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Label Polynomial Discriminant Galois group Class group
26.2.6244937422177169834030564821847469401.1 x26 - x - 1 \( 73\cdot 181\cdot 2385857\cdot 32375941061\cdot 6118709648547401 \) $S_{26}$ (as 26T96) Trivial (GRH)
26.0.25215465800528516345023177885287234666496.1 x26 - 2x13 + 2 \( -\,2^{38}\cdot 13^{26} \) $C_2\times F_{13}$ (as 26T10) Trivial (GRH)
26.0.77724605779030132647467635994070771372987.1 x26 - 3x13 + 3 \( -\,3^{25}\cdot 13^{26} \) $C_2\times F_{13}$ (as 26T10) Trivial (GRH)
26.0.1201507202980564696903888106396747076468736.1 x26 - 4x + 4 \( -\,2^{26}\cdot 11\cdot 5351\cdot 322710411593\cdot 942553212724915163 \) $S_{26}$ (as 26T96) Trivial (GRH)
26.2.5960464477539154233330193268616658399616009.1 x26 - 4x - 1 \( 29\cdot 10128571112394569\cdot 20292423834064993115883509 \) $S_{26}$ (as 26T96) Trivial (GRH)
26.2.5960470633658642707157310796674288400203776.1 x26 - 2x - 1 \( 2^{27}\cdot 7417\cdot 22861\cdot 53970181\cdot 4852810050936915961 \) $S_{26}$ (as 26T96) Trivial (GRH)
26.26.12790771483610519443342791266451996229460693.1 x26 - x25 - 25x24 + 24x23 + 276x22 - 253x21 - 1771x20 + 1540x19 + 7315x18 - 5985x17 - 20349x16 + 15504x15 + 38760x14 - 27132x13 - 50388x12 + 31824x11 + 43758x10 - 24310x9 - 24310x8 + 11440x7 + 8008x6 - 3003x5 - 1365x4 + 364x3 + 91x2 - 13x - 1 \( 53^{25} \) $C_{26}$ (as 26T1) Trivial (GRH)
26.2.109243012396503865449214936618136513193967616.1 x26 - 4x - 4 \( 2^{26}\cdot 6733\cdot 11138847809333\cdot 21705255151207321321 \) $S_{26}$ (as 26T96) Trivial (GRH)
26.0.200604631360390543398429873236273026387935232.1 x26 - 2x + 2 \( -\,2^{26}\cdot 471266581969\cdot 6342995795806711798279927 \) $S_{26}$ (as 26T96) Trivial (GRH)
26.0.206565095749111763928417350002382492940669607.1 x26 - x + 2 \( -\,31\cdot 2143\cdot 2713\cdot 7727\cdot 758671\cdot 195505457062666900180454399 \) $S_{26}$ (as 26T96) Trivial (GRH)
26.0.206565095837929605898429873236273026387935232.1 x26 + 2 \( -\,2^{51}\cdot 13^{26} \) $C_2\times F_{13}$ (as 26T10) Trivial (GRH)
26.2.206565095837929605898429873236273026387935232.1 x26 - 2 \( 2^{51}\cdot 13^{26} \) $C_2\times F_{13}$ (as 26T10) Trivial (GRH)
26.2.212525560315468668398429873236273026387935232.1 x26 - 2x - 2 \( 2^{26}\cdot 3\cdot 67\cdot 107\cdot 5867\cdot 10536636742939\cdot 2381953897662043 \) $S_{26}$ (as 26T96) Trivial (GRH)
26.2.27338662801166956620931510927975177764892578125.1 x26 - 5 \( 5^{25}\cdot 13^{26} \) $C_2\times F_{13}$ (as 26T10) Trivial (GRH)
26.2.225763037443343983968209361295448843442312686849.1 x26 - 3x + 1 \( 17\cdot 47\cdot 457\cdot 58031\cdot 959677\cdot 10678056923\cdot 1039710637886321095943 \) $S_{26}$ (as 26T96) Trivial (GRH)
26.2.225763037455656223128623675917042192019113094401.1 x26 - 3x - 1 \( 97\cdot 1027188157\cdot 761641463933293\cdot 2974955834015001526633 \) $S_{26}$ (as 26T96) Trivial (GRH)
26.2.225969602545338033154314948479481790757100825857.1 x26 - 3x - 2 \( 22739663746473685987\cdot 9937244678052017295688440011 \) $S_{26}$ (as 26T96) Trivial (GRH)
26.0.275852727404510985186163978883510976421015681999.1 x26 - x25 + 2x24 + 48x23 - 41x22 + 75x21 + 827x20 - 597x19 + 990x18 + 6414x17 - 3755x16 + 5397x15 + 23537x14 - 10353x13 + 15676x12 + 35758x11 - 6997x10 + 39165x9 + 14468x8 + 8338x7 + 43270x6 - 25107x5 + 25775x4 - 10788x3 - 8746x2 + 10048x + 4289 \( -\,79^{25} \) $C_{26}$ (as 26T1) $[265]$ (GRH)
26.0.384766437057818380952237905666104641217782272563.1 x26 - x25 + 25x24 - 14x23 + 405x22 - 192x21 + 3603x20 - 1111x19 + 22650x18 - 5414x17 + 87624x16 - 5096x15 + 234451x14 - 19756x13 + 367484x12 - 30562x11 + 404986x10 - 57146x9 + 232119x8 - 34742x7 + 91429x6 - 16226x5 + 7319x4 + 98x3 + 168x2 - 10x + 1 \( -\,3^{13}\cdot 53^{24} \) $C_{26}$ (as 26T1) $[53, 53]$ (GRH)
26.2.3305785123966891271739006552418919035749682642944.1 x26 - 4x + 1 \( 2^{26}\cdot 3\cdot 149\cdot 977\cdot 3541\cdot 12747387209041\cdot 2498880811540538989 \) $S_{26}$ (as 26T96) Trivial (GRH)
26.0.4990246961229047120192449009721354684714164966143.1 x26 - 3x + 3 \( -\,3^{25}\cdot 37\cdot 193\cdot 397\cdot 3673\cdot 565614067938252407382930781 \) $S_{26}$ (as 26T96) $[2]$ (GRH)
26.0.5216004038214069684678365528327600202444877856768.1 x26 - 2x + 3 \( -\,2^{27}\cdot 47\cdot 349\cdot 1395923\cdot 415496197\cdot 4084851144240798246517 \) $S_{26}$ (as 26T96) Trivial (GRH)
26.0.5216009998678458405898895515804366311911430591143.1 x26 - x + 3 \( -\,59\cdot 71\cdot 33563\cdot 396349\cdot 15944389\cdot 1472102329\cdot 3987894255883125121 \) $S_{26}$ (as 26T96) Trivial (GRH)
26.2.5216009998678547223740865528327600202444877856768.1 x26 - 3 \( 2^{26}\cdot 3^{25}\cdot 13^{26} \) $C_2\times F_{13}$ (as 26T10) Trivial (GRH)
26.2.5216009998678636041582835540850834092978325122393.1 x26 - x - 3 \( 2083\cdot 1519447\cdot 1648024217388452125665771097137180469093 \) $S_{26}$ (as 26T96) Trivial (GRH)
26.2.5441773036128047327289282046933845720175590747393.1 x26 - 3x - 3 \( 3^{25}\cdot 19\cdot 9619\cdot 306629767564201\cdot 114607019135083291 \) $S_{26}$ (as 26T96) Trivial (GRH)
26.0.16195738565069746760238624235485184480969630941184.1 x26 + 49x24 + 994x22 + 10915x20 + 71324x18 + 287620x16 + 721007x14 + 1111118x12 + 1019820x10 + 521449x8 + 129173x6 + 10874x4 + 236x2 + 1 \( -\,2^{26}\cdot 53^{24} \) $C_{26}$ (as 26T1) $[14209]$ (GRH)
26.0.20392621164064374190468609000303545984542460445839.1 x26 - x25 + 28x24 - 29x23 + 276x22 - 306x21 + 1038x20 - 1375x19 + 54x18 - 1586x17 - 8106x16 - 449x15 - 5336x14 - 49021x13 + 97058x12 - 111859x11 + 338650x10 + 82909x9 + 16023x8 + 521830x7 - 124280x6 - 1299383x5 + 3115247x4 - 2524927x3 + 1035234x2 + 2787416x + 1009861 \( -\,3^{13}\cdot 53^{25} \) $C_{26}$ (as 26T1) $[32510]$ (GRH)
26.26.294598768324608440893618976324163386033790283203125.1 x26 - 11x25 - 7x24 + 468x23 - 1046x22 - 6960x21 + 26796x20 + 40357x19 - 278503x18 + 355x17 + 1499785x16 - 1077692x15 - 4479644x14 + 5284410x13 + 7470556x12 - 11963101x11 - 6678940x10 + 14762504x9 + 2744933x8 - 10366844x7 - 29320x6 + 4079010x5 - 378384x4 - 821546x3 + 120702x2 + 64121x - 11789 \( 5^{13}\cdot 53^{24} \) $C_{26}$ (as 26T1) Trivial (GRH)
26.2.399999793434904162070394101570126763726973612064768.1 x26 - 4x + 2 \( 2^{51}\cdot 7\cdot 17\cdot 41\cdot 1889\cdot 639679\cdot 30130415360166750515609 \) $S_{26}$ (as 26T96) Trivial (GRH)
26.2.400000206565095837929605898429873236273026387935232.1 x26 - 4x - 2 \( 2^{51}\cdot 3\cdot 11\cdot 73\cdot 1409\cdot 10429777\cdot 5017733838435325202707 \) $S_{26}$ (as 26T96) Trivial (GRH)
26.2.405216009998678547223740865528327600202444877856768.1 x26 - 4x - 3 \( 2^{26}\cdot 67\cdot 373\cdot 241614544568768461952201497979035283557 \) $S_{26}$ (as 26T96) Trivial (GRH)
26.0.858374143948696578292647084480714777491390439882752.1 x26 + 53x24 + 1166x22 + 13939x20 + 99640x18 + 442444x16 + 1229759x14 + 2105054x12 + 2133568x10 + 1209089x8 + 365117x6 + 53318x4 + 2968x2 + 53 \( -\,2^{26}\cdot 53^{25} \) $C_{26}$ (as 26T1) $[195474]$ (GRH)
26.0.1732793613976706876091650397068785799342044590637056.1 x26 - 2x + 4 \( -\,2^{24}\cdot 3\cdot 7\cdot 331\cdot 347\cdot 1627\cdot 49019\cdot 1249111\cdot 102017147\cdot 4213315416817943 \) $S_{26}$ (as 26T96) Trivial (GRH)
26.2.1732793616956939114861181647068785799342044590637056.1 x26 - 2x - 4 \( 2^{24}\cdot 71593\cdot 343928521\cdot 4194577183575531075991971526697 \) $S_{26}$ (as 26T96) Trivial (GRH)
26.0.5567067695110660347277981181082226208360544116097363.1 x26 - x25 + 37x24 - 118x23 + 1008x22 - 3235x21 + 16642x20 - 51633x19 + 196206x18 - 526339x17 + 1528709x16 - 3470974x15 + 8121237x14 - 15101678x13 + 27024309x12 - 37166826x11 + 48531861x10 - 47702921x9 + 49613581x8 - 37639084x7 + 35389248x6 - 18788771x5 + 15390312x4 - 4606662x3 + 4701993x2 - 643428x + 85849 \( -\,3^{13}\cdot 79^{24} \) $C_{26}$ (as 26T1) $[57473]$ (GRH)
26.0.6930948698829842481802115671756536951850447649657599.1 x26 - 3x + 4 \( -\,2063\cdot 73532749\cdot 551943907461461\cdot 82778530085158225548195457 \) $S_{26}$ (as 26T96) $[2]$ (GRH)
26.0.6931174461867291893087822118262619963477644915282599.1 x26 - x + 4 \( -\,3\cdot 19\cdot 31\cdot 71\cdot 197\cdot 3701\cdot 5317453\cdot 31322273\cdot 135060203\cdot 3368544526633678033 \) $S_{26}$ (as 26T96) $[2]$ (GRH)
26.2.6931174461867292070723506058287666431258711809813849.1 x26 - x - 4 \( 385720241\cdot 17969434126396524964121615951929435902376489 \) $S_{26}$ (as 26T96) Trivial (GRH)
26.26.15613734721204247367361805745180659459790885009765625.1 x26 - x25 - 78x24 + 77x23 + 2608x22 - 2532x21 - 49206x20 + 46749x19 + 580404x18 - 533706x17 - 4483638x16 + 3900033x15 + 23134676x14 - 18225371x13 - 80012336x12 + 52642857x11 + 183881042x10 - 85848429x9 - 274320987x8 + 59188590x7 + 250434704x6 + 15619489x5 - 117142919x4 - 37579021x3 + 14295304x2 + 7895450x + 798709 \( 5^{13}\cdot 53^{25} \) $C_{26}$ (as 26T1) $[2]$ (GRH)
26.0.23382739460171668835485199054409361747964940454234567.1 x26 - 11x25 + 32x24 + 72x23 - 470x22 - 300x21 + 5790x20 - 11543x19 + 2138x18 - 1493x17 + 126811x16 - 489500x15 + 1145956x14 - 2174910x13 + 4404928x12 - 9349303x11 + 21707936x10 - 45568357x9 + 94651964x8 - 167065424x7 + 281189852x6 - 383212608x5 + 505907604x4 - 494051417x3 + 493165779x2 - 275771917x + 183561919 \( -\,7^{13}\cdot 53^{24} \) $C_{26}$ (as 26T1) $[1152931]$ (GRH)
26.0.73386655124093395346715550870539255750179290771484375.1 x26 - 3x + 5 \( -\,5^{23}\cdot 61\cdot 331\cdot 449\cdot 63806909\cdot 3529639661\cdot 3015121007861 \) $S_{26}$ (as 26T96) $[2]$ (GRH)
26.0.85463837848355618843993505004759251339989023133673251.1 x26 - x25 + 3x24 - 11x23 + 44x22 + 444x21 + 172x20 - 1660x19 - 4713x18 - 12939x17 + 26193x16 + 35200x15 - 140905x14 + 424503x13 + 143672x12 - 1088095x11 + 163498x10 - 410278x9 + 3177833x8 - 3344770x7 + 4162585x6 - 2783945x5 + 3599581x4 - 4829444x3 + 1868225x2 + 472321x + 4461913 \( -\,131^{25} \) $C_{26}$ (as 26T1) $[3, 3, 795]$ (GRH)
26.2.132343681998485749432201649865665728970327492866283857.1 x26 - 5x + 3 \( 2483561677\cdot 4048108812907452661\cdot 13163642696128058233262881 \) $S_{26}$ (as 26T96) $[2]$ (GRH)
26.2.132348897801919332141495784832764183334256911356205393.1 x26 - 5x + 2 \( 257\cdot 68112155980159\cdot 7560709958859746994536436073044299311 \) $S_{26}$ (as 26T96) Trivial (GRH)
26.2.132348898008484421823305810524036745773855649343936849.1 x26 - 5x + 1 \( 3\cdot 521\cdot 2833\cdot 4591297\cdot 17894485991227\cdot 363797878228018421962279049 \) $S_{26}$ (as 26T96) Trivial (GRH)
26.2.132348898008484434135544970938351367367204226144344401.1 x26 - 5x - 1 \( 17\cdot 3761\cdot 2736736843085821\cdot 756371290213139834941092507237413 \) $S_{26}$ (as 26T96) Trivial (GRH)
26.2.132348898215049523817354996629623929806802964132075857.1 x26 - 5x - 2 \( 3\cdot 19\cdot 41\cdot 443\cdot 1481\cdot 8314099\cdot 221768083\cdot 2040445848379\cdot 22943703711693769 \) $S_{26}$ (as 26T96) Trivial (GRH)
26.2.132354114018483106526649131596722384170732382621997393.1 x26 - 5x - 3 \( 7\cdot 31\cdot 463\cdot 4201\cdot 553051\cdot 33033233903239\cdot 17164365913041862059163147 \) $S_{26}$ (as 26T96) Trivial (GRH)
26.0.132675490325051365459874809737094631268103216670179328.1 x26 - 2x25 - 21x24 + 38x23 + 294x22 - 464x21 - 1357x20 + 1930x19 + 9504x18 - 8228x17 + 25716x16 - 28630x15 + 286963x14 - 378044x13 + 2103312x12 - 1678782x11 + 11411452x10 - 5574160x9 + 50609745x8 - 14301644x7 + 160353701x6 - 26227056x5 + 361035384x4 - 44819066x3 + 515469360x2 - 43859864x + 329025401 \( -\,2^{39}\cdot 53^{24} \) $C_{26}$ (as 26T1) $[1064051]$ (GRH)

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