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Label Polynomial Discriminant Galois group Class group
26.2.287...125.1 x26 - 2x25 - 4x24 + 16x23 - 11x22 - 29x21 + 88x20 - 189x19 + 510x18 - 655x17 + 132x16 - 179x15 + 449x14 + 1090x13 + 114x12 - 781x11 - 543x10 - 58x9 + 245x8 + 173x7 + 196x6 + 159x5 + 34x4 - 4x3 + 6x2 - 6x - 1 \( 5^{13}\cdot 191^{12} \) $D_{26}$ (as 26T3) trivial (GRH)
26.2.624...401.1 x26 - x - 1 \( 73\cdot 181\cdot 2385857\cdot 32375941061\cdot 6118709648547401 \) $S_{26}$ (as 26T96) trivial (GRH)
26.0.549...875.1 x26 - 2x25 + 5x24 - 26x23 + 53x22 - 54x21 + 268x20 - 237x19 + 744x18 + 440x17 + 1338x16 - 3330x15 - 8756x14 + 7284x13 + 63381x12 + 167449x11 + 262693x10 + 320455x9 + 419505x8 + 480606x7 + 569660x6 + 459537x5 + 397335x4 + 258066x3 + 85342x2 + 34263x + 39371 \( -\,5^{13}\cdot 191^{13} \) $D_{26}$ (as 26T3) $[4]$ (GRH)
26.2.129...328.1 x26 - 8x24 + 24x22 - 16x20 + 176x18 - 608x16 + 320x14 + 3712x12 + 1280x10 - 17408x8 + 22528x6 + 98304x4 + 65536x2 - 8192 \( 2^{39}\cdot 191^{12} \) $D_{26}$ (as 26T3) trivial (GRH)
26.0.115...543.1 x26 - x25 + 11x24 - 20x23 + 107x22 - 382x21 + 1248x20 - 3197x19 + 6521x18 - 10581x17 + 13912x16 - 15385x15 + 14827x14 - 15025x13 + 15241x12 - 12717x11 + 9243x10 - 4542x9 - 233x8 + 4189x7 - 7810x6 + 6629x5 - 1342x4 - 1780x3 + 1964x2 - 1216x + 361 \( -\,23^{13}\cdot 73^{12} \) $D_{26}$ (as 26T3) $[3]$ (GRH)
26.0.252...496.1 x26 - 2x13 + 2 \( -\,2^{38}\cdot 13^{26} \) $C_2\times F_{13}$ (as 26T10) trivial (GRH)
26.2.602...128.1 x26 - 12x24 + 44x22 - 24x20 - 272x18 + 1312x16 - 1408x14 - 3328x12 + 30208x10 - 19456x8 + 46080x6 + 204800x4 + 131072x2 - 8192 \( 2^{39}\cdot 263^{12} \) $D_{26}$ (as 26T3) trivial (GRH)
26.0.777...987.1 x26 - 3x13 + 3 \( -\,3^{25}\cdot 13^{26} \) $C_2\times F_{13}$ (as 26T10) trivial (GRH)
26.2.252...432.1 x26 - 12x24 + 54x22 - 54x20 + 891x18 - 4617x16 + 3645x14 + 63423x12 + 32805x10 - 669222x8 + 1299078x6 + 8503056x4 + 8503056x2 - 1594323 \( 2^{26}\cdot 3^{13}\cdot 191^{12} \) $D_{26}$ (as 26T3) n/a
26.2.713...893.1 x26 - x25 - 37x24 + 36x23 + 656x22 - 602x21 - 7532x20 + 5987x19 + 63242x18 - 39168x17 - 407978x16 + 177750x15 + 2044391x14 - 593805x13 - 7863783x12 + 1620832x11 + 22802242x10 - 3804296x9 - 48757198x8 + 7281003x7 + 74301119x6 - 12442481x5 - 74591007x4 + 16397553x3 + 41639217x2 - 9412671x - 11716513 \( 13^{13}\cdot 191^{12} \) $D_{26}$ (as 26T3) n/a
26.2.955...125.1 x26 - 4x25 - x24 + 12x23 - 20x22 - 91x21 + 245x20 + 945x19 + 237x18 - 2538x17 - 3465x16 + 4625x15 + 16764x14 + 17173x13 + 6911x12 - 948x11 + 1857x10 + 6384x9 + 2100x8 - 1050x7 + 280x6 + 490x5 - 352x4 - 172x3 - 11x2 + 8x - 1 \( 5^{13}\cdot 19^{12}\cdot 29^{12} \) $D_{26}$ (as 26T3) trivial (GRH)
26.0.120...736.1 x26 - 4x + 4 \( -\,2^{26}\cdot 11\cdot 5351\cdot 322710411593\cdot 942553212724915163 \) $S_{26}$ (as 26T96) trivial (GRH)
26.0.167...007.1 x26 - 8x25 + 22x24 - 43x23 + 115x22 - 151x21 + 220x20 - 577x19 + 509x18 - 1015x17 + 1547x16 - 884x15 + 2815x14 - 3027x13 + 2341x12 - 3581x11 + 6893x10 + 2193x9 + 12186x8 - 1094x7 + 906x6 - 2074x5 + 14041x4 + 14998x3 + 13037x2 + 4230x + 1325 \( -\,7^{13}\cdot 401^{12} \) $D_{26}$ (as 26T3) trivial (GRH)
26.0.463...123.1 x26 - 9x24 - 20x23 - 12x22 + 186x21 + 794x20 - 27x19 - 4404x18 - 5528x17 + 1038x16 + 13671x15 + 59660x14 + 64299x13 - 161565x12 - 318218x11 + 37881x10 + 189642x9 - 55703x8 + 873384x7 + 1978515x6 - 188640x5 - 4211379x4 - 4130865x3 + 1301535x2 + 4678236x + 2259171 \( -\,3^{13}\cdot 1093^{12} \) $D_{26}$ (as 26T3) trivial (GRH)
26.2.486...125.1 x26 - 4x25 + 20x24 - 36x23 + 151x22 - 166x21 + 575x20 - 1143x19 + 1160x18 - 4286x17 + 2641x16 - 4158x15 + 10417x14 + 3815x13 + 21287x12 + 17505x11 + 19313x10 + 20293x9 + 10822x8 + 10971x7 + 6883x6 + 3740x5 + 2969x4 + 837x3 + 388x2 + 17x - 1 \( 5^{13}\cdot 631^{12} \) $D_{26}$ (as 26T3) trivial (GRH)
26.2.596...009.1 x26 - 4x - 1 \( 29\cdot 10128571112394569\cdot 20292423834064993115883509 \) $S_{26}$ (as 26T96) trivial (GRH)
26.2.596...776.1 x26 - 2x - 1 \( 2^{27}\cdot 7417\cdot 22861\cdot 53970181\cdot 4852810050936915961 \) $S_{26}$ (as 26T96) trivial (GRH)
26.2.117...632.1 x26 - 18x24 + 99x22 - 81x20 - 1377x18 + 9963x16 - 16038x14 - 56862x12 + 774198x10 - 747954x8 + 2657205x6 + 17714700x4 + 17006112x2 - 1594323 \( 2^{26}\cdot 3^{13}\cdot 263^{12} \) $D_{26}$ (as 26T3) n/a
26.26.127...693.1 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)
26.2.144...125.1 x26 - 3x25 + 8x24 - 23x23 - 44x22 + 17x21 + 450x20 - 860x19 + 3401x18 + 4044x17 - 12200x16 - 9996x15 + 5376x14 - 176112x13 - 67837x12 - 1501x11 - 261354x10 - 143521x9 - 1171x8 - 152170x7 - 30780x6 - 39875x5 - 16350x4 - 26625x3 - 13000x2 - 6875x - 3125 \( 5^{13}\cdot 691^{12} \) $D_{26}$ (as 26T3) trivial (GRH)
26.2.233...497.1 x26 - x25 - 50x24 + 48x23 + 1188x22 - 1066x21 - 17960x20 + 14231x19 + 194023x18 - 126696x17 - 1579415x16 + 794998x15 + 9883811x14 - 3670079x13 - 47524550x12 + 13070104x11 + 173418938x10 - 37145018x9 - 469905596x8 + 84248201x7 + 912345834x6 - 152992905x5 - 1188256605x4 + 203114817x3 + 913828487x2 - 132782216x - 329129521 \( 17^{13}\cdot 191^{12} \) $D_{26}$ (as 26T3) n/a
26.2.331...693.1 x26 - x25 - 45x24 + 44x23 + 912x22 - 836x21 - 11055x20 + 9149x19 + 89968x18 - 63863x17 - 520434x16 + 297998x15 + 2198217x14 - 952653x13 - 6808591x12 + 2140242x11 + 15236220x10 - 3364016x9 - 23680109x8 + 2956997x7 + 23956149x6 - 618594x5 - 14015975x4 - 2419867x3 + 3438259x2 + 3561247x - 1990843 \( 13^{13}\cdot 263^{12} \) $D_{26}$ (as 26T3) n/a
26.0.105...671.1 x26 - 4x25 + 29x24 - 114x23 + 437x22 - 1233x21 + 3738x20 - 6943x19 + 17106x18 - 22984x17 + 59870x16 - 97147x15 + 263098x14 - 450753x13 + 813670x12 - 1048444x11 + 1103470x10 - 985605x9 + 369592x8 - 235197x7 - 276734x6 + 186178x5 - 88862x4 + 240404x3 + 178609x2 + 96160x + 61675 \( -\,31^{13}\cdot 113^{12} \) $D_{26}$ (as 26T3) $[3]$ (GRH)
26.2.109...616.1 x26 - 4x - 4 \( 2^{26}\cdot 6733\cdot 11138847809333\cdot 21705255151207321321 \) $S_{26}$ (as 26T96) trivial (GRH)
26.0.200...232.1 x26 - 2x + 2 \( -\,2^{26}\cdot 471266581969\cdot 6342995795806711798279927 \) $S_{26}$ (as 26T96) trivial (GRH)
26.0.206...607.1 x26 - x + 2 \( -\,31\cdot 2143\cdot 2713\cdot 7727\cdot 758671\cdot 195505457062666900180454399 \) $S_{26}$ (as 26T96) trivial (GRH)
26.0.206...232.1 x26 + 2 \( -\,2^{51}\cdot 13^{26} \) $C_2\times F_{13}$ (as 26T10) trivial (GRH)
26.2.206...232.1 x26 - 2 \( 2^{51}\cdot 13^{26} \) $C_2\times F_{13}$ (as 26T10) trivial (GRH)
26.2.212...232.1 x26 - 2x - 2 \( 2^{26}\cdot 3\cdot 67\cdot 107\cdot 5867\cdot 10536636742939\cdot 2381953897662043 \) $S_{26}$ (as 26T96) trivial (GRH)
26.0.526...875.1 x26 - 8x25 + 14x24 + 18x23 - 92x22 + 514x21 - 1212x20 - 596x19 + 954x18 - 2053x17 + 29744x16 - 4491x15 + 71256x14 - 216720x13 - 344608x12 + 50717x11 + 1942970x10 + 2307612x9 + 264538x8 - 5680405x7 - 6094469x6 - 2337568x5 + 3586683x4 + 5626157x3 + 5313221x2 + 843733x + 496261 \( -\,5^{13}\cdot 19^{13}\cdot 29^{13} \) $D_{26}$ (as 26T3) $[2, 4]$ (GRH)
26.0.199...875.1 x26 - 6x25 + 34x24 - 149x23 + 724x22 - 3027x21 + 10234x20 - 26698x19 + 56427x18 - 101122x17 + 164719x16 - 254230x15 + 377196x14 - 535703x13 + 716143x12 - 954928x11 + 1568217x10 - 3148667x9 + 5745440x8 - 8171380x7 + 9122775x6 - 8433000x5 + 7096875x4 - 5099875x3 + 3012500x2 - 717500x + 153125 \( -\,5^{12}\cdot 691^{13} \) $D_{26}$ (as 26T3) $[5]$ (GRH)
26.0.308...216.1 x26 + 6x24 + 189x22 + 2700x20 + 22032x18 + 262683x16 + 3276126x14 + 20111652x12 + 46005732x10 - 38618046x8 - 195511239x6 - 5668704x4 + 416649744x2 + 419306949 \( -\,2^{26}\cdot 3^{13}\cdot 263^{13} \) $D_{26}$ (as 26T3) n/a
26.0.445...927.1 x26 - 2x25 + 17x24 - 98x23 + 152x22 - 696x21 + 1597x20 + 1896x19 + 20067x18 + 156392x17 + 357813x16 - 241572x15 - 6441785x14 - 21049242x13 - 6337440x12 + 144534568x11 + 455484358x10 + 307770160x9 - 848362260x8 - 452511774x7 + 6860115833x6 + 21793527372x5 + 15854969370x4 - 22167126630x3 - 34371344111x2 - 12604846614x + 29070259637 \( -\,17^{13}\cdot 191^{13} \) $D_{26}$ (as 26T3) n/a
26.2.273...125.1 x26 - 5 \( 5^{25}\cdot 13^{26} \) $C_2\times F_{13}$ (as 26T10) trivial (GRH)
26.2.225...849.1 x26 - 3x + 1 \( 17\cdot 47\cdot 457\cdot 58031\cdot 959677\cdot 10678056923\cdot 1039710637886321095943 \) $S_{26}$ (as 26T96) trivial (GRH)
26.2.225...401.1 x26 - 3x - 1 \( 97\cdot 1027188157\cdot 761641463933293\cdot 2974955834015001526633 \) $S_{26}$ (as 26T96) trivial (GRH)
26.2.225...857.1 x26 - 3x - 2 \( 22739663746473685987\cdot 9937244678052017295688440011 \) $S_{26}$ (as 26T96) trivial (GRH)
26.0.275...999.1 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)
26.0.384...563.1 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)
26.2.330...944.1 x26 - 4x + 1 \( 2^{26}\cdot 3\cdot 149\cdot 977\cdot 3541\cdot 12747387209041\cdot 2498880811540538989 \) $S_{26}$ (as 26T96) trivial (GRH)
26.0.499...143.1 x26 - 3x + 3 \( -\,3^{25}\cdot 37\cdot 193\cdot 397\cdot 3673\cdot 565614067938252407382930781 \) $S_{26}$ (as 26T96) $[2]$ (GRH)
26.0.521...768.1 x26 - 2x + 3 \( -\,2^{27}\cdot 47\cdot 349\cdot 1395923\cdot 415496197\cdot 4084851144240798246517 \) $S_{26}$ (as 26T96) trivial (GRH)
26.0.521...143.1 x26 - x + 3 \( -\,59\cdot 71\cdot 33563\cdot 396349\cdot 15944389\cdot 1472102329\cdot 3987894255883125121 \) $S_{26}$ (as 26T96) trivial (GRH)
26.2.521...768.1 x26 - 3 \( 2^{26}\cdot 3^{25}\cdot 13^{26} \) $C_2\times F_{13}$ (as 26T10) trivial (GRH)
26.2.521...393.1 x26 - x - 3 \( 2083\cdot 1519447\cdot 1648024217388452125665771097137180469093 \) $S_{26}$ (as 26T96) trivial (GRH)
26.2.544...393.1 x26 - 3x - 3 \( 3^{25}\cdot 19\cdot 9619\cdot 306629767564201\cdot 114607019135083291 \) $S_{26}$ (as 26T96) trivial (GRH)
26.0.161...184.1 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)
26.0.203...839.1 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)
26.2.214...688.1 x26 - 13x25 + 121x24 - 802x23 + 4651x22 - 22825x21 + 98893x20 - 371962x19 + 1240872x18 - 3661594x17 + 9598744x16 - 22249906x15 + 46158003x14 - 86354433x13 + 145428273x12 - 217463318x11 + 270662252x10 - 252429562x9 + 127602004x8 + 63980066x7 - 189163921x6 + 167659735x5 - 112782103x4 + 89161818x3 - 55238589x2 + 18143595x - 204972201 \( 2^{24}\cdot 53^{25} \) $D_{26}$ (as 26T3) $[13]$ (GRH)
26.26.294...125.1 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)
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