| 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 |
| 17.17.160...921.1 |
$x^{17} - x^{16} - 48 x^{15} + 105 x^{14} + 763 x^{13} - 2579 x^{12} - 3653 x^{11} + 23311 x^{10} - 11031 x^{9} - 74838 x^{8} + 107759 x^{7} + 50288 x^{6} - 198615 x^{5} + 102976 x^{4} + 58507 x^{3} - 75722 x^{2} + 25763 x - 2837$ |
$17$ |
[17,0] |
$103^{16}$ |
$1$ |
$78.4214801453$ |
$78.42148014526065$ |
|
✓ |
|
$C_{17}$ (as 17T1) |
trivial |
$2$ |
$16$ |
$30768108227.3$ |
| 17.17.154...041.1 |
$x^{17} - x^{16} - 64 x^{15} + 43 x^{14} + 1478 x^{13} - 932 x^{12} - 16008 x^{11} + 12183 x^{10} + 86347 x^{9} - 84507 x^{8} - 213223 x^{7} + 271237 x^{6} + 152800 x^{5} - 314540 x^{4} + 100605 x^{3} + 20132 x^{2} - 13981 x + 1681$ |
$17$ |
[17,0] |
$137^{16}$ |
$1$ |
$102.572542825$ |
$102.57254282521204$ |
|
✓ |
|
$C_{17}$ (as 17T1) |
trivial |
$2$ |
$16$ |
$559957546560$ |
| 17.17.113...161.1 |
$x^{17} - x^{16} - 112 x^{15} + 47 x^{14} + 3976 x^{13} - 4314 x^{12} - 64388 x^{11} + 136247 x^{10} + 422013 x^{9} - 1631073 x^{8} + 411840 x^{7} + 5840196 x^{6} - 11894369 x^{5} + 10635750 x^{4} - 4739804 x^{3} + 938485 x^{2} - 54850 x + 619$ |
$17$ |
[17,0] |
$239^{16}$ |
$1$ |
$173.177769645$ |
$173.17776964513632$ |
|
✓ |
|
$C_{17}$ (as 17T1) |
trivial |
$2$ |
$16$ |
$24055588816300$ |
| 17.17.236...361.1 |
$x^{17} - 136 x^{15} - 85 x^{14} + 6154 x^{13} + 6545 x^{12} - 119680 x^{11} - 168555 x^{10} + 998835 x^{9} + 1749300 x^{8} - 2783546 x^{7} - 6581040 x^{6} - 678725 x^{5} + 3813882 x^{4} + 770593 x^{3} - 616267 x^{2} - 82620 x + 577$ |
$17$ |
[17,0] |
$17^{32}$ |
$1$ |
$207.080471963$ |
$207.08047196297318$ |
|
✓ |
|
$C_{17}$ (as 17T1) |
trivial |
$2$ |
$16$ |
$111156254553000$ |
| 17.17.622...001.1 |
$x^{17} - x^{16} - 144 x^{15} + 241 x^{14} + 6894 x^{13} - 14938 x^{12} - 127923 x^{11} + 323969 x^{10} + 847982 x^{9} - 2194186 x^{8} - 2617873 x^{7} + 6091397 x^{6} + 3745755 x^{5} - 7069429 x^{4} - 1600190 x^{3} + 3100257 x^{2} - 220118 x - 208777$ |
$17$ |
[17,0] |
$307^{16}$ |
$1$ |
$219.197763206$ |
$219.19776320615284$ |
|
✓ |
|
$C_{17}$ (as 17T1) |
trivial |
$2$ |
$16$ |
$501600232257889.1$ |
| 17.17.613...441.1 |
$x^{17} - x^{16} - 192 x^{15} + 273 x^{14} + 14752 x^{13} - 28028 x^{12} - 571107 x^{11} + 1411675 x^{10} + 11275657 x^{9} - 36814399 x^{8} - 91832077 x^{7} + 461179352 x^{6} - 109192148 x^{5} - 1929139488 x^{4} + 3679722325 x^{3} - 2767754010 x^{2} + 828153361 x - 45886883$ |
$17$ |
[17,0] |
$409^{16}$ |
$1$ |
$287.139225868$ |
$287.139225868099$ |
|
✓ |
|
$C_{17}$ (as 17T1) |
trivial |
$2$ |
$16$ |
$37559948173498540$ |
| 17.17.220...001.1 |
$x^{17} - x^{16} - 208 x^{15} - 17 x^{14} + 15287 x^{13} + 13881 x^{12} - 487578 x^{11} - 703261 x^{10} + 6754359 x^{9} + 10540902 x^{8} - 41136753 x^{7} - 57683825 x^{6} + 92010954 x^{5} + 95287840 x^{4} - 17501435 x^{3} - 25026156 x^{2} - 563260 x + 1246103$ |
$17$ |
[17,0] |
$443^{16}$ |
$1$ |
$309.551504258$ |
$309.5515042584762$ |
|
✓ |
|
$C_{17}$ (as 17T1) |
trivial |
$2$ |
$16$ |
$2360552434044002.5$ |
| 17.17.397...041.1 |
$x^{17} - x^{16} - 288 x^{15} + 265 x^{14} + 26034 x^{13} - 40228 x^{12} - 875968 x^{11} + 2022008 x^{10} + 8464009 x^{9} - 27681440 x^{8} - 8855367 x^{7} + 101412811 x^{6} - 87313302 x^{5} - 38624139 x^{4} + 67164168 x^{3} - 7149746 x^{2} - 7878215 x - 664471$ |
$17$ |
[17,0] |
$613^{16}$ |
$1$ |
$420.234991066$ |
$420.23499106575036$ |
|
✓ |
|
$C_{17}$ (as 17T1) |
trivial |
$2$ |
$16$ |
$40860825172254010$ |
| 17.17.942...921.1 |
$x^{17} - x^{16} - 304 x^{15} + 1117 x^{14} + 25631 x^{13} - 126439 x^{12} - 773932 x^{11} + 4360454 x^{10} + 10731832 x^{9} - 64676368 x^{8} - 79260104 x^{7} + 441919082 x^{6} + 345306489 x^{5} - 1259087517 x^{4} - 718017711 x^{3} + 1025767171 x^{2} + 183044979 x - 202031659$ |
$17$ |
[17,0] |
$647^{16}$ |
$1$ |
$442.137111896$ |
$442.13711189623245$ |
|
✓ |
|
$C_{17}$ (as 17T1) |
trivial |
$2$ |
$16$ |
$53927069890502120$ |
| 17.17.258...281.1 |
$x^{17} - x^{16} - 432 x^{15} + 1911 x^{14} + 56071 x^{13} - 377127 x^{12} - 2275999 x^{11} + 22947072 x^{10} - 5751373 x^{9} - 395586237 x^{8} + 1094097337 x^{7} - 39485017 x^{6} - 2920148551 x^{5} + 2341974035 x^{4} + 1284864535 x^{3} - 1464500037 x^{2} - 140787928 x + 238840843$ |
$17$ |
[17,0] |
$919^{16}$ |
$1$ |
$615.180887424$ |
$615.1808874238469$ |
|
✓ |
|
$C_{17}$ (as 17T1) |
trivial |
$2$ |
$16$ |
$935275490448786200$ |
| 17.17.462...121.1 |
$x^{17} - x^{16} - 448 x^{15} + 1309 x^{14} + 75494 x^{13} - 374314 x^{12} - 5597667 x^{11} + 41830550 x^{10} + 136426018 x^{9} - 1919481097 x^{8} + 2548312782 x^{7} + 27117309376 x^{6} - 105628969954 x^{5} + 34101907629 x^{4} + 457076113374 x^{3} - 817186035962 x^{2} + 323264486326 x + 117028501127$ |
$17$ |
[17,0] |
$953^{16}$ |
$1$ |
$636.578756865$ |
$636.5787568645812$ |
|
✓ |
|
$C_{17}$ (as 17T1) |
trivial |
$2$ |
$16$ |
$1792851846429171700$ |
