| 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 |
| 43.1.171...443.1 |
$x^{43} - x - 1$ |
$43$ |
[1,21] |
$-\,109\cdot 809\cdot 397519523\cdot 49\!\cdots\!61$ |
$4$ |
$42.9913070099$ |
$1.3112453023551685e+35$ |
|
|
✓ |
$S_{43}$ (as 43T10) |
not computed |
$2$ |
$21$ |
|
| 43.1.174...571.1 |
$x^{43} + x - 1$ |
$43$ |
[1,21] |
$-\,59\cdot 397\cdot 877\cdot 935899\cdot 2402649604770175349\cdot 37\!\cdots\!51$ |
$6$ |
$43.0086198004$ |
$1.3226452398347625e+35$ |
|
|
✓ |
$S_{43}$ (as 43T10) |
not computed |
$2$ |
$21$ |
|
| 43.1.736...104.1 |
$x^{43} - 4 x - 4$ |
$43$ |
[1,21] |
$-\,2^{42}\cdot 13\cdot 10239413\cdot 21464295562499\cdot 7440631653201968227\cdot 787580389820760746433715250923$ |
$6$ |
$84.5554977562$ |
$2.5465322118830868e+35$ |
|
|
? |
$S_{43}$ (as 43T10) |
not computed |
$2$ |
$21$ |
|
| 43.1.749...416.1 |
$x^{43} - 2 x - 2$ |
$43$ |
[1,21] |
$-\,2^{42}\cdot 5577217\cdot 417006008813\cdot 34910848872522797\cdot 201068225194855523\cdot 1043987668577822729$ |
$6$ |
$84.5904566931$ |
$2.569264622895059e+35$ |
|
|
✓ |
$S_{43}$ (as 43T10) |
not computed |
$2$ |
$21$ |
|
| 43.1.762...664.1 |
$x^{43} - x - 2$ |
$43$ |
[1,21] |
$-\,2^{43}\cdot 20380951\cdot 61480213\cdot 69\!\cdots\!91$ |
$4$ |
$84.6248191691$ |
|
|
|
✓ |
$S_{43}$ (as 43T10) |
not computed |
$2$ |
$21$ |
|
| 43.1.762...487.1 |
$x^{43} - x - 4$ |
$43$ |
[1,21] |
$-\,229\cdot 293\cdot 4986887\cdot 566527637659\cdot 4239521573605607851\cdot 94\!\cdots\!37$ |
$6$ |
$84.6248191691$ |
$2.7618602778968733e+41$ |
|
|
? |
$S_{43}$ (as 43T10) |
not computed |
$2$ |
$21$ |
|
| 43.1.762...728.1 |
$x^{43} - 2$ |
$43$ |
[1,21] |
$-\,2^{42}\cdot 43^{43}$ |
$2$ |
$84.6248191691$ |
$92.16816149710422$ |
|
|
✓ |
$F_{43}$ (as 43T8) |
not computed |
$2$ |
$21$ |
|
| 43.1.775...040.1 |
$x^{43} + 2 x - 2$ |
$43$ |
[1,21] |
$-\,2^{42}\cdot 5\cdot 19\cdot 4987\cdot 11154877\cdot 914818621983827673311\cdot 36\!\cdots\!97$ |
$7$ |
$84.6586054265$ |
$2.6141364721574758e+35$ |
|
|
✓ |
$S_{43}$ (as 43T10) |
not computed |
$2$ |
$21$ |
|
| 43.1.789...352.1 |
$x^{43} + 4 x - 4$ |
$43$ |
[1,21] |
$-\,2^{42}\cdot 90073\cdot 2923961\cdot 68\!\cdots\!71$ |
$4$ |
$84.691834691$ |
$2.636286003332312e+35$ |
|
|
? |
$S_{43}$ (as 43T10) |
not computed |
$2$ |
$21$ |
|
| 43.3.492...621.1 |
$x^{43} - 3 x - 1$ |
$43$ |
[3,20] |
$193\cdot 25\!\cdots\!97$ |
$2$ |
$115.510260058$ |
$2.2199442846773814e+44$ |
|
|
✓ |
$S_{43}$ (as 43T10) |
not computed |
$2$ |
$22$ |
|
| 43.1.492...856.1 |
$x^{43} + 3 x - 2$ |
$43$ |
[1,21] |
$-\,2^{43}\cdot 83\cdot 67\!\cdots\!29$ |
$3$ |
$115.510264216$ |
|
|
|
✓ |
$S_{43}$ (as 43T10) |
not computed |
$2$ |
$21$ |
|
| 43.1.189...651.1 |
$x^{43} - 2 x - 3$ |
$43$ |
[1,21] |
$-\,3^{42}\cdot 139\cdot 12\!\cdots\!01$ |
$3$ |
$125.745909717$ |
|
|
|
✓ |
$S_{43}$ (as 43T10) |
not computed |
$2$ |
$21$ |
|
| 43.1.189...899.1 |
$x^{43} - x - 3$ |
$43$ |
[1,21] |
$-\,3^{43}\cdot 3929\cdot 27164077\cdot 1696291894163\cdot 4471934430678427\cdot 71\!\cdots\!89$ |
$6$ |
$125.74590972$ |
|
|
|
✓ |
$S_{43}$ (as 43T10) |
not computed |
$2$ |
$21$ |
|
| 43.1.189...963.1 |
$x^{43} - 3$ |
$43$ |
[1,21] |
$-\,3^{42}\cdot 43^{43}$ |
$2$ |
$125.74590972$ |
$136.9547306384759$ |
|
|
✓ |
$F_{43}$ (as 43T8) |
not computed |
$2$ |
$21$ |
|
| 43.1.194...091.1 |
$x^{43} + 3 x - 3$ |
$43$ |
[1,21] |
$-\,3^{42}\cdot 11\cdot 4458821\cdot 2188196233\cdot 250952988948637\cdot 66\!\cdots\!49$ |
$6$ |
$125.820903255$ |
$3.900894748874076e+35$ |
|
|
✓ |
$S_{43}$ (as 43T10) |
not computed |
$2$ |
$21$ |
|
| 43.1.335...704.1 |
$x^{43} - 2 x - 4$ |
$43$ |
[1,21] |
$-\,2^{82}\cdot 17\cdot 911\cdot 1321\cdot 196825567\cdot 17\!\cdots\!89$ |
$6$ |
$149.628879545$ |
|
|
|
? |
$S_{43}$ (as 43T10) |
not computed |
$2$ |
$21$ |
|
| 43.43.995...529.1 |
$x^{43} - x^{42} - 84 x^{41} + 79 x^{40} + 3160 x^{39} - 2786 x^{38} - 70521 x^{37} + 58076 x^{36} + 1042773 x^{35} - 798942 x^{34} - 10810701 x^{33} + 7671648 x^{32} + 81126975 x^{31} - 53056499 x^{30} - 448758019 x^{29} + 268953093 x^{28} + 1846875875 x^{27} - 1007873658 x^{26} - 5671315301 x^{25} + 2797394685 x^{24} + 12962901258 x^{23} - 5730420663 x^{22} - 21895326590 x^{21} + 8590544711 x^{20} + 27001558938 x^{19} - 9297003415 x^{18} - 23896748020 x^{17} + 7121607714 x^{16} + 14834334408 x^{15} - 3755010451 x^{14} - 6269987218 x^{13} + 1310830451 x^{12} + 1732796449 x^{11} - 287529242 x^{10} - 294221159 x^{9} + 37041429 x^{8} + 27505221 x^{7} - 2599666 x^{6} - 1134285 x^{5} + 90620 x^{4} + 12893 x^{3} - 370 x^{2} - 54 x - 1$ |
$43$ |
[43,0] |
$173^{42}$ |
$1$ |
$153.461175075$ |
$153.46117507511823$ |
|
✓ |
|
$C_{43}$ (as 43T1) |
trivial |
$2$ |
$42$ |
$2657880348049265700000000000000000$ |
| 43.1.116...403.1 |
$x^{43} + 4 x - 1$ |
$43$ |
[1,21] |
$-\,181\cdot 155556871099633\cdot 21154104412279303\cdot 19\!\cdots\!37$ |
$4$ |
$154.013680078$ |
$1.0777670745654398e+47$ |
|
|
✓ |
$S_{43}$ (as 43T10) |
not computed |
$2$ |
$21$ |
|
| 43.1.116...624.1 |
$x^{43} + 4 x - 2$ |
$43$ |
[1,21] |
$-\,2^{42}\cdot 13\cdot 53\cdot 359\cdot 379\cdot 397\cdot 15583\cdot 15667\cdot 16763\cdot 1652591\cdot 7443949\cdot 81974567114861\cdot 17\!\cdots\!91$ |
$13$ |
$154.013680078$ |
$1.0114031480275054e+41$ |
|
|
✓ |
$S_{43}$ (as 43T10) |
not computed |
$2$ |
$21$ |
|
| 43.1.116...859.1 |
$x^{43} + 4 x - 3$ |
$43$ |
[1,21] |
$-\,3^{42}\cdot 17\cdot 251\cdot 24\!\cdots\!53$ |
$4$ |
$154.014265194$ |
|
|
|
✓ |
$S_{43}$ (as 43T10) |
not computed |
$2$ |
$21$ |
|
| 43.1.335...584.1 |
$x^{43} - 3 x - 4$ |
$43$ |
[1,21] |
$-\,2^{42}\cdot 5736251\cdot 13\!\cdots\!71$ |
$3$ |
$166.543255696$ |
|
|
|
✓ |
$S_{43}$ (as 43T10) |
not computed |
$2$ |
$21$ |
|
| 43.1.426...432.1 |
$x^{43} + 5 x - 2$ |
$43$ |
[1,21] |
$-\,2^{43}\cdot 48\!\cdots\!29$ |
$2$ |
$186.409446144$ |
|
|
|
? |
$S_{43}$ (as 43T10) |
not computed |
$2$ |
$21$ |
|
| 43.3.170...493.1 |
$x^{43} - 5 x - 1$ |
$43$ |
[3,20] |
$67\cdot 25\!\cdots\!79$ |
$2$ |
$192.517100097$ |
$1.306442173756887e+49$ |
|
|
✓ |
$S_{43}$ (as 43T10) |
not computed |
$2$ |
$22$ |
|
| 43.1.377...875.1 |
$x^{43} - 5 x - 5$ |
$43$ |
[1,21] |
$-\,5^{42}\cdot 1201\cdot 3109\cdot 627374521\cdot 70\!\cdots\!83$ |
$5$ |
$206.888556661$ |
$6.2041015477474564e+35$ |
|
|
✓ |
$S_{43}$ (as 43T10) |
not computed |
$2$ |
$21$ |
|
| 43.1.394...811.1 |
$x^{43} - x - 5$ |
$43$ |
[1,21] |
$-\,4378013\cdot 253946916604529\cdot 37511360891773121\cdot 94\!\cdots\!83$ |
$4$ |
$207.101547263$ |
$6.279743224460784e+49$ |
|
|
✓ |
$S_{43}$ (as 43T10) |
not computed |
$2$ |
$21$ |
|
| 43.1.394...875.1 |
$x^{43} - 5$ |
$43$ |
[1,21] |
$-\,5^{42}\cdot 43^{43}$ |
$2$ |
$207.101547263$ |
$225.5623000662761$ |
|
|
✓ |
$F_{43}$ (as 43T8) |
not computed |
$2$ |
$21$ |
|
| 43.1.394...003.1 |
$x^{43} + 3 x - 5$ |
$43$ |
[1,21] |
$-\,4787\cdot 56783432887\cdot 65016935311\cdot 22\!\cdots\!17$ |
$4$ |
$207.101547263$ |
$6.279743224500022e+49$ |
|
|
✓ |
$S_{43}$ (as 43T10) |
not computed |
$2$ |
$21$ |
|
| 43.1.411...875.1 |
$x^{43} + 5 x - 5$ |
$43$ |
[1,21] |
$-\,5^{42}\cdot 68281\cdot 26\!\cdots\!67$ |
$3$ |
$207.305717468$ |
$6.4786917631280636e+35$ |
|
|
✓ |
$S_{43}$ (as 43T10) |
not computed |
$2$ |
$21$ |
|
| 43.43.444...961.1 |
$x^{43} - x^{42} - 210 x^{41} + 177 x^{40} + 19424 x^{39} - 12392 x^{38} - 1053196 x^{37} + 410572 x^{36} + 37567316 x^{35} - 4029555 x^{34} - 936601673 x^{33} - 185951871 x^{32} + 16894280750 x^{31} + 8734312688 x^{30} - 224649876009 x^{29} - 189102381409 x^{28} + 2218265633870 x^{27} + 2604819705111 x^{26} - 16218499586789 x^{25} - 24791417254787 x^{24} + 86521587673786 x^{23} + 168116844068603 x^{22} - 325504806681996 x^{21} - 819692515707425 x^{20} + 795734675389219 x^{19} + 2859558999201013 x^{18} - 937302717934781 x^{17} - 7011360351157045 x^{16} - 902655412698460 x^{15} + 11681897146129224 x^{14} + 5604720542659268 x^{13} - 12486138055465655 x^{12} - 9886946345787043 x^{11} + 7728522779787490 x^{10} + 9075115953805640 x^{9} - 2183897418754987 x^{8} - 4579013283800046 x^{7} - 40649514655288 x^{6} + 1249295360564226 x^{5} + 160575454035341 x^{4} - 166814479770181 x^{3} - 29312399288701 x^{2} + 7715035819499 x + 1403424452501$ |
$43$ |
[43,0] |
$431^{42}$ |
$1$ |
$374.291838114$ |
$374.29183811372997$ |
|
✓ |
|
$C_{43}$ (as 43T1) |
not computed |
$2$ |
$42$ |
|
| 43.43.101...009.1 |
$x^{43} - x^{42} - 462 x^{41} + 301 x^{40} + 94630 x^{39} - 49892 x^{38} - 11463758 x^{37} + 6368083 x^{36} + 921810336 x^{35} - 636827636 x^{34} - 52222121579 x^{33} + 47086072273 x^{32} + 2155113502777 x^{31} - 2510570612339 x^{30} - 65969924993323 x^{29} + 96629348183472 x^{28} + 1509193690295722 x^{27} - 2705517116526302 x^{26} - 25775660913572833 x^{25} + 55430418074111539 x^{24} + 325598895562519548 x^{23} - 832294062829303477 x^{22} - 2983438147701667253 x^{21} + 9129779342869086290 x^{20} + 19125104314160845818 x^{19} - 72594260758345520281 x^{18} - 79441906767691419891 x^{17} + 413102772817597404709 x^{16} + 166866840849449475306 x^{15} - 1650628224018564426381 x^{14} + 139804498689687778120 x^{13} + 4502348802434562518439 x^{12} - 1981830512581480780535 x^{11} - 8037383143222291539220 x^{10} + 5701308150866478483031 x^{9} + 8799946070456643867879 x^{8} - 8188607772821299311768 x^{7} - 5304980067316890480275 x^{6} + 6100770874409784770241 x^{5} + 1408273844297690430983 x^{4} - 2063406363097082700573 x^{3} - 90731765675438007935 x^{2} + 193966087122261586736 x + 18221685305593614631$ |
$43$ |
[43,0] |
$947^{42}$ |
$1$ |
$807.481419163$ |
$807.4814191627743$ |
|
✓ |
|
$C_{43}$ (as 43T1) |
not computed |
$2$ |
$42$ |
|
| 43.43.162...801.1 |
$x^{43} - 903 x^{41} - 645 x^{40} + 358276 x^{39} + 487362 x^{38} - 82668446 x^{37} - 161379172 x^{36} + 12386889944 x^{35} + 31035129471 x^{34} - 1275092913940 x^{33} - 3868686195114 x^{32} + 93052767268909 x^{31} + 330473143424644 x^{30} - 4897798025442393 x^{29} - 19967338988758228 x^{28} + 187329847291648022 x^{27} + 869728040966016241 x^{26} - 5201925841676982029 x^{25} - 27621776964130665961 x^{24} + 103748981858304966660 x^{23} + 643326429466437698421 x^{22} - 1445787294046167541816 x^{21} - 10999588529245966977339 x^{20} + 13140703542377826450494 x^{19} + 137573117593988043652238 x^{18} - 60838518194479293931722 x^{17} - 1247516677692517201034941 x^{16} - 134666416459554320685647 x^{15} + 8070410654031859605939559 x^{14} + 4203376282667672263555078 x^{13} - 36228120784944419229616219 x^{12} - 30515963297503545387850753 x^{11} + 107534691527795878017440861 x^{10} + 119306453339061961678830425 x^{9} - 192818992256047972290970619 x^{8} - 263326021640166500214931210 x^{7} + 170563929616560831037152772 x^{6} + 294222510747058121054570076 x^{5} - 33622183448420036732904682 x^{4} - 118832831442545361067982885 x^{3} - 7933826886293481520543865 x^{2} + 14571491290875996179048369 x + 2572343484535669027372727$ |
$43$ |
[43,0] |
$43^{84}$ |
$1$ |
$1552.24987718$ |
$1552.2498771818027$ |
|
✓ |
|
$C_{43}$ (as 43T1) |
not computed |
$2$ |
$42$ |
|
