| 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 |
| 45.15.174...691.1 |
$x^{45} - 12 x^{44} + 42 x^{43} + 36 x^{42} - 525 x^{41} + 702 x^{40} + 2050 x^{39} - 5802 x^{38} - 2832 x^{37} + 26919 x^{36} - 20811 x^{35} - 75546 x^{34} + 201699 x^{33} - 97125 x^{32} - 532302 x^{31} + 1289591 x^{30} - 477339 x^{29} - 2405610 x^{28} + 4128988 x^{27} - 1666824 x^{26} - 5259345 x^{25} + 9273382 x^{24} + 3749217 x^{23} - 15223818 x^{22} - 9661128 x^{21} + 33692574 x^{20} - 4282803 x^{19} - 38096273 x^{18} + 36480543 x^{17} - 14154921 x^{16} + 10925288 x^{15} - 437979 x^{14} - 36804246 x^{13} + 57064132 x^{12} - 25852146 x^{11} - 34300866 x^{10} + 48986404 x^{9} - 2084457 x^{8} - 23365995 x^{7} + 5433983 x^{6} + 5348430 x^{5} - 1230861 x^{4} - 665734 x^{3} + 68376 x^{2} + 38973 x + 2969$ |
$45$ |
[15,15] |
$-\,3^{60}\cdot 11^{39}$ |
$2$ |
$34.57020859771022$ |
$37.44683262965639$ |
|
|
? |
$S_3\times C_{15}$ (as 45T3) |
trivial |
$2$ |
$29$ |
$495912260998404300$ |
| 45.1.246...829.1 |
$x^{45} - x - 1$ |
$45$ |
[1,22] |
$29\cdot 41\cdot 1451\cdot 23184662326519\cdot 476883331418375569\cdot 12\!\cdots\!01$ |
$6$ |
$44.9916992758$ |
$1.5684797436619337e+37$ |
|
|
✓ |
$S_{45}$ (as 45T10923) |
not computed |
$2$ |
$22$ |
|
| 45.15.226...891.1 |
$x^{45} - 3 x^{44} + 19 x^{43} - 46 x^{42} + 57 x^{41} - 164 x^{40} - 1542 x^{39} + 2752 x^{38} - 13177 x^{37} + 27636 x^{36} - 5513 x^{35} + 194674 x^{34} - 95004 x^{33} + 1568504 x^{32} - 4411428 x^{31} + 7701411 x^{30} - 22788169 x^{29} + 356245 x^{28} + 13001022 x^{27} - 120681074 x^{26} + 379138834 x^{25} - 251876102 x^{24} + 576442931 x^{23} + 394617661 x^{22} - 1914308187 x^{21} + 1873927920 x^{20} - 5326366508 x^{19} + 1371219529 x^{18} + 2001539759 x^{17} - 9889048234 x^{16} + 22330230077 x^{15} - 9918095549 x^{14} + 1934927850 x^{13} + 41001461054 x^{12} - 37979697765 x^{11} + 8169529015 x^{10} + 13175783912 x^{9} - 55418628407 x^{8} + 2188320806 x^{7} - 1793697518 x^{6} - 21729183123 x^{5} - 927541692 x^{4} + 301468299 x^{3} + 1484196634 x^{2} + 59977427 x - 879691$ |
$45$ |
[15,15] |
$-\,11^{39}\cdot 31^{30}$ |
$2$ |
$78.84632509790313$ |
$85.40721213930478$ |
|
|
? |
$S_3\times C_{15}$ (as 45T3) |
not computed |
$2$ |
$29$ |
|
| 45.1.421...456.1 |
$x^{45} - 4 x - 4$ |
$45$ |
[1,22] |
$2^{44}\cdot 61\cdot 6357179\cdot 171802225249\cdot 418161846581\cdot 8092657633001\cdot 14050885843711\cdot 75717538318411921$ |
$8$ |
$88.5581252469$ |
$3.050140550022972e+37$ |
|
|
? |
$S_{45}$ (as 45T10923) |
not computed |
$2$ |
$22$ |
|
| 45.1.429...728.1 |
$x^{45} - 2 x - 2$ |
$45$ |
[1,22] |
$2^{44}\cdot 79\cdot 1013\cdot 30\!\cdots\!79$ |
$4$ |
$88.5914985881$ |
$3.076108281330727e+37$ |
|
|
✓ |
$S_{45}$ (as 45T10923) |
not computed |
$2$ |
$22$ |
|
| 45.1.436...704.1 |
$x^{45} - x - 2$ |
$45$ |
[1,22] |
$2^{44}\cdot 24\!\cdots\!69$ |
$2$ |
$88.6243277641$ |
|
|
|
✓ |
$S_{45}$ (as 45T10923) |
not computed |
$2$ |
$22$ |
|
| 45.1.436...000.1 |
$x^{45} - 2$ |
$45$ |
[1,22] |
$2^{44}\cdot 3^{90}\cdot 5^{45}$ |
$3$ |
$88.6243277641$ |
$146.98092591465368$ |
|
|
✓ |
$D_{45}:C_{12}$ (as 45T144) |
not computed |
$2$ |
$22$ |
|
| 45.1.450...544.1 |
$x^{45} + 4 x - 4$ |
$45$ |
[1,22] |
$2^{44}\cdot 523\cdot 326083\cdot 86999456098802843\cdot 17\!\cdots\!07$ |
$5$ |
$88.6884233855$ |
$3.1527284230016683e+37$ |
|
|
? |
$S_{45}$ (as 45T10923) |
not computed |
$2$ |
$22$ |
|
| 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 |
$2$ |
$44$ |
$604682720155280400000000000000$ |
| 45.45.436...561.1 |
$x^{45} - x^{44} - 76 x^{43} + 71 x^{42} + 2587 x^{41} - 2253 x^{40} - 52277 x^{39} + 42329 x^{38} + 700945 x^{37} - 526048 x^{36} - 6604336 x^{35} + 4578520 x^{34} + 45186997 x^{33} - 28840788 x^{32} - 228874394 x^{31} + 134081171 x^{30} + 867295136 x^{29} - 465239246 x^{28} - 2469432362 x^{27} + 1211308198 x^{26} + 5279515898 x^{25} - 2368332022 x^{24} - 8432662207 x^{23} + 3466272920 x^{22} + 9971146414 x^{21} - 3771201953 x^{20} - 8615444602 x^{19} + 3016692905 x^{18} + 5349176614 x^{17} - 1747589185 x^{16} - 2338480852 x^{15} + 719039461 x^{14} + 702585559 x^{13} - 204971923 x^{12} - 140848481 x^{11} + 39126498 x^{10} + 18138585 x^{9} - 4764404 x^{8} - 1426972 x^{7} + 345013 x^{6} + 64118 x^{5} - 13350 x^{4} - 1490 x^{3} + 225 x^{2} + 15 x - 1$ |
$45$ |
[45,0] |
$11^{36}\cdot 19^{40}$ |
$2$ |
$93.279028795$ |
$93.27902879504832$ |
|
✓ |
? |
$C_{45}$ (as 45T1) |
trivial |
$2$ |
$44$ |
$1164989215047236500000000000000$ |
| 45.45.940...689.1 |
$x^{45} - 81 x^{43} + 2943 x^{41} - 63576 x^{39} + 912699 x^{37} - 256 x^{36} - 9221688 x^{35} + 11619 x^{34} + 67767147 x^{33} - 228393 x^{32} - 369266337 x^{31} + 2577030 x^{30} + 1508018391 x^{29} - 18638901 x^{28} - 4636251652 x^{27} + 91308222 x^{26} + 10725370218 x^{25} - 311639850 x^{24} - 18578308230 x^{23} + 749536389 x^{22} + 23873708220 x^{21} - 1268865972 x^{20} - 22446274041 x^{19} + 1494154410 x^{18} + 15154469253 x^{17} - 1197712170 x^{16} - 7173383040 x^{15} + 633986568 x^{14} + 2312491545 x^{13} - 213869688 x^{12} - 490418469 x^{11} + 44511588 x^{10} + 65361426 x^{9} - 5507676 x^{8} - 5123475 x^{7} + 385695 x^{6} + 214380 x^{5} - 14391 x^{4} - 4176 x^{3} + 243 x^{2} + 27 x - 1$ |
$45$ |
[45,0] |
$3^{110}\cdot 11^{36}$ |
$2$ |
$99.8643658547$ |
$99.86436585474138$ |
|
✓ |
? |
$C_{45}$ (as 45T1) |
trivial |
$2$ |
$44$ |
$7652474177847196000000000000000$ |
| 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 |
$2$ |
$44$ |
$36716059087827736000000000000000$ |
| 45.1.461...549.1 |
$x^{45} + x - 3$ |
$45$ |
[1,22] |
$41\cdot 281\cdot 2689\cdot 3061\cdot 9790127\cdot 49\!\cdots\!43$ |
$6$ |
$114.60665493$ |
$2.1489253433498218e+46$ |
|
|
? |
$S_{45}$ (as 45T10923) |
not computed |
$2$ |
$22$ |
|
| 45.3.605...203.1 |
$x^{45} - 3 x - 1$ |
$45$ |
[3,21] |
$-\,3^{45}\cdot 66012539\cdot 28278051239\cdot 68372307116461\cdot 16\!\cdots\!41$ |
$5$ |
$121.353626895$ |
|
|
|
✓ |
$S_{45}$ (as 45T10923) |
not computed |
$2$ |
$23$ |
|
| 45.1.605...453.1 |
$x^{45} + 3 x - 1$ |
$45$ |
[1,22] |
$3^{45}\cdot 991\cdot 5482500513935539\cdot 37\!\cdots\!79$ |
$4$ |
$121.353626895$ |
|
|
|
✓ |
$S_{45}$ (as 45T10923) |
not computed |
$2$ |
$22$ |
|
| 45.1.605...328.1 |
$x^{45} + 3 x - 2$ |
$45$ |
[1,22] |
$2^{44}\cdot 3^{45}\cdot 8431\cdot 40996793\cdot 141817543613\cdot 23\!\cdots\!89$ |
$6$ |
$121.353628837$ |
|
|
|
✓ |
$S_{45}$ (as 45T10923) |
not computed |
$2$ |
$22$ |
|
| 45.1.244...853.1 |
$x^{45} - 2 x - 3$ |
$45$ |
[1,22] |
$1294351\cdot 15211842839\cdot 12\!\cdots\!77$ |
$3$ |
$131.744069354$ |
$4.9425282889746475e+47$ |
|
|
✓ |
$S_{45}$ (as 45T10923) |
not computed |
$2$ |
$22$ |
|
| 45.1.244...829.1 |
$x^{45} - x - 3$ |
$45$ |
[1,22] |
$394759\cdot 17295724778674525629079\cdot 35\!\cdots\!89$ |
$3$ |
$131.744069355$ |
$4.94252828970459e+47$ |
|
|
✓ |
$S_{45}$ (as 45T10923) |
not computed |
$2$ |
$22$ |
|
| 45.1.244...125.1 |
$x^{45} - 3$ |
$45$ |
[1,22] |
$3^{134}\cdot 5^{45}$ |
$2$ |
$131.744069355$ |
$185.67544290878192$ |
|
|
✓ |
$D_{45}:C_{12}$ (as 45T144) |
not computed |
$2$ |
$22$ |
|
| 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...321.1 |
$x^{45} - x^{44} - 88 x^{43} + 83 x^{42} + 3486 x^{41} - 3092 x^{40} - 82393 x^{39} + 68502 x^{38} + 1298642 x^{37} - 1008411 x^{36} - 14455343 x^{35} + 10441803 x^{34} + 117428375 x^{33} - 78557259 x^{32} - 709738502 x^{31} + 437535596 x^{30} + 3225742725 x^{29} - 1822257498 x^{28} - 11074210163 x^{27} + 5697019051 x^{26} + 28704796942 x^{25} - 13361047180 x^{24} - 55904143642 x^{23} + 23423035295 x^{22} + 81043444290 x^{21} - 30561670072 x^{20} - 86189587932 x^{19} + 29605929893 x^{18} + 65831554861 x^{17} - 21311114591 x^{16} - 35027996039 x^{15} + 11388975649 x^{14} + 12410963786 x^{13} - 4429059287 x^{12} - 2711901594 x^{11} + 1176564667 x^{10} + 302440276 x^{9} - 189664142 x^{8} - 3791931 x^{7} + 14878752 x^{6} - 2048263 x^{5} - 256726 x^{4} + 86268 x^{3} - 7415 x^{2} + 215 x - 1$ |
$45$ |
[45,0] |
$181^{44}$ |
$1$ |
$161.253050772$ |
$161.25305077236845$ |
|
✓ |
|
$C_{45}$ (as 45T1) |
trivial |
$2$ |
$44$ |
$2805249427577283000000000000000000000$ |
| 45.3.253...304.1 |
$x^{45} - 4 x - 2$ |
$45$ |
[3,21] |
$-\,2^{44}\cdot 2834789\cdot 50\!\cdots\!71$ |
$3$ |
$161.80483586$ |
$2.3658609889501404e+43$ |
|
|
✓ |
$S_{45}$ (as 45T10923) |
not computed |
$2$ |
$23$ |
|
| 45.1.253...429.1 |
$x^{45} + 4 x - 1$ |
$45$ |
[1,22] |
$41\cdot 547\cdot 107899001480198069\cdot 10\!\cdots\!83$ |
$4$ |
$161.80483586$ |
$5.038586138694119e+49$ |
|
|
✓ |
$S_{45}$ (as 45T10923) |
not computed |
$2$ |
$22$ |
|
| 45.1.253...304.1 |
$x^{45} + 4 x - 2$ |
$45$ |
[1,22] |
$2^{44}\cdot 7\cdot 2687\cdot 76\!\cdots\!41$ |
$4$ |
$161.80483586$ |
$2.365860988954207e+43$ |
|
|
✓ |
$S_{45}$ (as 45T10923) |
not computed |
$2$ |
$22$ |
|
| 45.45.165...961.1 |
$x^{45} - 4 x^{44} - 114 x^{43} + 468 x^{42} + 5696 x^{41} - 24132 x^{40} - 165566 x^{39} + 729869 x^{38} + 3130045 x^{37} - 14526130 x^{36} - 40702810 x^{35} + 202181480 x^{34} + 374739344 x^{33} - 2040701711 x^{32} - 2468141099 x^{31} + 15280860430 x^{30} + 11523689449 x^{29} - 86102308596 x^{28} - 36476021474 x^{27} + 368042106614 x^{26} + 66266177672 x^{25} - 1197228116258 x^{24} + 511532340 x^{23} + 2959992694385 x^{22} - 394556499523 x^{21} - 5529580093472 x^{20} + 1265687493078 x^{19} + 7719490702430 x^{18} - 2271295840968 x^{17} - 7914078560767 x^{16} + 2645087732416 x^{15} + 5804631677810 x^{14} - 2048306537737 x^{13} - 2929193071000 x^{12} + 1039444940408 x^{11} + 957147248584 x^{10} - 333732759991 x^{9} - 182597145321 x^{8} + 64595300484 x^{7} + 16257686900 x^{6} - 6916885901 x^{5} - 166352258 x^{4} + 298954277 x^{3} - 40977465 x^{2} + 2118031 x - 36851$ |
$45$ |
[45,0] |
$11^{36}\cdot 37^{40}$ |
$2$ |
$168.682968895$ |
$168.6829688952757$ |
|
✓ |
|
$C_{45}$ (as 45T1) |
trivial |
$2$ |
$44$ |
$1875607941327826500000000000000000000$ |
| 45.1.191...432.1 |
$x^{45} - 2 x - 4$ |
$45$ |
[1,22] |
$2^{86}\cdot 166289\cdot 17194056911\cdot 97370596099401809\cdot 89\!\cdots\!83$ |
$5$ |
$169.244390536$ |
|
|
|
? |
$S_{45}$ (as 45T10923) |
not computed |
$2$ |
$22$ |
|
| 45.1.191...568.1 |
$x^{45} + 2 x - 4$ |
$45$ |
[1,22] |
$2^{86}\cdot 59\cdot 42\!\cdots\!43$ |
$3$ |
$169.244390536$ |
|
|
|
? |
$S_{45}$ (as 45T10923) |
not computed |
$2$ |
$22$ |
|
| 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 |
$2$ |
$44$ |
|
| 45.1.767...672.1 |
$x^{45} - 3 x - 4$ |
$45$ |
[1,22] |
$2^{89}\cdot 3^{45}\cdot 61\cdot 1183211\cdot 1595562959\cdot 36\!\cdots\!03$ |
$6$ |
$174.53936573$ |
|
|
|
✓ |
$S_{45}$ (as 45T10923) |
not computed |
$2$ |
$22$ |
|
| 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 |
$2$ |
$44$ |
|
| 45.45.299...625.1 |
$x^{45} - 5 x^{44} - 120 x^{43} + 570 x^{42} + 6560 x^{41} - 29130 x^{40} - 216795 x^{39} + 884935 x^{38} + 4846835 x^{37} - 17873115 x^{36} - 77748559 x^{35} + 254358990 x^{34} + 926664900 x^{33} - 2637505030 x^{32} - 8389061335 x^{31} + 20318079721 x^{30} + 58494148730 x^{29} - 117428976980 x^{28} - 316667682495 x^{27} + 510052425895 x^{26} + 1335050206763 x^{25} - 1653394093375 x^{24} - 4375338382740 x^{23} + 3923851568060 x^{22} + 11069977015865 x^{21} - 6532787291841 x^{20} - 21348397264600 x^{19} + 6845293868685 x^{18} + 30760204370920 x^{17} - 2712180162090 x^{16} - 32145143355065 x^{15} - 3532224571660 x^{14} + 23314933370325 x^{13} + 6500465979650 x^{12} - 10976198292280 x^{11} - 4703287953351 x^{10} + 3011509345140 x^{9} + 1752830160915 x^{8} - 400149323895 x^{7} - 327698710405 x^{6} + 19849150584 x^{5} + 30510229725 x^{4} + 7497705 x^{3} - 1362119415 x^{2} - 14453695 x + 22808701$ |
$45$ |
[45,0] |
$5^{72}\cdot 19^{40}$ |
$2$ |
$179.896152255$ |
$179.89615225547942$ |
|
✓ |
? |
$C_{45}$ (as 45T1) |
trivial |
$2$ |
$44$ |
$4022487388915899600000000000000000000$ |
| 45.3.118...000.1 |
$x^{45} - 5 x - 2$ |
$45$ |
[3,21] |
$-\,2^{44}\cdot 5^{45}\cdot 73\cdot 44175746519\cdot 6490952564449\cdot 14705222713099\cdot 7728853529686445339$ |
$7$ |
$185.499010511$ |
|
|
|
? |
$S_{45}$ (as 45T10923) |
not computed |
$2$ |
$23$ |
|
| 45.3.233...875.1 |
$x^{45} - 5 x - 3$ |
$45$ |
[3,21] |
$-\,5^{43}\cdot 157\cdot 1531\cdot 4729\cdot 4801\cdot 15817\cdot 31873\cdot 97849\cdot 18359951437\cdot 35107655355337\cdot 11818574496687068323309$ |
$11$ |
$188.293867872$ |
|
|
|
? |
$S_{45}$ (as 45T10923) |
not computed |
$2$ |
$23$ |
|
| 45.45.644...625.1 |
$x^{45} - 135 x^{43} - 45 x^{42} + 8145 x^{41} + 5076 x^{40} - 290700 x^{39} - 253620 x^{38} + 6857235 x^{37} + 7452610 x^{36} - 113268978 x^{35} - 144333495 x^{34} + 1355213265 x^{33} + 1957216455 x^{32} - 11983335705 x^{31} - 19266777171 x^{30} + 79141746870 x^{29} + 140783463765 x^{28} - 391240008255 x^{27} - 773615354895 x^{26} + 1437267934764 x^{25} + 3215872493700 x^{24} - 3839971488165 x^{23} - 10109340177300 x^{22} + 7085017431465 x^{21} + 23873005106874 x^{20} - 7751347674075 x^{19} - 41764000577760 x^{18} + 1270029598110 x^{17} + 52868417349600 x^{16} + 10969424061639 x^{15} - 46623586775670 x^{14} - 19170786833010 x^{13} + 26882974463550 x^{12} + 16378966497285 x^{11} - 8981328155022 x^{10} - 7825331392520 x^{9} + 1236586926825 x^{8} + 1998991148400 x^{7} + 84870189090 x^{6} - 236319447555 x^{5} - 31508573040 x^{4} + 10090496085 x^{3} + 1414058625 x^{2} - 109748520 x - 10224199$ |
$45$ |
[45,0] |
$3^{110}\cdot 5^{72}$ |
$2$ |
$192.596507455$ |
$192.59650745479388$ |
|
✓ |
? |
$C_{45}$ (as 45T1) |
not computed |
$2$ |
$44$ |
|
| 45.1.145...000.1 |
$x^{45} + 5 x - 2$ |
$45$ |
[1,22] |
$2^{42}\cdot 5^{46}\cdot 53\cdot 22846124160878734429091761\cdot 19\!\cdots\!97$ |
$5$ |
$196.120232448$ |
|
|
|
|
$S_{45}$ (as 45T10923) |
not computed |
$2$ |
$22$ |
|
| 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 |
$2$ |
$44$ |
|
| 45.3.582...875.1 |
$x^{45} - 5 x - 1$ |
$45$ |
[3,21] |
$-\,5^{45}\cdot 13\cdot 47\cdot 241\cdot 313\cdot 10159\cdot 1560681193\cdot 441481146991\cdot 24561359840613046207\cdot 258812619101427272051$ |
$10$ |
$202.256044825$ |
|
|
|
✓ |
$S_{45}$ (as 45T10923) |
not computed |
$2$ |
$23$ |
|
| 45.1.582...125.1 |
$x^{45} + 5 x - 1$ |
$45$ |
[1,22] |
$5^{46}\cdot 101\cdot 677\cdot 119549\cdot 842977\cdot 818961053\cdot 72\!\cdots\!73$ |
$7$ |
$202.256044825$ |
|
|
|
✓ |
$S_{45}$ (as 45T10923) |
not computed |
$2$ |
$22$ |
|
| 45.1.582...125.1 |
$x^{45} + 5 x - 3$ |
$45$ |
[1,22] |
$5^{46}\cdot 29\cdot 699023939659537\cdot 20\!\cdots\!01$ |
$4$ |
$202.256044843$ |
|
|
|
✓ |
$S_{45}$ (as 45T10923) |
not computed |
$2$ |
$22$ |
|
| 45.1.583...000.1 |
$x^{45} + 5 x - 4$ |
$45$ |
[1,22] |
$2^{89}\cdot 5^{46}\cdot 149\cdot 44\!\cdots\!01$ |
$4$ |
$202.261961044$ |
|
|
|
✓ |
$S_{45}$ (as 45T10923) |
not computed |
$2$ |
$22$ |
|
| 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 |
$2$ |
$44$ |
|
| 45.45.690...281.1 |
$x^{45} - 4 x^{44} - 146 x^{43} + 698 x^{42} + 8985 x^{41} - 51888 x^{40} - 296427 x^{39} + 2177976 x^{38} + 5305247 x^{37} - 57476954 x^{36} - 34012820 x^{35} + 1002110429 x^{34} - 626632964 x^{33} - 11753633659 x^{32} + 18688879395 x^{31} + 91599636078 x^{30} - 237738671647 x^{29} - 440115277508 x^{28} + 1861290436646 x^{27} + 876346054868 x^{26} - 9636797401413 x^{25} + 3638557275086 x^{24} + 33031864898329 x^{23} - 35155604700368 x^{22} - 70196515943930 x^{21} + 133850962002890 x^{20} + 68063148815178 x^{19} - 296060971462243 x^{18} + 63115875057640 x^{17} + 386991855136149 x^{16} - 292070548579474 x^{15} - 252378957195025 x^{14} + 393110942284862 x^{13} - 3989425272418 x^{12} - 248373295675609 x^{11} + 116468486134606 x^{10} + 55635812822046 x^{9} - 63558461838326 x^{8} + 10039317831256 x^{7} + 9501878099079 x^{6} - 4834005607020 x^{5} + 527330092663 x^{4} + 166660835109 x^{3} - 51025747438 x^{2} + 4407259697 x - 98524081$ |
$45$ |
[45,0] |
$19^{40}\cdot 31^{36}$ |
$2$ |
$213.677710939$ |
$213.67771093936358$ |
|
✓ |
|
$C_{45}$ (as 45T1) |
trivial |
$2$ |
$44$ |
$560427797213053600000000000000000000000$ |
| 45.1.141...125.1 |
$x^{45} - 5$ |
$45$ |
[1,22] |
$3^{90}\cdot 5^{89}$ |
$2$ |
$217.095015089$ |
$290.51052800882655$ |
|
|
✓ |
$D_{45}:C_{12}$ (as 45T144) |
not computed |
$2$ |
$22$ |
|
| 45.45.148...969.1 |
$x^{45} - 9 x^{44} - 117 x^{43} + 1356 x^{42} + 4455 x^{41} - 86382 x^{40} + 4596 x^{39} + 3024342 x^{38} - 5886234 x^{37} - 62776190 x^{36} + 223064037 x^{35} + 751420521 x^{34} - 4412144961 x^{33} - 3725440704 x^{32} + 54057041307 x^{31} - 28786222110 x^{30} - 426126343077 x^{29} + 673008341841 x^{28} + 2086637912508 x^{27} - 5873721786378 x^{26} - 5053254569676 x^{25} + 30385493847345 x^{24} - 5904503198856 x^{23} - 98922911866245 x^{22} + 93605350409913 x^{21} + 191046717571311 x^{20} - 349809055484526 x^{19} - 147155959283342 x^{18} + 707251464652203 x^{17} - 217826629489476 x^{16} - 797405893685064 x^{15} + 705978096992721 x^{14} + 378713501361567 x^{13} - 782478874269585 x^{12} + 139525392055671 x^{11} + 385252617992454 x^{10} - 250562776470715 x^{9} - 36607492213488 x^{8} + 95351499735039 x^{7} - 31186566059442 x^{6} - 5609742817023 x^{5} + 6576945066567 x^{4} - 1857401457582 x^{3} + 224711418717 x^{2} - 8430571116 x - 155181097$ |
$45$ |
[45,0] |
$3^{110}\cdot 31^{36}$ |
$2$ |
$228.762985377$ |
$228.76298537732032$ |
|
✓ |
? |
$C_{45}$ (as 45T1) |
not computed |
$2$ |
$44$ |
|
| 45.45.112...281.1 |
$x^{45} - x^{44} - 132 x^{43} + 301 x^{42} + 7581 x^{41} - 27065 x^{40} - 236809 x^{39} + 1229173 x^{38} + 3960874 x^{37} - 33065607 x^{36} - 18797995 x^{35} + 555716542 x^{34} - 619527603 x^{33} - 5732299123 x^{32} + 15235581842 x^{31} + 30609318626 x^{30} - 168897578817 x^{29} + 17112929652 x^{28} + 1054352970448 x^{27} - 1501837759883 x^{26} - 3320354588485 x^{25} + 10782132568732 x^{24} - 107051646226 x^{23} - 36936809485370 x^{22} + 41830258905956 x^{21} + 53083505529011 x^{20} - 152445251342987 x^{19} + 42842896041923 x^{18} + 229594603485553 x^{17} - 272222797945867 x^{16} - 70739760279828 x^{15} + 364126674087072 x^{14} - 209159107972130 x^{13} - 142016333800362 x^{12} + 231101895832035 x^{11} - 63870399263881 x^{10} - 62082302112786 x^{9} + 49149720219336 x^{8} - 3670701881262 x^{7} - 8040338248733 x^{6} + 2565873490427 x^{5} + 306896523050 x^{4} - 230447557112 x^{3} + 11171763392 x^{2} + 5932497375 x - 637239997$ |
$45$ |
[45,0] |
$271^{44}$ |
$1$ |
$239.278295664$ |
$239.27829566371238$ |
|
✓ |
|
$C_{45}$ (as 45T1) |
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 |
$2$ |
$44$ |
|
| 45.45.162...641.1 |
$x^{45} - 4 x^{44} - 182 x^{43} + 580 x^{42} + 15229 x^{41} - 35784 x^{40} - 771497 x^{39} + 1192202 x^{38} + 26249095 x^{37} - 21282586 x^{36} - 630350986 x^{35} + 101314575 x^{34} + 10957230656 x^{33} + 4486413137 x^{32} - 139417559409 x^{31} - 128053969474 x^{30} + 1299055132435 x^{29} + 1816090021004 x^{28} - 8766783201604 x^{27} - 16658946907076 x^{26} + 41634175647095 x^{25} + 105419181053468 x^{24} - 129801264303153 x^{23} - 468263377533416 x^{22} + 210417608171782 x^{21} + 1454214352745320 x^{20} + 113648989333176 x^{19} - 3097196961798623 x^{18} - 1450605309591570 x^{17} + 4363534978783893 x^{16} + 3500531720706214 x^{15} - 3807203164617687 x^{14} - 4497701352355764 x^{13} + 1760587964112158 x^{12} + 3382378542501223 x^{11} - 165688879950870 x^{10} - 1480388191573288 x^{9} - 205996027224400 x^{8} + 358811476146228 x^{7} + 88160595048203 x^{6} - 42989403930482 x^{5} - 13014696239433 x^{4} + 1879419740489 x^{3} + 646702182070 x^{2} + 19352782133 x - 2280393187$ |
$45$ |
[45,0] |
$19^{40}\cdot 41^{36}$ |
$2$ |
$267.2372247$ |
$267.2372246999024$ |
|
✓ |
? |
$C_{45}$ (as 45T1) |
not computed |
$2$ |
$44$ |
|
| 45.45.105...761.1 |
$x^{45} - 4 x^{44} - 194 x^{43} + 836 x^{42} + 16500 x^{41} - 76882 x^{40} - 811248 x^{39} + 4130184 x^{38} + 25559474 x^{37} - 145049280 x^{36} - 538597921 x^{35} + 3530594867 x^{34} + 7615564821 x^{33} - 61610572814 x^{32} - 68317895227 x^{31} + 786429242050 x^{30} + 287086043611 x^{29} - 7425134094508 x^{28} + 1391788361320 x^{27} + 52087220030130 x^{26} - 32183862662002 x^{25} - 271116028008606 x^{24} + 264064430436474 x^{23} + 1039304723755570 x^{22} - 1345885450620938 x^{21} - 2889398096911074 x^{20} + 4691240971935913 x^{19} + 5661912712400497 x^{18} - 11481658937434788 x^{17} - 7388527635358822 x^{16} + 19748315799639590 x^{15} + 5543796759733632 x^{14} - 23515522924776395 x^{13} - 895060410571712 x^{12} + 18817979236586386 x^{11} - 2391413888018270 x^{10} - 9652129249107031 x^{9} + 2328285637187904 x^{8} + 2951322314183680 x^{7} - 960094366581828 x^{6} - 477351520888160 x^{5} + 190413802657905 x^{4} + 31093339218140 x^{3} - 15654659537914 x^{2} - 188842256201 x + 306884845321$ |
$45$ |
[45,0] |
$11^{36}\cdot 73^{40}$ |
$2$ |
$308.603704387$ |
$308.6037043871589$ |
|
✓ |
? |
$C_{45}$ (as 45T1) |
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 |
$2$ |
$44$ |
|
