| 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 |
| 41.41.579...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 |
$2$ |
$40$ |
$29837391421490950000000000$ |
| 41.41.556...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 |
$2$ |
$40$ |
|
