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Label Polynomial Discriminant Galois group Class group
41.1.1318788372436565706966337480963346255985889330161650994325137953641.1 x41 - x - 1 \( 2251\cdot 272583857708203\cdot 761889448323748621067\cdot 2821028813073407561156582291 \) $S_{41}$ (as 41T10) Trivial (GRH)
41.1.3438740475870829672142694556791350302292427122659925573655422607717853822976.1 x41 + 4x - 4 \( 2^{40}\cdot 63506090654183\cdot 49247500694181610257024215345813183672691438654247 \) $S_{41}$ (as 41T10) n/a
41.41.57959375186337998161464929843210464026538099255933595673241672975683189751201.1 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 \( 83^{40} \) $C_{41}$ (as 41T1) Trivial (GRH)
41.1.1410146310196242615582623734722557917230960361093027177982041370003573535932416.1 x41 - 4x - 4 \( 2^{40}\cdot 2313020109848347\cdot 2947885124842583399107\cdot 188093758458159369641352727129 \) $S_{41}$ (as 41T10) n/a
41.1.1436730870111940933040699875928164808750960361093027177982041370003573535932416.1 x41 - 2x - 2 \( 2^{40}\cdot 3\cdot 53\cdot 67\cdot 19183\cdot 332415773971\cdot 2121795341959\cdot 9065714275532504603626040222095031 \) $S_{41}$ (as 41T10) n/a
41.1.1463315430027627161240579870842024638510960361093027177982041370003573535932416.1 x41 - x - 2 \( 2^{40}\cdot 139\cdot 1289\cdot 7427974564146547173354624805148970848998383277213672939957571 \) $S_{41}$ (as 41T10) n/a
41.1.1463315430027639250498776006138655422510960361093027177982041370003573535932416.1 x41 - x - 4 \( 2^{40}\cdot 1330877630632711998713399230963346255985889330161650994325137953641 \) $S_{41}$ (as 41T10) n/a
41.1.1463315430027639250498776017133771700270960361093027177982041370003573535932416.1 x41 - 2 \( 2^{40}\cdot 41^{41} \) $F_{41}$ (as 41T8) n/a
41.1.1489899989943337567956852158339378591790960361093027177982041370003573535932416.1 x41 + 2x - 2 \( 2^{40}\cdot 29\cdot 5227\cdot 7297\cdot 6697657\cdot 53935240897410251303\cdot 3391305552057089043750010190521 \) $S_{41}$ (as 41T10) n/a
41.1.440932933706155962814077165280529917580949550960361093027177982041370003573535932416.1 x41 + 3x - 2 \( 2^{40}\cdot 11\cdot 367\cdot 104399\cdot 13038909447397913\cdot 19797069953357319509\cdot 3686170645074380678869761671 \) $S_{41}$ (as 41T10) n/a
41.1.15739433529784122314867560891297447239069722808004066932604530641678516894079375714441.1 x41 - 3x - 3 \( 3^{40}\cdot 7\cdot 32261\cdot 253464984011\cdot 1238514877771\cdot 76247312349973837\cdot 239507603770962778439 \) $S_{41}$ (as 41T10) n/a
41.1.16180364973590288334344070099725818817272080568004066932604530641678516894079375714441.1 x41 - 2x - 3 \( 19\cdot 23\cdot 31\cdot 23297\cdot 24551\cdot 61559\cdot 192233\cdot 176464153390395305528183888414950811261883583614896533439444867 \) $S_{41}$ (as 41T10) n/a
41.1.16180365000174848250030298299605813731131910328004066932604530641678516894079375714441.1 x41 - x - 3 \( 307\cdot 5719838273\cdot 9214381503814281413477697919440786583995873890980828623574102928033757331 \) $S_{41}$ (as 41T10) n/a
41.1.16180365000174848250042387557801960022878972088004066932604530641678516894079375714441.1 x41 - 3 \( 3^{40}\cdot 41^{41} \) $F_{41}$ (as 41T8) n/a
41.1.16621296470565574185217214224306472806688221368004066932604530641678516894079375714441.1 x41 + 3x - 3 \( 3^{40}\cdot 11\cdot 123191\cdot 11537809\cdot 901418971\cdot 13197674429\cdot 39039118092749\cdot 188276273322445488239 \) $S_{41}$ (as 41T10) n/a
41.3.58460065491772801298119754058152544769103530018769039638906972822017958629996426464067584.1 x41 - 4x - 2 \( -\,2^{40}\cdot 859\cdot 228505873\cdot 270875010079051181133537860467814565805024528624116298098176646437 \) $S_{41}$ (as 41T10) n/a
41.1.402233082604850119106625535044231327991520299999161762756610493407000559357491685521096704.1 x41 - 2x - 4 \( 2^{78}\cdot 3\cdot 2358722227395221\cdot 188078897856263176711325004764153112359707183458007 \) $S_{41}$ (as 41T10) n/a
41.1.402233082604863411386583384202960366062123103444921762756610493407000559357491685521096704.1 x41 + 2x - 4 \( 2^{78}\cdot 2339\cdot 1104312393641791\cdot 515247576164649945279684004095435656157313243709 \) $S_{41}$ (as 41T10) n/a
41.1.1608931889487956670260482663667716883594502997638887051026441973628002237429966742084386816.1 x41 - 3x - 4 \( 2^{80}\cdot 7\cdot 37\cdot 67\cdot 108499\cdot 543997\cdot 270310655161\cdot 312570029227603619\cdot 15379092216330540575461 \) $S_{41}$ (as 41T10) n/a
41.1.1608932330419427060986417850583641584253578553949927051026441973628002237429966742084386816.1 x41 + x - 4 \( 2^{80}\cdot 3\cdot 263\cdot 587\cdot 6397\cdot 336221\cdot 7665197\cdot 4370168129\cdot 621071121653\cdot 64218333671912404841959 \) $S_{41}$ (as 41T10) n/a
41.1.137438953472000365828857506909812624694004283442925067740090273256794495510342500893383983104.1 x41 + 5x - 2 \( 2^{38}\cdot 163\cdot 743\cdot 10289\cdot 104597\cdot 31257021937\cdot 13675604446553671\cdot 95253739993542479\cdot 94216078858946850824041 \) $S_{41}$ (as 41T10) n/a
41.3.549755797707634999825151749957612442198039977121027911995933067395469358321483105920624285559.1 x41 - 5x - 3 \( -\,13\cdot 3357247\cdot 6299663\cdot 93408687929\cdot 21406150874383295497255645104194557906460721068839149774069949627547 \) $S_{41}$ (as 41T10) n/a
41.3.549755813887998536684569972360749501223982866228299729039638906972822017958629996426464067584.1 x41 - 5x - 2 \( -\,2^{40}\cdot 3\cdot 13\cdot 27277\cdot 84809\cdot 128519\cdot 211271\cdot 11833317469\cdot 17248570555075397865783802800145486112371296607457 \) $S_{41}$ (as 41T10) n/a
41.3.549755813887999999999999998669122369367288001286600759036653744014110669838349005674862046359.1 x41 - 5x - 1 \( -\,3\cdot 7\cdot 115979\cdot 1907696227638017\cdot 118321033765788067146948309346329110271424126239710539838101455451743953 \) $S_{41}$ (as 41T10) n/a
41.1.549755813888000000000000001330877630632711998713399240963346255985889330161650994325137953641.1 x41 + 5x - 1 \( 43\cdot 191\cdot 9901\cdot 55082201453159\cdot 467781923539898069\cdot 251911473477379412779567\cdot 1041564752951083406029502313101 \) $S_{41}$ (as 41T10) n/a
41.1.551364746218419427060986417838494383388107286806888167051026441973628002237429966742084386816.1 x41 + 5x - 4 \( 2^{80}\cdot 53\cdot 2252852353\cdot 11587626304193\cdot 329637233487635949869536097749879917871587493 \) $S_{41}$ (as 41T10) n/a
41.1.1283833969310844157793821918315841741975003697170552382810292282092632376588881015777587890625.1 x41 - 5x - 5 \( 5^{40}\cdot 245129\cdot 204113313923\cdot 2821257079027332182203537535940041590484330884147 \) $S_{41}$ (as 41T10) n/a
41.1.12104203077620104184027669117449267026454247037233252405292630538833691389299929141998291015625.1 x41 - 4x - 5 \( 5^{40}\cdot 23\cdot 43\cdot 7678031\cdot 175262852236380367365665984222062198000689367124639488243 \) $S_{41}$ (as 41T10) n/a
41.1.12104261537244665949753671329667749011270520490725722165292630538833691389299929141998291015625.1 x41 - 3x - 5 \( 5^{40}\cdot 1330877630584231070838702018991508903663186455464060108951402353513 \) $S_{41}$ (as 41T10) n/a
41.1.12104261537685597393559837349144258219698892068928079925292630538833691389299929141998291015625.1 x41 - 2x - 5 \( 3\cdot 5^{40}\cdot 13\cdot 157\cdot 6298160107\cdot 50991976651363487\cdot 676796839638163123435461975358062127 \) $S_{41}$ (as 41T10) n/a
41.1.12104261537685597420144397264830486419578886982787909685292630538833691389299929141998291015625.1 x41 - x - 5 \( 5^{41}\cdot 7033139213\cdot 64812836603\cdot 37176884662660649\cdot 15706697658577462999892991283 \) $S_{41}$ (as 41T10) n/a
41.1.12104261537685597420144397264842575677775033274534971445292630538833691389299929141998291015625.1 x41 - 5 \( 5^{40}\cdot 41^{41} \) $F_{41}$ (as 41T8) n/a
41.1.12104261537685597420144397264854664935971179566282033205292630538833691389299929141998291015625.1 x41 + x - 5 \( 3\cdot 5^{40}\cdot 7\cdot 11287\cdot 706035413231\cdot 1169722373977559\cdot 6798780558470760707379065694407899 \) $S_{41}$ (as 41T10) n/a
41.1.12104261537685597446728957180540893135851174480141862965292630538833691389299929141998291015625.1 x41 + 2x - 5 \( 5^{40}\cdot 29\cdot 131\cdot 163\cdot 2089\cdot 1028828029177577129098281451318255701434213699137392499501 \) $S_{41}$ (as 41T10) n/a
41.1.12104261538126528890535123200017402344279546058344220725292630538833691389299929141998291015625.1 x41 + 3x - 5 \( 5^{40}\cdot 11\cdot 89\cdot 3571\cdot 20521\cdot 218655088207\cdot 84841331383637730695700527999490480420941303 \) $S_{41}$ (as 41T10) n/a
41.1.12654017351573597420144397264842575677775033274534971445292630538833691389299929141998291015625.1 x41 + 5x - 5 \( 5^{40}\cdot 19\cdot 607\cdot 1420817\cdot 36720491\cdot 2312274212437627784352237135454468699991228948791 \) $S_{41}$ (as 41T10) n/a
41.41.5569004076505768771305960217126445703759867401876857883756301108406604311389659436574913426754343247431380601178401.1 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 \( 739^{40} \) $C_{41}$ (as 41T1) n/a
41.41.374736748996787359631305155092300401320167420349192445441530719220110866474778641166604150096881944963931329952344801.1 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 \( 821^{40} \) $C_{41}$ (as 41T1) n/a
41.41.1053679516786758709720897165633610283654902079788240782212064028656008150674955537661019599453337948495954124897145643786946499201.1 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 \( 41^{80} \) $C_{41}$ (as 41T1) n/a



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