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Label Polynomial Discriminant Galois group Class group
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 \( 83^{40} \) $C_{41}$ (as 41T1) trivial (GRH)
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 \( 739^{40} \) $C_{41}$ (as 41T1) n/a
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 \( 821^{40} \) $C_{41}$ (as 41T1) n/a
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 \( 41^{80} \) $C_{41}$ (as 41T1) n/a
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