| 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 |
| 41.1.131...641.1 |
$x^{41} - x - 1$ |
$41$ |
[1,20] |
$2251\cdot 272583857708203\cdot 761889448323748621067\cdot 2821028813073407561156582291$ |
$4$ |
$40.9908758335$ |
$1.1483851150361388e+33$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
trivial |
$2$ |
$20$ |
$28450692757863310$ |
| 41.1.343...976.1 |
$x^{41} + 4 x - 4$ |
$41$ |
[1,20] |
$2^{40}\cdot 63506090654183\cdot 49\!\cdots\!47$ |
$3$ |
$69.5586596583$ |
$1.0997338366416402e+32$ |
|
|
? |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.41.579...201.1 |
$x^{41} - x^{40} - 40 x^{39} + 39 x^{38} + 741 x^{37} - 703 x^{36} - 8436 x^{35} + 7770 x^{34} + 66045 x^{33} - 58905 x^{32} - 376992 x^{31} + 324632 x^{30} + 1623160 x^{29} - 1344904 x^{28} - 5379616 x^{27} + 4272048 x^{26} + 13884156 x^{25} - 10518300 x^{24} - 28048800 x^{23} + 20160075 x^{22} + 44352165 x^{21} - 30045015 x^{20} - 54627300 x^{19} + 34597290 x^{18} + 51895935 x^{17} - 30421755 x^{16} - 37442160 x^{15} + 20058300 x^{14} + 20058300 x^{13} - 9657700 x^{12} - 7726160 x^{11} + 3268760 x^{10} + 2042975 x^{9} - 735471 x^{8} - 346104 x^{7} + 100947 x^{6} + 33649 x^{5} - 7315 x^{4} - 1540 x^{3} + 210 x^{2} + 21 x - 1$ |
$41$ |
[41,0] |
$83^{40}$ |
$1$ |
$74.5197363392$ |
$74.51973633924607$ |
|
✓ |
✓ |
$C_{41}$ (as 41T1) |
trivial |
$2$ |
$40$ |
$29837391421490950000000000$ |
| 41.1.141...416.1 |
$x^{41} - 4 x - 4$ |
$41$ |
[1,20] |
$2^{40}\cdot 2313020109848347\cdot 2947885124842583399107\cdot 188093758458159369641352727129$ |
$4$ |
$80.5526095167$ |
$2.2269987591329257e+33$ |
|
|
? |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.143...416.1 |
$x^{41} - 2 x - 2$ |
$41$ |
[1,20] |
$2^{40}\cdot 3\cdot 53\cdot 67\cdot 19183\cdot 332415773971\cdot 2121795341959\cdot 90\!\cdots\!31$ |
$8$ |
$80.5893122191$ |
$2.2478928141179964e+33$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.146...416.1 |
$x^{41} - x - 2$ |
$41$ |
[1,20] |
$2^{40}\cdot 139\cdot 1289\cdot 74\!\cdots\!71$ |
$4$ |
$80.6253582462$ |
|
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.146...416.1 |
$x^{41} - x - 4$ |
$41$ |
[1,20] |
$2^{40}\cdot 13\!\cdots\!41$ |
$2$ |
$80.6253582462$ |
|
|
|
? |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.146...416.1 |
$x^{41} - 2$ |
$41$ |
[1,20] |
$2^{40}\cdot 41^{41}$ |
$2$ |
$80.6253582462$ |
$88.06927966939196$ |
|
|
✓ |
$F_{41}$ (as 41T8) |
not computed |
$2$ |
$20$ |
|
| 41.1.148...416.1 |
$x^{41} + 2 x - 2$ |
$41$ |
[1,20] |
$2^{40}\cdot 29\cdot 5227\cdot 7297\cdot 6697657\cdot 53935240897410251303\cdot 33\!\cdots\!21$ |
$7$ |
$80.6607709621$ |
$2.2891088582526597e+33$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.440...416.1 |
$x^{41} + 3 x - 2$ |
$41$ |
[1,20] |
$2^{40}\cdot 11\cdot 367\cdot 104399\cdot 13038909447397913\cdot 19797069953357319509\cdot 3686170645074380678869761671$ |
$7$ |
$109.674748522$ |
|
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.157...441.1 |
$x^{41} - 3 x - 3$ |
$41$ |
[1,20] |
$3^{40}\cdot 7\cdot 32261\cdot 253464984011\cdot 1238514877771\cdot 76247312349973837\cdot 239507603770962778439$ |
$7$ |
$119.667259082$ |
$3.3231780104649844e+33$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.161...441.1 |
$x^{41} - 2 x - 3$ |
$41$ |
[1,20] |
$19\cdot 23\cdot 31\cdot 23297\cdot 24551\cdot 61559\cdot 192233\cdot 17\!\cdots\!67$ |
$8$ |
$119.747928028$ |
$4.0224824391897956e+42$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.161...441.1 |
$x^{41} - x - 3$ |
$41$ |
[1,20] |
$307\cdot 5719838273\cdot 92\!\cdots\!31$ |
$3$ |
$119.747928032$ |
$4.022482442494292e+42$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.161...441.1 |
$x^{41} - 3$ |
$41$ |
[1,20] |
$3^{40}\cdot 41^{41}$ |
$2$ |
$119.747928032$ |
$130.8039305884991$ |
|
|
✓ |
$F_{41}$ (as 41T8) |
not computed |
$2$ |
$20$ |
|
| 41.1.166...441.1 |
$x^{41} + 3 x - 3$ |
$41$ |
[1,20] |
$3^{40}\cdot 11\cdot 123191\cdot 11537809\cdot 901418971\cdot 13197674429\cdot 39039118092749\cdot 188276273322445488239$ |
$8$ |
$119.826480163$ |
$3.415006263366723e+33$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.3.584...584.1 |
$x^{41} - 4 x - 2$ |
$41$ |
[3,19] |
$-\,2^{40}\cdot 859\cdot 228505873\cdot 27\!\cdots\!37$ |
$4$ |
$146.232986193$ |
$4.534376065245929e+38$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$21$ |
|
| 41.1.402...704.1 |
$x^{41} - 2 x - 4$ |
$41$ |
[1,20] |
$2^{78}\cdot 3\cdot 2358722227395221\cdot 18\!\cdots\!07$ |
$4$ |
$153.276321083$ |
|
|
|
? |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.402...704.1 |
$x^{41} + 2 x - 4$ |
$41$ |
[1,20] |
$2^{78}\cdot 2339\cdot 1104312393641791\cdot 51\!\cdots\!09$ |
$4$ |
$153.276321083$ |
|
|
|
? |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.160...816.1 |
$x^{41} - 3 x - 4$ |
$41$ |
[1,20] |
$2^{80}\cdot 7\cdot 37\cdot 67\cdot 108499\cdot 543997\cdot 270310655161\cdot 312570029227603619\cdot 15379092216330540575461$ |
$9$ |
$158.547520704$ |
|
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.160...816.1 |
$x^{41} + x - 4$ |
$41$ |
[1,20] |
$2^{80}\cdot 3\cdot 263\cdot 587\cdot 6397\cdot 336221\cdot 7665197\cdot 4370168129\cdot 621071121653\cdot 64218333671912404841959$ |
$10$ |
$158.547521764$ |
|
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.137...104.1 |
$x^{41} + 5 x - 2$ |
$41$ |
[1,20] |
$2^{38}\cdot 163\cdot 743\cdot 10289\cdot 104597\cdot 31257021937\cdot 13675604446553671\cdot 95253739993542479\cdot 94216078858946850824041$ |
$9$ |
$176.714005801$ |
|
|
|
|
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.3.549...559.1 |
$x^{41} - 5 x - 3$ |
$41$ |
[3,19] |
$-\,13\cdot 3357247\cdot 6299663\cdot 93408687929\cdot 21\!\cdots\!47$ |
$5$ |
$182.79123261$ |
$2.344687181070505e+46$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$21$ |
|
| 41.3.549...584.1 |
$x^{41} - 5 x - 2$ |
$41$ |
[3,19] |
$-\,2^{40}\cdot 3\cdot 13\cdot 27277\cdot 84809\cdot 128519\cdot 211271\cdot 11833317469\cdot 17\!\cdots\!57$ |
$9$ |
$182.791232741$ |
|
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$21$ |
|
| 41.3.549...359.1 |
$x^{41} - 5 x - 1$ |
$41$ |
[3,19] |
$-\,3\cdot 7\cdot 115979\cdot 1907696227638017\cdot 11\!\cdots\!53$ |
$5$ |
$182.791232741$ |
$2.3446872155748193e+46$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$21$ |
|
| 41.1.549...641.1 |
$x^{41} + 5 x - 1$ |
$41$ |
[1,20] |
$43\cdot 191\cdot 9901\cdot 55082201453159\cdot 467781923539898069\cdot 251911473477379412779567\cdot 10\!\cdots\!01$ |
$7$ |
$182.791232741$ |
$2.3446872155748193e+46$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.551...816.1 |
$x^{41} + 5 x - 4$ |
$41$ |
[1,20] |
$2^{80}\cdot 53\cdot 2252852353\cdot 11587626304193\cdot 32\!\cdots\!93$ |
$5$ |
$182.804262015$ |
|
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.128...625.1 |
$x^{41} - 5 x - 5$ |
$41$ |
[1,20] |
$5^{40}\cdot 245129\cdot 204113313923\cdot 28\!\cdots\!47$ |
$4$ |
$186.611859549$ |
$1.8062435116388302e+33$ |
|
|
? |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.121...625.1 |
$x^{41} - 4 x - 5$ |
$41$ |
[1,20] |
$5^{40}\cdot 23\cdot 43\cdot 7678031\cdot 17\!\cdots\!43$ |
$5$ |
$197.108685196$ |
|
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.121...625.1 |
$x^{41} - 3 x - 5$ |
$41$ |
[1,20] |
$5^{40}\cdot 13\!\cdots\!13$ |
$2$ |
$197.108708415$ |
|
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.121...625.1 |
$x^{41} - 2 x - 5$ |
$41$ |
[1,20] |
$3\cdot 5^{40}\cdot 13\cdot 157\cdot 6298160107\cdot 50991976651363487\cdot 67\!\cdots\!27$ |
$7$ |
$197.108708415$ |
|
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.121...625.1 |
$x^{41} - x - 5$ |
$41$ |
[1,20] |
$5^{41}\cdot 7033139213\cdot 64812836603\cdot 37176884662660649\cdot 15706697658577462999892991283$ |
$5$ |
$197.108708415$ |
|
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.121...625.1 |
$x^{41} - 5$ |
$41$ |
[1,20] |
$5^{40}\cdot 41^{41}$ |
$2$ |
$197.108708415$ |
$215.30722274348358$ |
|
|
✓ |
$F_{41}$ (as 41T8) |
not computed |
$2$ |
$20$ |
|
| 41.1.121...625.1 |
$x^{41} + x - 5$ |
$41$ |
[1,20] |
$3\cdot 5^{40}\cdot 7\cdot 11287\cdot 706035413231\cdot 1169722373977559\cdot 67\!\cdots\!99$ |
$7$ |
$197.108708415$ |
|
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.121...625.1 |
$x^{41} + 2 x - 5$ |
$41$ |
[1,20] |
$5^{40}\cdot 29\cdot 131\cdot 163\cdot 2089\cdot 10\!\cdots\!01$ |
$6$ |
$197.108708415$ |
|
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.121...625.1 |
$x^{41} + 3 x - 5$ |
$41$ |
[1,20] |
$5^{40}\cdot 11\cdot 89\cdot 3571\cdot 20521\cdot 218655088207\cdot 84\!\cdots\!03$ |
$7$ |
$197.108708415$ |
|
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.126...625.1 |
$x^{41} + 5 x - 5$ |
$41$ |
[1,20] |
$5^{40}\cdot 19\cdot 607\cdot 1420817\cdot 36720491\cdot 23\!\cdots\!91$ |
$6$ |
$197.322360921$ |
$5.670692287910047e+33$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.41.556...401.1 |
$x^{41} - x^{40} - 360 x^{39} + 745 x^{38} + 56451 x^{37} - 169135 x^{36} - 5037002 x^{35} + 19221892 x^{34} + 281906305 x^{33} - 1293434183 x^{32} - 10337722909 x^{31} + 55807085286 x^{30} + 252777087235 x^{29} - 1613716714335 x^{28} - 4112155095553 x^{27} + 32113136009541 x^{26} + 43177039971301 x^{25} - 446781341742247 x^{24} - 262923207247335 x^{23} + 4379546308331567 x^{22} + 474335495077459 x^{21} - 30267239554430324 x^{20} + 5902126403913719 x^{19} + 146509496594642143 x^{18} - 56363172819685690 x^{17} - 489681930758553989 x^{16} + 246552011225708759 x^{15} + 1105369786197101758 x^{14} - 636716564586328491 x^{13} - 1632560051818863682 x^{12} + 995239432812617607 x^{11} + 1514536703235322325 x^{10} - 898680726508319339 x^{9} - 853943547109610470 x^{8} + 424335389068850481 x^{7} + 299252740781325936 x^{6} - 91861302074915780 x^{5} - 62873369979635247 x^{4} + 4140602930707759 x^{3} + 6001367177186495 x^{2} + 926057723623551 x + 39010859256913$ |
$41$ |
[41,0] |
$739^{40}$ |
$1$ |
$629.038896617$ |
$629.0388966174669$ |
|
✓ |
|
$C_{41}$ (as 41T1) |
not computed |
$2$ |
$40$ |
|
| 41.41.374...801.1 |
$x^{41} - x^{40} - 400 x^{39} + 267 x^{38} + 70434 x^{37} - 25456 x^{36} - 7231147 x^{35} + 643597 x^{34} + 483795648 x^{33} + 68617520 x^{32} - 22359647160 x^{31} - 7251158053 x^{30} + 739255603225 x^{29} + 335708547372 x^{28} - 17885796411269 x^{27} - 9479269329758 x^{26} + 321562652641396 x^{25} + 177909044828159 x^{24} - 4339729918343900 x^{23} - 2288515231871121 x^{22} + 44211233079107427 x^{21} + 20209478217861146 x^{20} - 340291820674520880 x^{19} - 118610646663806737 x^{18} + 1969458668208622674 x^{17} + 410494333593592611 x^{16} - 8467703539109471908 x^{15} - 372233629251247247 x^{14} + 26446416435739805624 x^{13} - 3641024063367368116 x^{12} - 57732002041736983193 x^{11} + 19074905803558500162 x^{10} + 82370621416601788582 x^{9} - 43840068640516285889 x^{8} - 67556477435299552660 x^{7} + 51180521959924527335 x^{6} + 23228035973272766493 x^{5} - 26391119726982867791 x^{4} + 202102108745982587 x^{3} + 4168134528839675291 x^{2} - 499943870456762867 x - 149270874547838371$ |
$41$ |
[41,0] |
$821^{40}$ |
$1$ |
$697.046284664$ |
$697.0462846642772$ |
|
✓ |
|
$C_{41}$ (as 41T1) |
not computed |
$2$ |
$40$ |
|
| 41.41.105...201.1 |
$x^{41} - 820 x^{39} - 533 x^{38} + 303031 x^{37} + 376913 x^{36} - 66737627 x^{35} - 118821690 x^{34} + 9764169434 x^{33} + 22080920476 x^{32} - 1002016650746 x^{31} - 2696024483356 x^{30} + 74276881167057 x^{29} + 228322554454083 x^{28} - 4038255389081271 x^{27} - 13810013721005555 x^{26} + 161957213612863355 x^{25} + 605630162979885300 x^{24} - 4783062094323192024 x^{23} - 19362795070723667202 x^{22} + 103087839028351278942 x^{21} + 450266165503910224663 x^{20} - 1593603545898162906857 x^{19} - 7540369918979718461657 x^{18} + 17171487184711671438215 x^{17} + 89253263738667697145313 x^{16} - 123172673161638273736870 x^{15} - 724697045982659590514328 x^{14} + 544476915889889670403041 x^{13} + 3855061119747652830292013 x^{12} - 1279320329561947245453521 x^{11} - 12510633939200726076347653 x^{10} + 1043523355082184352460715 x^{9} + 22013783610841586394614893 x^{8} + 598853130650094992883999 x^{7} - 16988637915887608842729071 x^{6} - 1349373804383563050067379 x^{5} + 3896754513924753580219610 x^{4} + 333868055127333108898601 x^{3} - 256246929318582500140348 x^{2} - 10590850429623318361311 x + 2727257042363914863401$ |
$41$ |
[41,0] |
$41^{80}$ |
$1$ |
$1402.47565155$ |
$1402.475651548207$ |
|
✓ |
|
$C_{41}$ (as 41T1) |
not computed |
$2$ |
$40$ |
|
