| 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 |
$2$ |
$16$ |
$30768108227.3$ |
| 17.17.234...609.1 |
$x^{17} - 4 x^{16} - 11 x^{15} + 53 x^{14} + 44 x^{13} - 271 x^{12} - 81 x^{11} + 676 x^{10} + 78 x^{9} - 866 x^{8} - 56 x^{7} + 563 x^{6} + 36 x^{5} - 176 x^{4} - 12 x^{3} + 23 x^{2} + x - 1$ |
$17$ |
[17,0] |
$19501\cdot 163667513\cdot 736214146077100976893$ |
$3$ |
$91.8335522446$ |
$4.847432404534953e+16$ |
|
|
✓ |
$S_{17}$ (as 17T10) |
trivial |
$2$ |
$16$ |
$384409141351$ |
| 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 |
$2$ |
$16$ |
$559957546560$ |
| 17.17.597...272.1 |
$x^{17} - 51 x^{15} + 1071 x^{13} - 11934 x^{11} + 75735 x^{9} - 272646 x^{7} + 520506 x^{5} - 446148 x^{3} + 111537 x - 22482$ |
$17$ |
[17,0] |
$2^{24}\cdot 3^{16}\cdot 17^{17}$ |
$3$ |
$127.200185081$ |
$158.09016490784836$ |
|
|
? |
$F_{17}$ (as 17T5) |
trivial |
$2$ |
$16$ |
$13029132161200$ |
| 17.17.827...000.1 |
$x^{17} - 85 x^{15} + 2975 x^{13} - 55250 x^{11} + 584375 x^{9} - 3506250 x^{7} + 11156250 x^{5} - 15937500 x^{3} + 6640625 x - 1737500$ |
$17$ |
[17,0] |
$2^{16}\cdot 5^{16}\cdot 17^{17}$ |
$3$ |
$148.465447605$ |
$180.79594174691047$ |
|
|
? |
$F_{17}$ (as 17T5) |
trivial |
$2$ |
$16$ |
$48080253767000$ |
| 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 |
$2$ |
$16$ |
$1792851846429171700$ |
| 17.17.897...201.1 |
$x^{17} - 4 x^{16} - 476 x^{15} + 3026 x^{14} + 82996 x^{13} - 736812 x^{12} - 6121180 x^{11} + 80531352 x^{10} + 108448584 x^{9} - 4267795762 x^{8} + 9723361580 x^{7} + 95353221324 x^{6} - 524744382701 x^{5} - 7660737412 x^{4} + 6800548404356 x^{3} - 21491689501032 x^{2} + 27480501953536 x - 12878683864992$ |
$17$ |
[17,0] |
$17^{12}\cdot 137^{16}$ |
$2$ |
$757.850081803$ |
$858.752101911667$ |
|
|
|
$C_{17}:C_{4}$ (as 17T3) |
$[17]$ |
$2$ |
$16$ |
$31945964915800000000$ |
| 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) |
$[17]$ |
$2$ |
$16$ |
$10720674608800000000000000$ |
| 17.17.132...625.1 |
$x^{17} - x^{16} - 209366104215680788999237026547641097698 x^{15} - 1366742178334204175438997589171142015450323754334864369224 x^{14} + 1370561167639445232641588842226596440326814811500377916577951156785205603616 x^{13} + 34209858818572450923271706624028583128577132326587729764418829056155931883100572576543824614528 x^{12} + 71060716298265833814190789484351947045094218086339373134017972529231516080624594299417621901900363029200839303680 x^{11} - 181236556545551870194910603673122664616069745538191536145261133196422743167811347834952322646822461893016382882736111475051779835904 x^{10} - 817453198936905169400742982687958866786256736846211649117725561020133238029973092638151864726931584027480499685581465329622501783309527162528308953088 x^{9} - 406211134121143976571685932629427590329091770245795527373565243496924271345193026030870366206101859233901646299537618309720564689896228499629423779408143210096201302016 x^{8} + 2063531180788517939004478109589742385478341534165997591626727610318370449381138162515361508202768867158479874086973104044545239342671435605273745820464492333093544875731405829610829512704 x^{7} + 2896803440617034044082414054987092761425750561697541270975110048759818875866509904308337299406705399859448559468574920740735545763509144483628181748157772929773317331584643514549841613609047826134345449472 x^{6} - 375728305046657587737437465141770466545137888085020499189518494157931590235776407255542703786899002623272850956760756590809799855663980937838753932085061186815235816159448759232674149349127567492283556692575228386248491008 x^{5} - 2028919226122184282547719212404001304737799778058571160592238734166677967718184072440967382731107200224913576726869639337803258702187932484385556935885816415960345072227073330391030176232986366904452017071983642624332203614381743366125649920 x^{4} - 60950714931147330950883801576283829013554502185033270196914465261994309923209703228786783036281560981312017861209153204720278213626389686597733457144020261637634080923052038123091922379051430144899539652593795568496537218812938586685114185884150715956330496 x^{3} + 473928342892602293775643808769935031032066044095325682751754761239780409526186786886030926973533412678310396818663456261230461382663715105662885481585059970820106413547922797015360830616935208666603580522235685986237133614930548698028016260214317835178831217789563984521723904 x^{2} - 65099622270587978065879038307806761197287013260747074255596854482937931422598383015653598654694045742457209039856196858466593297405172185778252691948608216506703929894692225332579595112013433301461138197138219492068735859226815044137679851709559000898305443997308036303693844239426410642407424 x + 2014755577973807885553442175684655281473176522202931711918446863791222851942996378810544272763907161070021710559899467068574306440431996593428915637864458100949970854924532577927598683969894319931563502807289188851993089743098110146672995634255495997519516339298306955127636879610909991217001038430549642838016$ |
$17$ |
[17,0] |
$5^{6}\cdot 11^{4}\cdot 75\!\cdots\!89^{2}$ |
$3$ |
$2.00085126165e+37$ |
|
|
|
? |
$A_{17}$ (as 17T9) |
not computed |
$2$ |
$16$ |
|
