| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Unit group torsion |
Unit group rank |
Regulator |
| 41.1.131...641.1 |
x41 - x - 1 |
$41$ |
[1,20] |
$2251\cdot 272583857708203\cdot 761889448323748621067\cdot 2821028813073407561156582291$ |
$4$ |
$40.9908758335$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
trivial |
$2$ |
$20$ |
$28450692757863310$ |
| 41.1.343...976.1 |
x41 + 4x - 4 |
$41$ |
[1,20] |
$2^{40}\cdot 63506090654183\cdot 49\!\cdots\!47$ |
$3$ |
$69.5586596583$ |
|
|
not computed |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
$$ |
| 41.41.579...201.1 |
x41 - x40 - 40x39 + 39x38 + 741x37 - 703x36 - 8436x35 + 7770x34 + 66045x33 - 58905x32 - 376992x31 + 324632x30 + 1623160x29 - 1344904x28 - 5379616x27 + 4272048x26 + 13884156x25 - 10518300x24 - 28048800x23 + 20160075x22 + 44352165x21 - 30045015x20 - 54627300x19 + 34597290x18 + 51895935x17 - 30421755x16 - 37442160x15 + 20058300x14 + 20058300x13 - 9657700x12 - 7726160x11 + 3268760x10 + 2042975x9 - 735471x8 - 346104x7 + 100947x6 + 33649x5 - 7315x4 - 1540x3 + 210x2 + 21x - 1 |
$41$ |
[41,0] |
$83^{40}$ |
$1$ |
$74.5197363392$ |
|
✓ |
✓ |
$C_{41}$ (as 41T1) |
trivial |
$2$ |
$40$ |
$29837391421490950000000000$ |
| 41.1.141...416.1 |
x41 - 4x - 4 |
$41$ |
[1,20] |
$2^{40}\cdot 2313020109848347\cdot 2947885124842583399107\cdot 188093758458159369641352727129$ |
$4$ |
$80.5526095167$ |
|
|
not computed |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
$$ |
| 41.1.143...416.1 |
x41 - 2x - 2 |
$41$ |
[1,20] |
$2^{40}\cdot 3\cdot 53\cdot 67\cdot 19183\cdot 332415773971\cdot 2121795341959\cdot 90\!\cdots\!31$ |
$8$ |
$80.5893122191$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
$$ |
| 41.1.146...416.1 |
x41 - x - 2 |
$41$ |
[1,20] |
$2^{40}\cdot 139\cdot 1289\cdot 74\!\cdots\!71$ |
$4$ |
$80.6253582462$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
$$ |
| 41.1.146...416.1 |
x41 - x - 4 |
$41$ |
[1,20] |
$2^{40}\cdot 13\!\cdots\!41$ |
$2$ |
$80.6253582462$ |
|
|
not computed |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
$$ |
| 41.1.146...416.1 |
x41 - 2 |
$41$ |
[1,20] |
$2^{40}\cdot 41^{41}$ |
$2$ |
$80.6253582462$ |
|
|
✓ |
$F_{41}$ (as 41T8) |
not computed |
$2$ |
$20$ |
$$ |
| 41.1.148...416.1 |
x41 + 2x - 2 |
$41$ |
[1,20] |
$2^{40}\cdot 29\cdot 5227\cdot 7297\cdot 6697657\cdot 53935240897410251303\cdot 33\!\cdots\!21$ |
$7$ |
$80.6607709621$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
$$ |
| 41.1.440...416.1 |
x41 + 3x - 2 |
$41$ |
[1,20] |
$2^{40}\cdot 11\cdot 367\cdot 104399\cdot 13038909447397913\cdot 19797069953357319509\cdot 3686170645074380678869761671$ |
$7$ |
$109.674748522$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
$$ |
| 41.1.157...441.1 |
x41 - 3x - 3 |
$41$ |
[1,20] |
$3^{40}\cdot 7\cdot 32261\cdot 253464984011\cdot 1238514877771\cdot 76247312349973837\cdot 239507603770962778439$ |
$7$ |
$119.667259082$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
$$ |
| 41.1.161...441.1 |
x41 - 2x - 3 |
$41$ |
[1,20] |
$19\cdot 23\cdot 31\cdot 23297\cdot 24551\cdot 61559\cdot 192233\cdot 17\!\cdots\!67$ |
$8$ |
$119.747928028$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
$$ |
| 41.1.161...441.1 |
x41 - x - 3 |
$41$ |
[1,20] |
$307\cdot 5719838273\cdot 92\!\cdots\!31$ |
$3$ |
$119.747928032$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
$$ |
| 41.1.161...441.1 |
x41 - 3 |
$41$ |
[1,20] |
$3^{40}\cdot 41^{41}$ |
$2$ |
$119.747928032$ |
|
|
✓ |
$F_{41}$ (as 41T8) |
not computed |
$2$ |
$20$ |
$$ |
| 41.1.166...441.1 |
x41 + 3x - 3 |
$41$ |
[1,20] |
$3^{40}\cdot 11\cdot 123191\cdot 11537809\cdot 901418971\cdot 13197674429\cdot 39039118092749\cdot 188276273322445488239$ |
$8$ |
$119.826480163$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
$$ |
| 41.3.584...584.1 |
x41 - 4x - 2 |
$41$ |
[3,19] |
$-\,2^{40}\cdot 859\cdot 228505873\cdot 27\!\cdots\!37$ |
$4$ |
$146.232986193$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$21$ |
$$ |
| 41.1.402...704.1 |
x41 - 2x - 4 |
$41$ |
[1,20] |
$2^{78}\cdot 3\cdot 2358722227395221\cdot 18\!\cdots\!07$ |
$4$ |
$153.276321083$ |
|
|
not computed |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
$$ |
| 41.1.402...704.1 |
x41 + 2x - 4 |
$41$ |
[1,20] |
$2^{78}\cdot 2339\cdot 1104312393641791\cdot 51\!\cdots\!09$ |
$4$ |
$153.276321083$ |
|
|
not computed |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
$$ |
| 41.1.160...816.1 |
x41 - 3x - 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 |
$2$ |
$20$ |
$$ |
| 41.1.160...816.1 |
x41 + x - 4 |
$41$ |
[1,20] |
$2^{80}\cdot 3\cdot 263\cdot 587\cdot 6397\cdot 336221\cdot 7665197\cdot 4370168129\cdot 621071121653\cdot 64218333671912404841959$ |
$10$ |
$158.547521764$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
$$ |
| 41.1.137...104.1 |
x41 + 5x - 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 |
$2$ |
$20$ |
$$ |
| 41.3.549...559.1 |
x41 - 5x - 3 |
$41$ |
[3,19] |
$-\,13\cdot 3357247\cdot 6299663\cdot 93408687929\cdot 21\!\cdots\!47$ |
$5$ |
$182.79123261$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$21$ |
$$ |
| 41.3.549...584.1 |
x41 - 5x - 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 |
$2$ |
$21$ |
$$ |
| 41.3.549...359.1 |
x41 - 5x - 1 |
$41$ |
[3,19] |
$-\,3\cdot 7\cdot 115979\cdot 1907696227638017\cdot 11\!\cdots\!53$ |
$5$ |
$182.791232741$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$21$ |
$$ |
| 41.1.549...641.1 |
x41 + 5x - 1 |
$41$ |
[1,20] |
$43\cdot 191\cdot 9901\cdot 55082201453159\cdot 467781923539898069\cdot 251911473477379412779567\cdot 10\!\cdots\!01$ |
$7$ |
$182.791232741$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
$$ |
| 41.1.551...816.1 |
x41 + 5x - 4 |
$41$ |
[1,20] |
$2^{80}\cdot 53\cdot 2252852353\cdot 11587626304193\cdot 32\!\cdots\!93$ |
$5$ |
$182.804262015$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
$$ |
| 41.1.128...625.1 |
x41 - 5x - 5 |
$41$ |
[1,20] |
$5^{40}\cdot 245129\cdot 204113313923\cdot 28\!\cdots\!47$ |
$4$ |
$186.611859549$ |
|
|
not computed |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
$$ |
| 41.1.121...625.1 |
x41 - 4x - 5 |
$41$ |
[1,20] |
$5^{40}\cdot 23\cdot 43\cdot 7678031\cdot 17\!\cdots\!43$ |
$5$ |
$197.108685196$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
$$ |
| 41.1.121...625.1 |
x41 - 3x - 5 |
$41$ |
[1,20] |
$5^{40}\cdot 13\!\cdots\!13$ |
$2$ |
$197.108708415$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
$$ |
| 41.1.121...625.1 |
x41 - 2x - 5 |
$41$ |
[1,20] |
$3\cdot 5^{40}\cdot 13\cdot 157\cdot 6298160107\cdot 50991976651363487\cdot 67\!\cdots\!27$ |
$7$ |
$197.108708415$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
$$ |
| 41.1.121...625.1 |
x41 - x - 5 |
$41$ |
[1,20] |
$5^{41}\cdot 7033139213\cdot 64812836603\cdot 37176884662660649\cdot 15706697658577462999892991283$ |
$5$ |
$197.108708415$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
$$ |
| 41.1.121...625.1 |
x41 - 5 |
$41$ |
[1,20] |
$5^{40}\cdot 41^{41}$ |
$2$ |
$197.108708415$ |
|
|
✓ |
$F_{41}$ (as 41T8) |
not computed |
$2$ |
$20$ |
$$ |
| 41.1.121...625.1 |
x41 + 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 |
$2$ |
$20$ |
$$ |
| 41.1.121...625.1 |
x41 + 2x - 5 |
$41$ |
[1,20] |
$5^{40}\cdot 29\cdot 131\cdot 163\cdot 2089\cdot 10\!\cdots\!01$ |
$6$ |
$197.108708415$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
$$ |
| 41.1.121...625.1 |
x41 + 3x - 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 |
$2$ |
$20$ |
$$ |
| 41.1.126...625.1 |
x41 + 5x - 5 |
$41$ |
[1,20] |
$5^{40}\cdot 19\cdot 607\cdot 1420817\cdot 36720491\cdot 23\!\cdots\!91$ |
$6$ |
$197.322360921$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
$$ |
| 41.41.556...401.1 |
x41 - x40 - 360x39 + 745x38 + 56451x37 - 169135x36 - 5037002x35 + 19221892x34 + 281906305x33 - 1293434183x32 - 10337722909x31 + 55807085286x30 + 252777087235x29 - 1613716714335x28 - 4112155095553x27 + 32113136009541x26 + 43177039971301x25 - 446781341742247x24 - 262923207247335x23 + 4379546308331567x22 + 474335495077459x21 - 30267239554430324x20 + 5902126403913719x19 + 146509496594642143x18 - 56363172819685690x17 - 489681930758553989x16 + 246552011225708759x15 + 1105369786197101758x14 - 636716564586328491x13 - 1632560051818863682x12 + 995239432812617607x11 + 1514536703235322325x10 - 898680726508319339x9 - 853943547109610470x8 + 424335389068850481x7 + 299252740781325936x6 - 91861302074915780x5 - 62873369979635247x4 + 4140602930707759x3 + 6001367177186495x2 + 926057723623551x + 39010859256913 |
$41$ |
[41,0] |
$739^{40}$ |
$1$ |
$629.038896617$ |
|
✓ |
|
$C_{41}$ (as 41T1) |
not computed |
$2$ |
$40$ |
$$ |
| 41.41.374...801.1 |
x41 - x40 - 400x39 + 267x38 + 70434x37 - 25456x36 - 7231147x35 + 643597x34 + 483795648x33 + 68617520x32 - 22359647160x31 - 7251158053x30 + 739255603225x29 + 335708547372x28 - 17885796411269x27 - 9479269329758x26 + 321562652641396x25 + 177909044828159x24 - 4339729918343900x23 - 2288515231871121x22 + 44211233079107427x21 + 20209478217861146x20 - 340291820674520880x19 - 118610646663806737x18 + 1969458668208622674x17 + 410494333593592611x16 - 8467703539109471908x15 - 372233629251247247x14 + 26446416435739805624x13 - 3641024063367368116x12 - 57732002041736983193x11 + 19074905803558500162x10 + 82370621416601788582x9 - 43840068640516285889x8 - 67556477435299552660x7 + 51180521959924527335x6 + 23228035973272766493x5 - 26391119726982867791x4 + 202102108745982587x3 + 4168134528839675291x2 - 499943870456762867x - 149270874547838371 |
$41$ |
[41,0] |
$821^{40}$ |
$1$ |
$697.046284664$ |
|
✓ |
|
$C_{41}$ (as 41T1) |
not computed |
$2$ |
$40$ |
$$ |
| 41.41.105...201.1 |
x41 - 820x39 - 533x38 + 303031x37 + 376913x36 - 66737627x35 - 118821690x34 + 9764169434x33 + 22080920476x32 - 1002016650746x31 - 2696024483356x30 + 74276881167057x29 + 228322554454083x28 - 4038255389081271x27 - 13810013721005555x26 + 161957213612863355x25 + 605630162979885300x24 - 4783062094323192024x23 - 19362795070723667202x22 + 103087839028351278942x21 + 450266165503910224663x20 - 1593603545898162906857x19 - 7540369918979718461657x18 + 17171487184711671438215x17 + 89253263738667697145313x16 - 123172673161638273736870x15 - 724697045982659590514328x14 + 544476915889889670403041x13 + 3855061119747652830292013x12 - 1279320329561947245453521x11 - 12510633939200726076347653x10 + 1043523355082184352460715x9 + 22013783610841586394614893x8 + 598853130650094992883999x7 - 16988637915887608842729071x6 - 1349373804383563050067379x5 + 3896754513924753580219610x4 + 333868055127333108898601x3 - 256246929318582500140348x2 - 10590850429623318361311x + 2727257042363914863401 |
$41$ |
[41,0] |
$41^{80}$ |
$1$ |
$1402.47565155$ |
|
✓ |
|
$C_{41}$ (as 41T1) |
not computed |
$2$ |
$40$ |
$$ |
