| 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 |
| 17.1.463...841.1 |
$x^{17} - x^{16} - x^{15} - x^{14} + x^{12} + 13 x^{11} + 7 x^{10} + 11 x^{9} + 4 x^{8} + x^{7} + 7 x^{6} + 23 x^{5} + 31 x^{4} + 42 x^{3} + 24 x^{2} + 6 x - 1$ |
$17$ |
[1,8] |
$383^{8}$ |
$1$ |
$16.4294472544$ |
$19.570385790780925$ |
|
|
? |
$D_{17}$ (as 17T2) |
trivial |
$2$ |
$8$ |
$2610.31631075$ |
| 17.1.930...721.1 |
$x^{17} - x^{16} + 4 x^{15} - 18 x^{14} + 11 x^{13} + 14 x^{12} + 21 x^{11} - 62 x^{10} + 14 x^{9} + 50 x^{8} + 54 x^{7} - 121 x^{6} - 7 x^{5} + 36 x^{4} + 64 x^{3} - 23 x^{2} + 43 x + 1$ |
$17$ |
[1,8] |
$991^{8}$ |
$1$ |
$25.6990467175$ |
$31.480152477394387$ |
|
|
|
$D_{17}$ (as 17T2) |
trivial |
$2$ |
$8$ |
$323467.453718$ |
| 17.1.183...561.1 |
$x^{17} - x^{16} + 5 x^{15} - 19 x^{14} + 26 x^{13} - 30 x^{12} + 44 x^{11} - 48 x^{10} + 39 x^{9} - 62 x^{8} + 30 x^{7} + 112 x^{6} - 4 x^{5} + 16 x^{4} - 62 x^{3} + 180 x^{2} + 35 x + 49$ |
$17$ |
[1,8] |
$13^{8}\cdot 83^{8}$ |
$2$ |
$26.7487941926$ |
$32.848135411313685$ |
|
|
? |
$D_{17}$ (as 17T2) |
trivial |
$2$ |
$8$ |
$257874.899874$ |
| 17.1.200...521.1 |
$x^{17} - 2 x^{16} + 4 x^{15} - 18 x^{14} + 10 x^{13} - 16 x^{12} + 44 x^{11} + 10 x^{10} + 72 x^{9} + 18 x^{8} + 134 x^{7} + 88 x^{6} + 275 x^{5} + 200 x^{4} + 220 x^{3} + 240 x^{2} + 80 x + 64$ |
$17$ |
[1,8] |
$1091^{8}$ |
$1$ |
$26.8883769874$ |
$33.03028912982749$ |
|
|
|
$D_{17}$ (as 17T2) |
trivial |
$2$ |
$8$ |
$1757145.67579$ |
| 17.1.105...401.1 |
$x^{17} - 3 x^{16} - 2 x^{15} + 24 x^{14} - 20 x^{13} - 80 x^{12} + 115 x^{11} + 27 x^{10} + 132 x^{9} - 302 x^{8} - 219 x^{7} - 172 x^{6} + 41 x^{5} - 25 x^{4} + 44 x^{3} + 39 x^{2} - 2 x - 23$ |
$17$ |
[1,8] |
$17^{8}\cdot 79^{8}$ |
$2$ |
$29.6507559794$ |
$36.64696440361739$ |
|
|
? |
$D_{17}$ (as 17T2) |
trivial |
$2$ |
$8$ |
$663161.006215$ |
| 17.1.160...625.1 |
$x^{17} - 4 x^{16} + x^{15} + 16 x^{14} - 30 x^{13} - 2 x^{12} + 88 x^{11} + 143 x^{10} + 133 x^{9} - 515 x^{8} - 803 x^{7} - 68 x^{6} + 1252 x^{5} + 2972 x^{4} + 2855 x^{3} + 1505 x^{2} + 550 x + 125$ |
$17$ |
[1,8] |
$5^{8}\cdot 283^{8}$ |
$2$ |
$30.3884754664$ |
$37.61648574760805$ |
|
|
|
$D_{17}$ (as 17T2) |
trivial |
$2$ |
$8$ |
$2534195.05633$ |
| 17.1.348...321.1 |
$x^{17} - 2 x^{16} - 3 x^{14} + 24 x^{13} + 18 x^{12} - 138 x^{10} - 203 x^{9} - 75 x^{8} + 352 x^{7} + 588 x^{6} + 384 x^{5} + 132 x^{4} + 493 x^{3} + 1015 x^{2} + 874 x + 337$ |
$17$ |
[1,8] |
$1559^{8}$ |
$1$ |
$31.8064953944$ |
$39.48417404479927$ |
|
|
? |
$D_{17}$ (as 17T2) |
trivial |
$2$ |
$8$ |
$432952.23952$ |
| 17.1.371...761.1 |
$x^{17} - x^{16} + 5 x^{15} + 9 x^{14} - 13 x^{13} + 17 x^{12} + 56 x^{11} - 62 x^{10} + 55 x^{9} - 535 x^{8} + 181 x^{7} - 1027 x^{6} + 661 x^{5} - 1041 x^{4} + 166 x^{3} - 416 x^{2} - 88 x - 16$ |
$17$ |
[1,8] |
$1571^{8}$ |
$1$ |
$31.921472057$ |
$39.63584236521283$ |
|
|
|
$D_{17}$ (as 17T2) |
trivial |
$2$ |
$8$ |
$8867681.2165$ |
| 17.1.584...121.1 |
$x^{17} - 2 x^{16} + 9 x^{15} - 23 x^{14} + 59 x^{13} - 112 x^{12} + 156 x^{11} - 49 x^{10} + 221 x^{9} - 25 x^{8} - 162 x^{7} - 4 x^{6} + 553 x^{5} + 1435 x^{4} + 1716 x^{3} + 1462 x^{2} + 615 x + 225$ |
$17$ |
[1,8] |
$1663^{8}$ |
$1$ |
$32.7879300307$ |
$40.779897008207364$ |
|
|
|
$D_{17}$ (as 17T2) |
trivial |
$2$ |
$8$ |
$3798575.81941$ |
| 17.1.102...241.1 |
$x^{17} - 7 x^{16} + 30 x^{15} - 61 x^{14} + 115 x^{13} - 158 x^{12} + 94 x^{11} - 111 x^{10} + 268 x^{9} - 411 x^{8} + 465 x^{7} - 473 x^{6} + 314 x^{5} - 109 x^{4} + 446 x^{3} - 498 x^{2} + 175 x + 1$ |
$17$ |
[1,8] |
$1783^{8}$ |
$1$ |
$33.8807935119$ |
$42.22558466143482$ |
|
|
|
$D_{17}$ (as 17T2) |
trivial |
$2$ |
$8$ |
$4818947.77807$ |
| 17.1.397...976.1 |
$x^{17} + 221 x^{15} - 850 x^{14} + 19601 x^{13} - 97036 x^{12} + 2452233 x^{11} - 5536254 x^{10} + 159332007 x^{9} - 1851117488 x^{8} + 12939379031 x^{7} - 45700927246 x^{6} + 12487240571 x^{5} + 217180838276 x^{4} - 328446625597 x^{3} + 138506493022 x^{2} + 2281813189964 x + 1767616042808$ |
$17$ |
[1,8] |
$2^{24}\cdot 17^{32}$ |
$2$ |
$550.963297739$ |
$585.7120239053163$ |
|
|
|
$D_{17}$ (as 17T2) |
$[17]$ |
$2$ |
$8$ |
$5054960379310000000$ |
| 17.17.544...441.1 |
$x^{17} - 3502 x^{15} - 21012 x^{14} + 3586048 x^{13} + 27140500 x^{12} - 1455974010 x^{11} - 13391942168 x^{10} + 247158969538 x^{9} + 2699830692822 x^{8} - 15367054046543 x^{7} - 210262575924428 x^{6} + 207808365630713 x^{5} + 5600534069106679 x^{4} + 891648638079425 x^{3} - 50160692092741008 x^{2} - 11309428987726617 x + 145001801906376687$ |
$17$ |
[17,0] |
$17^{24}\cdot 103^{16}$ |
$2$ |
$4280.94250015$ |
$4652.957318416284$ |
|
|
|
$D_{17}$ (as 17T2) |
$[17]$ |
$2$ |
$16$ |
$10720674608800000000000000$ |
