| 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 |
| 45.45.977...089.1 |
$x^{45} - x^{44} - 72 x^{43} + 67 x^{42} + 2321 x^{41} - 2007 x^{40} - 44393 x^{39} + 35655 x^{38} + 562984 x^{37} - 420187 x^{36} - 5012298 x^{35} + 3480849 x^{34} + 32367724 x^{33} - 20955723 x^{32} - 154542085 x^{31} + 93497512 x^{30} + 551503498 x^{29} - 312562651 x^{28} - 1478859633 x^{27} + 786888918 x^{26} + 2984367290 x^{25} - 1493106677 x^{24} - 4527360022 x^{23} + 2130398676 x^{22} + 5146818792 x^{21} - 2274599139 x^{20} - 4361796744 x^{19} + 1804001386 x^{18} + 2733500368 x^{17} - 1051995625 x^{16} - 1251105602 x^{15} + 444673277 x^{14} + 410259354 x^{13} - 133494819 x^{12} - 93584992 x^{11} + 27616610 x^{10} + 14189768 x^{9} - 3755862 x^{8} - 1331682 x^{7} + 310282 x^{6} + 69020 x^{5} - 13468 x^{4} - 1660 x^{3} + 232 x^{2} + 16 x - 1$ |
$45$ |
[45,0] |
$7^{30}\cdot 31^{42}$ |
$2$ |
$90.226949455$ |
$90.2269494549658$ |
|
✓ |
? |
$C_3\times C_{15}$ (as 45T2) |
trivial |
$2$ |
$44$ |
$604682720155280400000000000000$ |
| 45.45.183...361.1 |
$x^{45} - 87 x^{43} - 4 x^{42} + 3402 x^{41} + 300 x^{40} - 79106 x^{39} - 10008 x^{38} + 1219668 x^{37} + 196264 x^{36} - 13165542 x^{35} - 2519472 x^{34} + 102436164 x^{33} + 22316760 x^{32} - 583045167 x^{31} - 140145264 x^{30} + 2440735434 x^{29} + 631757436 x^{28} - 7504722910 x^{27} - 2050106328 x^{26} + 16845457116 x^{25} + 4771066968 x^{24} - 27354225744 x^{23} - 7899876240 x^{22} + 31819110888 x^{21} + 9218870784 x^{20} - 26289431304 x^{19} - 7517163552 x^{18} + 15324352272 x^{17} + 4245866400 x^{16} - 6258116631 x^{15} - 1643669037 x^{14} + 1770836592 x^{13} + 429144192 x^{12} - 340508538 x^{11} - 73586928 x^{10} + 43022076 x^{9} + 7934841 x^{8} - 3375522 x^{7} - 502012 x^{6} + 149688 x^{5} + 16758 x^{4} - 3200 x^{3} - 252 x^{2} + 24 x + 1$ |
$45$ |
[45,0] |
$3^{60}\cdot 31^{42}$ |
$2$ |
$106.683990948$ |
$106.68399094818109$ |
|
✓ |
? |
$C_3\times C_{15}$ (as 45T2) |
not computed |
$2$ |
$44$ |
|
| 45.45.295...689.1 |
$x^{45} - 3 x^{44} - 108 x^{43} + 296 x^{42} + 5217 x^{41} - 13005 x^{40} - 149828 x^{39} + 337863 x^{38} + 2868057 x^{37} - 5809689 x^{36} - 38881407 x^{35} + 70098207 x^{34} + 387120467 x^{33} - 613625013 x^{32} - 2896408122 x^{31} + 3972622452 x^{30} + 16519787829 x^{29} - 19205853294 x^{28} - 72406643558 x^{27} + 69489283683 x^{26} + 244599321027 x^{25} - 187254237300 x^{24} - 635787323022 x^{23} + 371102281773 x^{22} + 1263897395760 x^{21} - 528600088722 x^{20} - 1901669780781 x^{19} + 520023114157 x^{18} + 2134290033054 x^{17} - 327330093672 x^{16} - 1754567507744 x^{15} + 107410900356 x^{14} + 1034842778925 x^{13} + 1036802542 x^{12} - 428135520330 x^{11} - 14111627571 x^{10} + 121049080943 x^{9} + 4346148948 x^{8} - 22551409551 x^{7} - 290753084 x^{6} + 2597605155 x^{5} - 77625633 x^{4} - 161647682 x^{3} + 13050165 x^{2} + 3741168 x - 437977$ |
$45$ |
[45,0] |
$3^{60}\cdot 7^{30}\cdot 11^{36}$ |
$3$ |
$107.813839968$ |
$107.81383996755932$ |
|
✓ |
? |
$C_3\times C_{15}$ (as 45T2) |
trivial |
$2$ |
$44$ |
$36716059087827736000000000000000$ |
| 45.45.113...889.1 |
$x^{45} - 12 x^{44} - 38 x^{43} + 936 x^{42} - 488 x^{41} - 32994 x^{40} + 61155 x^{39} + 695151 x^{38} - 1826452 x^{37} - 9745559 x^{36} + 31398650 x^{35} + 95576968 x^{34} - 363031278 x^{33} - 668271620 x^{32} + 3006554151 x^{31} + 3299628259 x^{30} - 18405469866 x^{29} - 10819187452 x^{28} + 84606290574 x^{27} + 17798672756 x^{26} - 293624042239 x^{25} + 25779977473 x^{24} + 766879229695 x^{23} - 259704306954 x^{22} - 1488735953755 x^{21} + 843265985246 x^{20} + 2094958274346 x^{19} - 1672596038928 x^{18} - 2036992655261 x^{17} + 2211683013511 x^{16} + 1229593352332 x^{15} - 1960884055901 x^{14} - 305227614428 x^{13} + 1128154934100 x^{12} - 126915280282 x^{11} - 391023252143 x^{10} + 124192084723 x^{9} + 69369604379 x^{8} - 37452923715 x^{7} - 3334757683 x^{6} + 4610823573 x^{5} - 413774775 x^{4} - 188088413 x^{3} + 35065204 x^{2} - 872335 x + 619$ |
$45$ |
[45,0] |
$13^{30}\cdot 31^{42}$ |
$2$ |
$136.322167425$ |
$136.32216742518625$ |
|
✓ |
? |
$C_3\times C_{15}$ (as 45T2) |
not computed |
$2$ |
$44$ |
|
| 45.45.217...129.1 |
$x^{45} - 12 x^{44} - 50 x^{43} + 1120 x^{42} - 626 x^{41} - 44264 x^{40} + 106520 x^{39} + 966733 x^{38} - 3644562 x^{37} - 12564205 x^{36} + 68449875 x^{35} + 92270622 x^{34} - 830216501 x^{33} - 202049055 x^{32} + 6933616229 x^{31} - 3181542881 x^{30} - 41084005259 x^{29} + 40234212427 x^{28} + 174510130968 x^{27} - 250382990469 x^{26} - 527354195438 x^{25} + 1015613064703 x^{24} + 1094857977723 x^{23} - 2871848912941 x^{22} - 1403630755463 x^{21} + 5763542313829 x^{20} + 629825101852 x^{19} - 8167242308412 x^{18} + 1257688359124 x^{17} + 7983130477206 x^{16} - 2778691581109 x^{15} - 5144196139934 x^{14} + 2589633668016 x^{13} + 2011525458240 x^{12} - 1316532612469 x^{11} - 396963769511 x^{10} + 358975449036 x^{9} + 14178066293 x^{8} - 45168898819 x^{7} + 5258463166 x^{6} + 1537215457 x^{5} - 288043322 x^{4} - 5291206 x^{3} + 2457345 x^{2} - 9309 x - 6089$ |
$45$ |
[45,0] |
$7^{30}\cdot 61^{42}$ |
$2$ |
$169.709650609$ |
$169.70965060856074$ |
|
✓ |
? |
$C_3\times C_{15}$ (as 45T2) |
not computed |
$2$ |
$44$ |
|
| 45.45.999...561.1 |
$x^{45} - 12 x^{44} - 68 x^{43} + 1390 x^{42} - 278 x^{41} - 68270 x^{40} + 176199 x^{39} + 1808389 x^{38} - 8154574 x^{37} - 26005805 x^{36} + 196321268 x^{35} + 127187382 x^{34} - 2913805970 x^{33} + 2272631340 x^{32} + 27669670927 x^{31} - 52510157887 x^{30} - 162002621792 x^{29} + 526806359978 x^{28} + 468745083598 x^{27} - 3175101889498 x^{26} + 532391340063 x^{25} + 12135569776697 x^{24} - 10651958891479 x^{23} - 28871893561060 x^{22} + 45196495080913 x^{21} + 38272655903792 x^{20} - 105664143365844 x^{19} - 13349385343870 x^{18} + 153132315545987 x^{17} - 41028745873427 x^{16} - 141811047613612 x^{15} + 76543731297893 x^{14} + 83515595010770 x^{13} - 65499266094722 x^{12} - 29808531214812 x^{11} + 32918818373161 x^{10} + 5404646072895 x^{9} - 10084991417837 x^{8} - 16286468525 x^{7} + 1821205338619 x^{6} - 180698614131 x^{5} - 173451418339 x^{4} + 28592722199 x^{3} + 6396948952 x^{2} - 1303357845 x - 3078919$ |
$45$ |
[45,0] |
$19^{30}\cdot 31^{42}$ |
$2$ |
$175.565824969$ |
$175.5658249685855$ |
|
✓ |
? |
$C_3\times C_{15}$ (as 45T2) |
not computed |
$2$ |
$44$ |
|
| 45.45.408...321.1 |
$x^{45} - 3 x^{44} - 126 x^{43} + 350 x^{42} + 7095 x^{41} - 18207 x^{40} - 237254 x^{39} + 560949 x^{38} + 5280957 x^{37} - 11465163 x^{36} - 83127609 x^{35} + 164960568 x^{34} + 959694733 x^{33} - 1729668720 x^{32} - 8316855543 x^{31} + 13495839126 x^{30} + 54911329452 x^{29} - 79318322604 x^{28} - 278624618803 x^{27} + 353264598507 x^{26} + 1090386630918 x^{25} - 1193881051406 x^{24} - 3286918329246 x^{23} + 3054422504946 x^{22} + 7584376524784 x^{21} - 5885779838802 x^{20} - 13239515051214 x^{19} + 8489225140885 x^{18} + 17170281215082 x^{17} - 9118144480932 x^{16} - 16115327765898 x^{15} + 7281918623109 x^{14} + 10535410010724 x^{13} - 4323241543716 x^{12} - 4518883017183 x^{11} + 1877328461526 x^{10} + 1138556965481 x^{9} - 554295751305 x^{8} - 124509763362 x^{7} + 91825606123 x^{6} - 3656082528 x^{5} - 5240896776 x^{4} + 961503906 x^{3} - 1541688 x^{2} - 11847522 x + 756289$ |
$45$ |
[45,0] |
$3^{60}\cdot 61^{42}$ |
$2$ |
$200.66402487$ |
$200.66402486963622$ |
|
✓ |
? |
$C_3\times C_{15}$ (as 45T2) |
not computed |
$2$ |
$44$ |
|
| 45.45.202...625.1 |
$x^{45} - 165 x^{43} - 25 x^{42} + 12060 x^{41} + 3486 x^{40} - 519330 x^{39} - 214140 x^{38} + 14776560 x^{37} + 7718745 x^{36} - 295077669 x^{35} - 182852610 x^{34} + 4284179615 x^{33} + 3016157820 x^{32} - 46197393465 x^{31} - 35772719505 x^{30} + 374607222195 x^{29} + 310484223975 x^{28} - 2298730688540 x^{27} - 1988244775980 x^{26} + 10695933805596 x^{25} + 9407317026635 x^{24} - 37696094037390 x^{23} - 32764647222885 x^{22} + 100289481110340 x^{21} + 83332538318277 x^{20} - 200279250507195 x^{19} - 152889355168310 x^{18} + 297466429398705 x^{17} + 198745289480940 x^{16} - 323624520119411 x^{15} - 178210655500665 x^{14} + 251547979741875 x^{13} + 105785393431525 x^{12} - 134218212107550 x^{11} - 38927292179565 x^{10} + 46104688292390 x^{9} + 7956837983055 x^{8} - 9173261413650 x^{7} - 765305596255 x^{6} + 891053703312 x^{5} + 40709257785 x^{4} - 38148076985 x^{3} - 1973427960 x^{2} + 606052050 x + 47691757$ |
$45$ |
[45,0] |
$3^{60}\cdot 5^{72}\cdot 7^{30}$ |
$3$ |
$207.927711304$ |
$207.92771130440346$ |
|
✓ |
? |
$C_3\times C_{15}$ (as 45T2) |
not computed |
$2$ |
$44$ |
|
| 45.45.252...929.1 |
$x^{45} - 12 x^{44} - 80 x^{43} + 1424 x^{42} + 1516 x^{41} - 74554 x^{40} + 63158 x^{39} + 2282501 x^{38} - 4255902 x^{37} - 45636421 x^{36} + 116693559 x^{35} + 630121996 x^{34} - 1971613347 x^{33} - 6193698077 x^{32} + 22855343401 x^{31} + 44007670585 x^{30} - 190617019593 x^{29} - 226920195907 x^{28} + 1172746429282 x^{27} + 842990049201 x^{26} - 5394671280584 x^{25} - 2206384597765 x^{24} + 18666651459717 x^{23} + 3871477687999 x^{22} - 48596558981735 x^{21} - 4036750693451 x^{20} + 94693820108958 x^{19} + 1546861746446 x^{18} - 136570614884744 x^{17} + 956863921562 x^{16} + 143064103358001 x^{15} + 102341290612 x^{14} - 105649963477592 x^{13} - 2816833651750 x^{12} + 52484763220205 x^{11} + 2919265367283 x^{10} - 16311452643376 x^{9} - 1104335997267 x^{8} + 2857645920655 x^{7} + 105919440856 x^{6} - 255094574859 x^{5} + 8466426668 x^{4} + 8654209646 x^{3} - 1026667213 x^{2} + 14388119 x + 1507921$ |
$45$ |
[45,0] |
$13^{30}\cdot 61^{42}$ |
$2$ |
$256.411056161$ |
$256.41105616096826$ |
|
✓ |
? |
$C_3\times C_{15}$ (as 45T2) |
not computed |
$2$ |
$44$ |
|
| 45.45.235...625.1 |
$x^{45} - 15 x^{44} - 90 x^{43} + 2245 x^{42} + 840 x^{41} - 149682 x^{40} + 233625 x^{39} + 5893830 x^{38} - 15309120 x^{37} - 153159405 x^{36} + 505833687 x^{35} + 2780167860 x^{34} - 10777640365 x^{33} - 36390969195 x^{32} + 160894854450 x^{31} + 349558305696 x^{30} - 1751940770010 x^{29} - 2483116182570 x^{28} + 14226276458010 x^{27} + 13037929556940 x^{26} - 87229174471284 x^{25} - 50137706272620 x^{24} + 406336593221610 x^{23} + 138267603359730 x^{22} - 1439822630956295 x^{21} - 262195938148443 x^{20} + 3868718864967360 x^{19} + 311910060390275 x^{18} - 7821266721741750 x^{17} - 175081417856730 x^{16} + 11738415157749574 x^{15} - 32411856380685 x^{14} - 12806776910595090 x^{13} + 44301971232950 x^{12} + 9836514943009755 x^{11} + 117791800035840 x^{10} - 5063789878500180 x^{9} - 176503490451285 x^{8} + 1618208036238660 x^{7} + 90536277582715 x^{6} - 283553373081756 x^{5} - 18640864878495 x^{4} + 21751317924475 x^{3} + 974579665770 x^{2} - 434206226325 x + 15265738099$ |
$45$ |
[45,0] |
$3^{60}\cdot 5^{72}\cdot 13^{30}$ |
$3$ |
$314.153991064$ |
$314.1539910636384$ |
|
✓ |
? |
$C_3\times C_{15}$ (as 45T2) |
not computed |
$2$ |
$44$ |
|
| 45.45.206...625.1 |
$x^{45} - 15 x^{44} - 120 x^{43} + 2785 x^{42} + 2040 x^{41} - 222342 x^{40} + 420425 x^{39} + 10024590 x^{38} - 35069730 x^{37} - 280556895 x^{36} + 1389459441 x^{35} + 4980489270 x^{34} - 34327919505 x^{33} - 52485204525 x^{32} + 576080544270 x^{31} + 196092367854 x^{30} - 6820772763030 x^{29} + 3051952728270 x^{28} + 57922300812880 x^{27} - 59937846525180 x^{26} - 353495076875202 x^{25} + 542694665981220 x^{24} + 1531071286376460 x^{23} - 3131712122030760 x^{22} - 4545064586341055 x^{21} + 12339167509476885 x^{20} + 8461213880546430 x^{19} - 33709107574234355 x^{18} - 6968642817313350 x^{17} + 63373889569191960 x^{16} - 7076452922900098 x^{15} - 80218608988132905 x^{14} + 26470314281644410 x^{13} + 66243722166245240 x^{12} - 32060240741785995 x^{11} - 34356066621763764 x^{10} + 20781515138515650 x^{9} + 10477766738441505 x^{8} - 7675031336820660 x^{7} - 1594722107742745 x^{6} + 1559444254090284 x^{5} + 49643486026125 x^{4} - 150881459933485 x^{3} + 10931860799430 x^{2} + 4297070637735 x - 401780151251$ |
$45$ |
[45,0] |
$3^{60}\cdot 5^{72}\cdot 19^{30}$ |
$3$ |
$404.590872123$ |
$404.59087212305565$ |
|
✓ |
? |
$C_3\times C_{15}$ (as 45T2) |
not computed |
$2$ |
$44$ |
|
