| 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 |
| 47.47.605...769.1 |
$x^{47} - x^{46} - 138 x^{45} + 315 x^{44} + 8338 x^{43} - 29804 x^{42} - 276833 x^{41} + 1433626 x^{40} + 5033859 x^{39} - 41190458 x^{38} - 30657314 x^{37} + 748097961 x^{36} - 742659788 x^{35} - 8506344013 x^{34} + 21519259357 x^{33} + 52948548811 x^{32} - 268879641855 x^{31} - 30332528938 x^{30} + 1920252236103 x^{29} - 2430736233424 x^{28} - 7367030656288 x^{27} + 21401598866455 x^{26} + 5373046913681 x^{25} - 89240242581627 x^{24} + 85735098102709 x^{23} + 174332690558567 x^{22} - 418760640969237 x^{21} + 24016008538438 x^{20} + 845143941649693 x^{19} - 850093833789498 x^{18} - 563502754038610 x^{17} + 1652337279635119 x^{16} - 688139958495907 x^{15} - 1132046847057208 x^{14} + 1399925903803443 x^{13} - 129366579867529 x^{12} - 739733924950208 x^{11} + 464611724348759 x^{10} + 61382685657965 x^{9} - 169596960618209 x^{8} + 46703998783537 x^{7} + 17972540150505 x^{6} - 11555848466611 x^{5} + 591153994800 x^{4} + 757301830397 x^{3} - 134933083169 x^{2} - 1756074840 x + 132954859$ |
$47$ |
[47,0] |
$283^{46}$ |
$1$ |
$250.969396701$ |
$250.96939670094406$ |
|
✓ |
|
$C_{47}$ (as 47T1) |
not computed |
$2$ |
$46$ |
|
| 47.47.466...641.1 |
$x^{47} - x^{46} - 322 x^{45} + 257 x^{44} + 46168 x^{43} - 32856 x^{42} - 3928972 x^{41} + 2800261 x^{40} + 223114373 x^{39} - 173143135 x^{38} - 9003548066 x^{37} + 7929128719 x^{36} + 268197678343 x^{35} - 271080896060 x^{34} - 6041385515832 x^{33} + 6979624724342 x^{32} + 104494842005772 x^{31} - 136657122243604 x^{30} - 1400247413062994 x^{29} + 2052225750352966 x^{28} + 14591458839594017 x^{27} - 23782847219941819 x^{26} - 118118630838181495 x^{25} + 213321125182479282 x^{24} + 738128822260196887 x^{23} - 1480085655858130569 x^{22} - 3514638820507932409 x^{21} + 7908202660646656434 x^{20} + 12455131093399060106 x^{19} - 32248927636656562527 x^{18} - 31433221457470396690 x^{17} + 98930979031819081241 x^{16} + 51111011671312688653 x^{15} - 223422112969694652903 x^{14} - 36045180999704955067 x^{13} + 359687682365174498379 x^{12} - 43326797472112521543 x^{11} - 392741974421328427418 x^{10} + 139313975200941570964 x^{9} + 266729246622027266884 x^{8} - 153819291119830123270 x^{7} - 92300136797476126809 x^{6} + 82337017997204992796 x^{5} + 4438182302442319866 x^{4} - 17703030829530739458 x^{3} + 4375073965542285492 x^{2} - 7552331260195558 x - 66410957360928749$ |
$47$ |
[47,0] |
$659^{46}$ |
$1$ |
$573.996347907$ |
$573.9963479072553$ |
|
✓ |
|
$C_{47}$ (as 47T1) |
not computed |
$2$ |
$46$ |
|
| 47.47.609...241.1 |
$x^{47} - x^{46} - 460 x^{45} + 327 x^{44} + 94524 x^{43} - 38110 x^{42} - 11539413 x^{41} + 809932 x^{40} + 937957195 x^{39} + 272017844 x^{38} - 53844657814 x^{37} - 36415505127 x^{36} + 2255802403789 x^{35} + 2452634499322 x^{34} - 70139481731357 x^{33} - 106937338241973 x^{32} + 1626084100876542 x^{31} + 3250400054052522 x^{30} - 27906088812601386 x^{29} - 70884683396944095 x^{28} + 346512540625848199 x^{27} + 1118163243198969746 x^{26} - 2955220812359278078 x^{25} - 12685164476223506555 x^{24} + 15046746180109293999 x^{23} + 101582059147167915284 x^{22} - 18312922973366227046 x^{21} - 554548726919125907181 x^{20} - 318711846399705268031 x^{19} + 1938753789920516494271 x^{18} + 2414984135254760303399 x^{17} - 3792697335240007382545 x^{16} - 8178953624841789295386 x^{15} + 2279595290530927592625 x^{14} + 14681478777833447802999 x^{13} + 5435523725560836559149 x^{12} - 12942546360599189199808 x^{11} - 11501227765200381452105 x^{10} + 3183515530405052075328 x^{9} + 7591082677180116655272 x^{8} + 2077754691851067407232 x^{7} - 1323128253866746375290 x^{6} - 896927209808036028574 x^{5} - 132715131473527952574 x^{4} + 23448602689225942698 x^{3} + 8115247135424866684 x^{2} + 574328145019154892 x - 1980612833005069$ |
$47$ |
[47,0] |
$941^{46}$ |
$1$ |
$813.432947308$ |
$813.4329473077595$ |
|
✓ |
|
$C_{47}$ (as 47T1) |
not computed |
$2$ |
$46$ |
|
| 47.47.680...841.1 |
$x^{47} - 1081 x^{45} - 705 x^{44} + 534061 x^{43} + 683944 x^{42} - 160057842 x^{41} - 299647654 x^{40} + 32561335719 x^{39} + 78763416061 x^{38} - 4767066709455 x^{37} - 13908937919967 x^{36} + 519679734845940 x^{35} + 1750397799006104 x^{34} - 43074182887990763 x^{33} - 162478138072805487 x^{32} + 2749329116777664352 x^{31} + 11358660939804373275 x^{30} - 136126237738133225032 x^{29} - 605463962245369166572 x^{28} + 5246767648352840100798 x^{27} + 24765274103500484906219 x^{26} - 157566416740809178648611 x^{25} - 778707155396426126313230 x^{24} + 3684240622296757942862071 x^{23} + 18785271879388363208006658 x^{22} - 66986754039408931327563467 x^{21} - 345795459416186142486923619 x^{20} + 946170254872545787018973465 x^{19} + 4814104180441102948763936108 x^{18} - 10375613255284454207094751556 x^{17} - 50032174963571133079560800941 x^{16} + 88105844627120217056303008521 x^{15} + 380945711116472915778482842595 x^{14} - 573465045108814971325177493888 x^{13} - 2067158816911927150047646995633 x^{12} + 2787145282695598886975483579427 x^{11} + 7670341992113409376277564204296 x^{10} - 9619799236229244848389374409877 x^{9} - 18271828994795512973409030766888 x^{8} + 21757031287162404406727090902813 x^{7} + 25318069661907634555608128065064 x^{6} - 28749901083465227418574423514388 x^{5} - 17172272828610619745842195295332 x^{4} + 19384902113022958413624018194070 x^{3} + 2828656546972432377231017394241 x^{2} - 5355885371863393108886638462583 x + 1052824394331287344099620777449$ |
$47$ |
[47,0] |
$47^{92}$ |
$1$ |
$1875.1785026$ |
$1875.1785026045545$ |
|
✓ |
|
$C_{47}$ (as 47T1) |
not computed |
$2$ |
$46$ |
|
