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Label Polynomial Discriminant Galois group Class group
28.0.3053134545970524535745336759489912159909.1 x28 - x27 + x26 - x25 + x24 - x23 + x22 - x21 + x20 - x19 + x18 - x17 + x16 - x15 + x14 - x13 + x12 - x11 + x10 - x9 + x8 - x7 + x6 - x5 + x4 - x3 + x2 - x + 1 \( 29^{27} \) $C_{28}$ (as 28T1) $[2, 2, 2]$ (GRH)
28.0.32702096625010337092624478622745455919933.1 x28 - x + 1 \( 17787551\cdot 1838482241035336291804559189893283 \) $S_{28}$ (as 28T1854) Trivial (GRH)
28.2.33588949601496412632520977883983755705539.1 x28 - x - 1 \( -\,349\cdot 14769635993383\cdot 6516302002526983353692617 \) $S_{28}$ (as 28T1854) Trivial (GRH)
28.0.503553375386417026489977159144851919778199649.1 x28 - x27 + 14x26 - 11x25 + 115x24 - 79x23 + 617x22 - 353x21 + 2421x20 - 1188x19 + 7015x18 - 2803x17 + 15415x16 - 5107x15 + 25195x14 - 6334x13 + 30532x12 - 6088x11 + 26057x10 - 3239x9 + 15207x8 - 1590x7 + 5362x6 - 70x5 + 1050x4 - 84x3 + 77x2 + 7x + 1 \( 3^{14}\cdot 29^{26} \) $C_2\times C_{14}$ (as 28T2) $[4, 4, 12]$ (GRH)
28.0.941583580117685398903952998389423397952028672.1 x28 - 3x14 + 3 \( 2^{28}\cdot 3^{27}\cdot 7^{28} \) $D_4\times F_7$ (as 28T41) Trivial (GRH)
28.28.14603047886206093768209337615200705673567789821.1 x28 - x27 - 28x26 + 28x25 + 349x24 - 349x23 - 2551x22 + 2551x21 + 12123x20 - 12123x19 - 39236x18 + 39236x17 + 88045x16 - 88045x15 - 136763x14 + 136763x13 + 144247x12 - 144247x11 - 99295x10 + 99295x9 + 41703x8 - 41703x7 - 9569x6 + 9569x5 + 987x4 - 987x3 - 28x2 + 28x + 1 \( 3^{14}\cdot 29^{27} \) $C_{28}$ (as 28T1) Trivial (GRH)
28.0.28261019450929335045240957686456444760176459776.1 x28 + 27x26 + 325x24 + 2300x22 + 10626x20 + 33649x18 + 74613x16 + 116280x14 + 125970x12 + 92378x10 + 43758x8 + 12376x6 + 1820x4 + 105x2 + 1 \( 2^{28}\cdot 29^{26} \) $C_2\times C_{14}$ (as 28T2) $[4, 4, 84]$ (GRH)
28.2.119031391573998606077977177245018890036706279424.1 x28 - 4x - 1 \( -\,2^{30}\cdot 313\cdot 354174511376228618158774900446574177 \) $S_{28}$ (as 28T1854) Trivial (GRH)
28.2.119031424719521595854656348569811317171530235904.1 x28 - 2x - 1 \( -\,2^{28}\cdot 5167\cdot 353915647\cdot 3141620149\cdot 77184457201040359 \) $S_{28}$ (as 28T1854) Trivial (GRH)
28.28.642581186433047492874742549394260203375244140625.1 x28 - x27 - 40x26 + 35x25 + 667x24 - 497x23 - 6073x22 + 3733x21 + 33381x20 - 16356x19 - 116335x18 + 43955x17 + 264151x16 - 74631x15 - 396001x14 + 80966x13 + 391804x12 - 55684x11 - 251669x10 + 23519x9 + 101079x8 - 5634x7 - 23674x6 + 574x5 + 2842x4 + 28x3 - 133x2 - 7x + 1 \( 5^{14}\cdot 29^{26} \) $C_2\times C_{14}$ (as 28T2) $[2]$ (GRH)
28.28.819569564076950716311987772907236898045117333504.1 x28 - 29x26 + 377x24 - 2900x22 + 14674x20 - 51359x18 + 127281x16 - 224808x14 + 281010x12 - 243542x10 + 140998x8 - 51272x6 + 10556x4 - 1015x2 + 29 \( 2^{28}\cdot 29^{27} \) $C_{28}$ (as 28T1) Trivial (GRH)
28.0.2105327011242178848592130424466919810093585268736.1 x28 - 4x + 4 \( 2^{28}\cdot 7842954290070305945694932432722001560381 \) $S_{28}$ (as 28T1854) Trivial (GRH)
28.2.2343389794390175813794693396461085937707434115072.1 x28 - 4x - 4 \( -\,2^{28}\cdot 1531\cdot 2383\cdot 51031\cdot 46889040281957983714550830849 \) $S_{28}$ (as 28T1854) Trivial (GRH)
28.0.4329685414058356179785542334930922683994094960640.1 x28 - 2x + 2 \( 2^{28}\cdot 5\cdot 3225867013676729932267622899212630602713 \) $S_{28}$ (as 28T1854) Trivial (GRH)
28.0.4448716805188928174143786050979756117181869491005.1 x28 - x + 2 \( 5\cdot 6249889\cdot 26339207\cdot 398948659\cdot 13547923849744568758845893 \) $S_{28}$ (as 28T1854) Trivial (GRH)
28.2.4448716805632354662386823820928005747801019383808.1 x28 - 2 \( -\,2^{83}\cdot 7^{28} \) $D_4\times F_7$ (as 28T41) Trivial (GRH)
28.0.4448716805632354662386823820928005747801019383808.1 x28 + 2 \( 2^{83}\cdot 7^{28} \) $D_4\times F_7$ (as 28T41) Trivial (GRH)
28.2.4567748197206353144988105306925088811607943806976.1 x28 - 2x - 2 \( -\,2^{28}\cdot 29\cdot 2411\cdot 243370014514934784554049882825862109 \) $S_{28}$ (as 28T1854) Trivial (GRH)
28.0.8602002546566250227508255640254075178338897178281.1 x28 - 56x25 - 7x24 - 14x23 + 1162x22 + 286x21 + 539x20 - 11074x19 - 4074x18 - 6433x17 + 48363x16 + 27475x15 + 29189x14 - 79527x13 - 90503x12 - 49217x11 + 5593x10 + 93345x9 + 89726x8 + 166311x7 + 114709x6 + 86730x5 + 11690x4 - 17626x3 + 25221x2 - 9401x + 6241 \( 3^{14}\cdot 7^{50} \) $C_2\times C_{14}$ (as 28T2) $[203]$ (GRH)
28.0.14121388821225670988853483488774192350843817726481.1 x28 - x27 - x26 - 50x25 + 45x24 + 41x23 + 923x22 - 740x21 - 566x20 - 7986x19 + 5482x18 + 3755x17 + 34135x16 - 15421x15 - 15266x14 - 71623x13 - 3964x12 + 45122x11 + 87041x10 + 49398x9 - 13057x8 - 105029x7 - 52559x6 - 58937x5 + 57132x4 + 53384x3 + 9659x2 + 13272x + 6241 \( 3^{14}\cdot 43^{26} \) $C_2\times C_{14}$ (as 28T2) $[203]$ (GRH)
28.0.18634854406558377293367533932433545897882080078125.1 x28 - x27 + 30x26 - 30x25 + 407x24 - 407x23 + 3307x22 - 3307x21 + 17981x20 - 17981x19 + 69340x18 - 69340x17 + 196621x16 - 196621x15 + 421429x14 - 421429x13 + 702439x12 - 702439x11 + 945981x10 - 945981x9 + 1086979x8 - 1086979x7 + 1138251x6 - 1138251x5 + 1148807x4 - 1148807x3 + 1149822x2 - 1149822x + 1149851 \( 5^{14}\cdot 29^{27} \) $C_{28}$ (as 28T1) $[2, 2, 2, 2, 1514]$ (GRH)
28.0.59692812354437378574125162510614243030548095703125.1 x28 - x27 + 13x26 - 18x25 + 139x24 + 6x23 + 1195x22 + 162x21 + 10698x20 - 2678x19 + 31811x18 - 10412x17 + 82335x16 - 59127x15 + 217167x14 - 143196x13 + 464676x12 - 285512x11 + 357781x10 - 176521x9 + 256648x8 + 112508x7 + 36201x6 + 9801x5 + 2858x4 + 449x3 + 67x2 + 9x + 1 \( 5^{21}\cdot 29^{24} \) $C_{28}$ (as 28T1) $[2, 2, 842]$ (GRH)
28.0.71403665296191917297019015087709113341743884283129.1 x28 - x27 + 41x26 - 34x25 + 814x24 - 569x23 + 10073x22 - 5894x21 + 85446x20 - 41430x19 + 517766x18 - 204124x17 + 2278084x16 - 713493x15 + 7270037x14 - 1746022x13 + 16581844x12 - 2930752x11 + 26206720x10 - 3163168x9 + 27305280x8 - 2133504x7 + 17228288x6 - 594944x5 + 5748736x4 - 229376x3 + 745472x2 + 57344x + 16384 \( 7^{14}\cdot 29^{26} \) $C_2\times C_{14}$ (as 28T2) $[2, 4, 4, 812]$ (GRH)
28.0.160727205638753900965518547139872645824181262352384.1 x28 - 25x26 + 411x24 - 3816x22 + 25427x20 - 105124x18 + 315729x16 - 623516x14 + 888182x12 - 737996x10 + 406547x8 - 33970x6 + 2123x4 - 53x2 + 1 \( 2^{28}\cdot 3^{14}\cdot 29^{24} \) $C_2\times C_{14}$ (as 28T2) $[4, 4, 28]$ (GRH)
28.0.463028542684026225381227850734902390950731116969984.1 x28 + 54x26 + 1300x24 + 18400x22 + 170016x20 + 1076768x18 + 4775232x16 + 14883840x14 + 32248320x12 + 47297536x10 + 44808192x8 + 25346048x6 + 7454720x4 + 860160x2 + 16384 \( 2^{42}\cdot 29^{26} \) $C_2\times C_{14}$ (as 28T2) $[4, 172, 172]$ (GRH)
28.28.463028542684026225381227850734902390950731116969984.1 x28 - 54x26 + 1300x24 - 18400x22 + 170016x20 - 1076768x18 + 4775232x16 - 14883840x14 + 32248320x12 - 47297536x10 + 44808192x8 - 25346048x6 + 7454720x4 - 860160x2 + 16384 \( 2^{42}\cdot 29^{26} \) $C_2\times C_{14}$ (as 28T2) Trivial (GRH)
28.0.482771783823117526797953812068649122826362283884544.1 x28 + 14x24 + 406x22 + 637x20 + 1736x18 + 25613x16 + 45672x14 + 146510x12 + 216314x10 + 175987x8 + 135485x6 + 138712x4 + 36281x2 + 6241 \( 2^{28}\cdot 7^{50} \) $C_2\times C_{14}$ (as 28T2) $[71]$ (GRH)
28.0.792537323068373529244880273632877655015215903801344.1 x28 - 3x26 + 18x24 + 304x22 - 431x20 + 627x18 + 12915x16 - 6007x14 + 76379x12 - 24573x10 + 152173x8 - 11756x6 + 110547x4 - 8906x2 + 6241 \( 2^{28}\cdot 43^{26} \) $C_2\times C_{14}$ (as 28T2) $[43]$ (GRH)
28.2.919973073089479921953602000000000000000000000000000.1 x28 - 5 \( -\,2^{28}\cdot 5^{27}\cdot 7^{28} \) $D_4\times F_7$ (as 28T41) Trivial (GRH)
28.28.2070706293589565601613551437543564286910572644210741.1 x28 - x27 - 57x26 + 57x25 + 1451x24 - 1451x23 - 21749x22 + 21749x21 + 213035x20 - 213035x19 - 1430453x18 + 1430453x17 + 6715531x16 - 6715531x15 - 22059893x14 + 22059893x13 + 49878667x12 - 49878667x11 - 74814837x10 + 74814837x9 + 69567115x8 - 69567115x7 - 35437941x6 + 35437941x5 + 7799435x4 - 7799435x3 - 515445x2 + 515445x - 40309 \( 7^{14}\cdot 29^{27} \) $C_{28}$ (as 28T1) Trivial (GRH)
28.0.3654513548980364725264702136425345220781793212890625.1 x28 - 5x27 + 47x26 - 152x25 + 1049x24 - 3001x23 + 14492x22 - 30908x21 + 115818x20 - 204097x19 + 649914x18 - 933216x17 + 2508376x16 - 2978786x15 + 7071411x14 - 6804920x13 + 13577493x12 - 10099944x11 + 17701828x10 - 9450995x9 + 11808392x8 - 1974799x7 + 3396106x6 - 287718x5 + 726277x4 + 16080x3 + 60245x2 - 6888x + 1681 \( 3^{14}\cdot 5^{14}\cdot 29^{24} \) $C_2\times C_{14}$ (as 28T2) $[4, 4, 452]$ (GRH)
28.0.9020522762586308771279473372699929575905800975548416.1 x28 + 197x24 + 9834x20 + 111451x16 + 395946x12 + 345566x8 + 1437x4 + 1 \( 2^{56}\cdot 29^{24} \) $C_2\times C_{14}$ (as 28T2) $[4, 4, 1204]$ (GRH)
28.2.10144175740535033505677411042314150782342217749732947.1 x28 - 3x + 1 \( -\,11\cdot 13\cdot 23\cdot 47\cdot 47470777\cdot 1382383981477549009491771296663714047117 \) $S_{28}$ (as 28T1854) Trivial (GRH)
28.2.10144175740601324551903917792039296238848946961358419.1 x28 - 3x - 1 \( -\,79\cdot 6399373412031876752263\cdot 20065603237699194720476206747 \) $S_{28}$ (as 28T1854) Trivial (GRH)
28.2.10148624457373811383453051240997651516343383374929491.1 x28 - 3x - 2 \( -\,29\cdot 53\cdot 1231\cdot 5363833169775281154988777361766198998409333053 \) $S_{28}$ (as 28T1854) Trivial (GRH)
28.0.10976959488814771402711672000547176203926080322265625.1 x28 - 112x25 + 49x24 + 154x23 + 2618x22 - 2414x21 - 3381x20 + 6370x19 + 38654x18 - 78533x17 - 109165x16 + 382109x15 - 209631x14 - 564725x13 + 940065x12 + 282121x11 - 787227x10 + 598339x9 + 1045310x8 - 124511x7 - 202517x6 + 343196x5 + 333200x4 + 51912x3 - 47341x2 - 9401x + 6241 \( 5^{14}\cdot 7^{50} \) $C_2\times C_{14}$ (as 28T2) $[127]$ (GRH)
28.0.13427827737836760536055607671312169337571202392129536.1 x28 + 58x26 + 1508x24 + 23200x22 + 234784x20 + 1643488x18 + 8145984x16 + 28775424x14 + 71938560x12 + 124693504x10 + 144381952x8 + 105005056x6 + 43237376x4 + 8314880x2 + 475136 \( 2^{42}\cdot 29^{27} \) $C_{28}$ (as 28T1) $[2, 2, 2, 48802]$ (GRH)
28.28.13427827737836760536055607671312169337571202392129536.1 x28 - 58x26 + 1508x24 - 23200x22 + 234784x20 - 1643488x18 + 8145984x16 - 28775424x14 + 71938560x12 - 124693504x10 + 144381952x8 - 105005056x6 + 43237376x4 - 8314880x2 + 475136 \( 2^{42}\cdot 29^{27} \) $C_{28}$ (as 28T1) Trivial (GRH)
28.0.18020212407199631553450678294049740884820855712890625.1 x28 - x27 + 5x26 + 98x25 - 43x24 + 277x23 + 2085x22 - 152x21 + 2790x20 + 2322x19 + 38446x18 - 13267x17 + 7013x16 - 52161x15 + 217434x14 - 199373x13 - 369218x12 - 846630x11 + 173519x10 + 680690x9 + 994183x8 + 128151x7 - 20587x6 - 51405x5 + 189716x4 + 67288x3 + 27471x2 - 13272x + 6241 \( 5^{14}\cdot 43^{26} \) $C_2\times C_{14}$ (as 28T2) $[1421]$ (GRH)
28.0.39980252956536233141313409161989698787991996663947761.1 x28 - 12x27 + 81x26 - 388x25 + 1591x24 - 5878x23 + 20190x22 - 63303x21 + 186224x20 - 511845x19 + 1342595x18 - 3302776x17 + 7789506x16 - 17272242x15 + 36946487x14 - 74021368x13 + 143721798x12 - 259144734x11 + 455881295x10 - 732077019x9 + 1159745156x8 - 1624224783x7 + 2293844933x6 - 2689454001x5 + 3335457433x4 - 2996413671x3 + 3196869115x2 - 1711780865x + 1532409301 \( 11^{14}\cdot 29^{26} \) $C_2\times C_{14}$ (as 28T2) $[16, 16, 3440]$ (GRH)
28.0.50201655190081835380839261671426578388690948486328125.1 x28 - x27 + 18x26 - 23x25 + 29x24 - 149x23 - 795x22 - 8x21 - 2927x20 + 667x19 + 13846x18 - 647x17 + 109320x16 + 98963x15 + 313397x14 + 494999x13 + 789626x12 + 291678x11 + 1921156x10 - 425111x9 + 1044768x8 + 1156338x7 - 1030264x6 + 642721x5 + 1780368x4 - 4481806x3 + 897127x2 + 1339909x + 1148111 \( 5^{21}\cdot 29^{26} \) $C_{28}$ (as 28T1) $[2, 2, 2, 2, 562]$ (GRH)
28.0.135171579942192030712001098144632895138136441638354944.1 x28 - 29x26 + 551x24 - 5916x22 + 45675x20 - 232000x18 + 854369x16 - 1923396x14 + 3056194x12 - 2610464x10 + 1563419x8 - 459186x6 + 96715x4 - 10933x2 + 841 \( 2^{28}\cdot 3^{14}\cdot 29^{26} \) $C_2\times C_{14}$ (as 28T2) $[2, 4, 4, 12]$ (GRH)
28.28.135171579942192030712001098144632895138136441638354944.1 x28 - 2x27 - 67x26 + 128x25 + 1915x24 - 3470x23 - 30502x22 + 51962x21 + 296883x20 - 470232x19 - 1822856x18 + 2646496x17 + 7045255x16 - 9204326x15 - 16632140x14 + 19086334x13 + 22549873x12 - 22027400x11 - 15790909x10 + 12642698x9 + 4786431x8 - 3052488x7 - 481394x6 + 260140x5 + 15255x4 - 7818x3 - 67x2 + 56x + 1 \( 2^{28}\cdot 3^{14}\cdot 29^{26} \) $C_2\times C_{14}$ (as 28T2) Trivial (GRH)
28.0.135171579942192030712001098144632895138136441638354944.2 x28 - 31x26 + 354x24 - 1731x22 + 2216x20 + 8564x18 - 4122x16 - 121607x14 + 165323x12 - 180077x10 + 1311812x8 - 3636433x6 + 15557681x4 + 4370782x2 + 2825761 \( 2^{28}\cdot 3^{14}\cdot 29^{26} \) $C_2\times C_{14}$ (as 28T2) $[2, 4, 4, 84]$ (GRH)
28.0.135171579942192030712001098144632895138136441638354944.3 x28 - 23x26 + 170x24 - 243x22 - 2160x20 + 8804x18 - 13066x16 - 10755x14 + 322699x12 - 596165x10 + 516968x8 + 3918063x6 - 1962803x4 - 4216942x2 + 3728761 \( 2^{28}\cdot 3^{14}\cdot 29^{26} \) $C_2\times C_{14}$ (as 28T2) $[2, 4, 12, 12]$ (GRH)
28.0.205102941494858641164670947835018741350400000000000000.1 x28 + 69x26 + 1974x24 + 30865x22 + 294090x20 + 1804843x18 + 7322517x16 + 19717109x14 + 34627149x12 + 38013350x10 + 24218096x8 + 8079074x6 + 1320817x4 + 92266x2 + 1681 \( 2^{28}\cdot 5^{14}\cdot 29^{24} \) $C_2\times C_{14}$ (as 28T2) $[4, 28, 812]$ (GRH)
28.0.242610241950435234690533858908055411895726700337848749.1 x28 - 3x + 3 \( 3^{27}\cdot 13\cdot 45673\cdot 586051\cdot 628025053\cdot 145586123452771747741 \) $S_{28}$ (as 28T1854) $[2]$ (GRH)
28.0.252754298659611839720841922043746138323258475768971264.1 x28 - 2x + 3 \( 2^{28}\cdot 3^{27}\cdot 13\cdot 6553\cdot 20327\cdot 42022097279\cdot 1696876609651 \) $S_{28}$ (as 28T1854) Trivial (GRH)
28.0.252754417691002970292836280287462187156691663543501629.1 x28 - x + 3 \( 3^{27}\cdot 11\cdot 23\cdot 83\cdot 3121\cdot 20446009\cdot 38719859\cdot 223913377\cdot 2853054979 \) $S_{28}$ (as 28T1854) Trivial (GRH)
28.2.252754417691003413719324523325232135406322282693394432.1 x28 - 3 \( -\,2^{56}\cdot 3^{27}\cdot 7^{28} \) $D_4\times F_7$ (as 28T41) Trivial (GRH)

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