$D_5\times S_3$ (as 15T7) |
trivial |
$2$ |
$14$ |
$23004967.3416$ |
| 15.15.497...584.1 |
$x^{15} - 3 x^{14} - 36 x^{13} + 166 x^{12} + 118 x^{11} - 1666 x^{10} + 2156 x^{9} + 2800 x^{8} - 7863 x^{7} + 2941 x^{6} + 4612 x^{5} - 3330 x^{4} - 348 x^{3} + 428 x^{2} + 16 x - 8$ |
$15$ |
[15,0] |
$2^{18}\cdot 11^{6}\cdot 101^{7}$ |
$3$ |
$51.6586489011$ |
$83.99053681782655$ |
|
|
|
$D_5\times S_3$ (as 15T7) |
trivial |
$2$ |
$14$ |
$754734243.281$ |
