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Label Polynomial Discriminant Galois group Class group
28.0.305...909.1 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)
28.0.327...933.1 x28 - x + 1 \( 17787551\cdot 1838482241035336291804559189893283 \) $S_{28}$ (as 28T1854) trivial (GRH)
28.2.335...539.1 x28 - x - 1 \( -\,349\cdot 14769635993383\cdot 6516302002526983353692617 \) $S_{28}$ (as 28T1854) trivial (GRH)
28.0.194...021.1 x28 + 28x24 - 14x23 - 35x22 - 19x21 + 1470x20 - 4557x19 + 9849x18 - 9660x17 + 2863x16 + 12915x15 - 18102x14 + 12103x13 - 2891x12 - 21119x11 + 2975x10 - 4704x9 + 70x8 + 13698x7 + 6909x6 + 4900x5 + 5047x4 + 1015x3 - 7x2 - 7x + 1 \( 3^{21}\cdot 7^{37} \) $D_{28}$ (as 28T10) trivial (GRH)
28.0.650...777.1 x28 - 2x27 + 4x26 - 10x25 + 5x24 + 7x23 - 18x22 - 225x21 - 120x20 + 1331x19 - 2152x18 + 4025x17 + 6967x16 - 15748x15 + 11604x14 - 4171x13 - 26180x12 + 37520x11 - 9040x10 + 16909x9 - 40976x8 - 11561x7 + 79270x6 - 49005x5 + 81626x4 - 70530x3 + 35205x2 - 15236x + 3229 \( 7^{21}\cdot 71^{13} \) $D_{28}$ (as 28T10) trivial (GRH)
28.2.462...167.1 x28 - 3x27 + 5x26 - 37x25 + 223x24 - 471x23 + 612x22 - 2497x21 + 8709x20 - 13185x19 + 9400x18 - 14827x17 + 46063x16 - 65223x15 + 33754x14 - 24986x13 + 51170x12 - 43382x11 - 84023x10 + 134581x9 - 102493x8 + 27983x7 - 169214x6 + 162210x5 - 64809x4 - 131662x3 + 54254x2 - 97483x - 91661 \( -\,7^{21}\cdot 71^{14} \) $D_{28}$ (as 28T10) trivial (GRH)
28.0.849...381.1 x28 - 8x27 + 39x26 - 147x25 + 484x24 - 1461x23 + 4001x22 - 10052x21 + 23841x20 - 52926x19 + 109173x18 - 208723x17 + 369896x16 - 608215x15 + 913744x14 - 1246890x13 + 1584122x12 - 1829692x11 + 1878311x10 - 1777347x9 + 1518093x8 - 1036936x7 + 598732x6 - 344364x5 + 177291x4 - 79332x3 + 46992x2 - 15367x + 6413 \( 11^{14}\cdot 181^{13} \) $D_{28}$ (as 28T10) trivial (GRH)
28.0.503...649.1 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)
28.2.725...875.1 x28 - 5x27 - 3x26 + 57x25 - 13x24 - 420x23 + 259x22 + 2099x21 - 1147x20 - 7975x19 + 7844x18 + 15881x17 - 34395x16 - 17074x15 + 107194x14 - 103829x13 + 94772x12 - 84342x11 - 113950x10 + 177636x9 - 26899x8 + 2410x7 + 74025x6 - 120275x5 - 49775x4 + 101875x3 - 41875x2 + 31250x - 15625 \( -\,5^{14}\cdot 499^{13} \) $D_{28}$ (as 28T10) trivial (GRH)
28.0.941...672.1 x28 - 3x14 + 3 \( 2^{28}\cdot 3^{27}\cdot 7^{28} \) $D_4\times F_7$ (as 28T41) trivial (GRH)
28.0.192...877.1 x28 - 12x27 + 74x26 - 288x25 + 773x24 - 1407x23 + 1601x22 - 676x21 - 794x20 + 2173x19 - 6644x18 + 23336x17 - 53512x16 + 82551x15 - 80880x14 + 23133x13 + 117766x12 - 327568x11 + 536090x10 - 646700x9 + 621936x8 - 488735x7 + 317878x6 - 166984x5 + 68952x4 - 21502x3 + 5711x2 - 1133x + 193 \( 43^{14}\cdot 53^{13} \) $D_{28}$ (as 28T10) $[3]$ (GRH)
28.2.265...875.1 x28 - 9x27 + 53x26 - 226x25 + 695x24 - 1455x23 + 1352x22 + 4587x21 - 26437x20 + 75511x19 - 148243x18 + 166438x17 - 8850x16 - 553583x15 + 1599191x14 - 2514414x13 + 2904360x12 - 819447x11 - 1193138x10 + 5517125x9 - 17624126x8 + 7384001x7 - 17552991x6 + 11860646x5 - 8713168x4 - 7406098x3 - 9688274x2 - 1853761x - 465059 \( -\,3^{14}\cdot 5^{21}\cdot 71^{13} \) $D_{28}$ (as 28T10) n/a
28.28.146...821.1 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)
28.0.204...801.1 x28 - 6x27 + 18x26 + 6x25 - 69x24 + 47x23 + 257x22 - 674x21 + 321x20 + 545x19 - 15x18 - 692x17 + 1854x16 - 6800x15 + 5094x14 + 6261x13 - 5929x12 + 6262x11 - 14458x10 - 7839x9 + 27851x8 - 6775x7 + 6005x6 - 1487x5 - 35142x4 + 22011x3 + 18446x2 - 12525x + 2675 \( 7^{14}\cdot 449^{13} \) $D_{28}$ (as 28T10) trivial (GRH)
28.0.282...776.1 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)
28.2.119...424.1 x28 - 4x - 1 \( -\,2^{30}\cdot 313\cdot 354174511376228618158774900446574177 \) $S_{28}$ (as 28T1854) trivial (GRH)
28.2.119...904.1 x28 - 2x - 1 \( -\,2^{28}\cdot 5167\cdot 353915647\cdot 3141620149\cdot 77184457201040359 \) $S_{28}$ (as 28T1854) trivial (GRH)
28.2.149...000.1 x28 + 5x26 - 70x24 - 325x22 + 1550x20 + 9000x18 - 17625x16 - 565625x14 - 3091250x12 - 7234375x10 - 16993750x8 - 9562500x6 - 23500000x4 - 1250000x2 - 5546875 \( -\,2^{28}\cdot 5^{21}\cdot 71^{13} \) $D_{28}$ (as 28T10) n/a
28.2.176...192.1 x28 - 4x26 - 30x24 - 16x22 + 656x20 + 480x18 + 3424x16 + 19424x14 - 154080x12 - 456704x10 + 937984x8 + 503040x6 - 4576768x4 - 11580416x2 - 4807552 \( -\,2^{77}\cdot 71^{13} \) $D_{28}$ (as 28T10) n/a
28.0.537...517.1 x28 - 24x26 + 286x24 - 2327x22 + 12825x20 - 40336x18 + 39135x16 + 152588x14 - 531606x12 + 381077x10 + 2209555x8 - 10321444x6 + 18143914x4 - 8922944x2 + 1423325 \( 19^{14}\cdot 197^{13} \) $D_{28}$ (as 28T10) $[29]$ (GRH)
28.28.642...625.1 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)
28.28.819...504.1 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)
28.0.210...736.1 x28 - 4x + 4 \( 2^{28}\cdot 7842954290070305945694932432722001560381 \) $S_{28}$ (as 28T1854) trivial (GRH)
28.2.234...072.1 x28 - 4x - 4 \( -\,2^{28}\cdot 1531\cdot 2383\cdot 51031\cdot 46889040281957983714550830849 \) $S_{28}$ (as 28T1854) trivial (GRH)
28.0.432...640.1 x28 - 2x + 2 \( 2^{28}\cdot 5\cdot 3225867013676729932267622899212630602713 \) $S_{28}$ (as 28T1854) trivial (GRH)
28.0.444...005.1 x28 - x + 2 \( 5\cdot 6249889\cdot 26339207\cdot 398948659\cdot 13547923849744568758845893 \) $S_{28}$ (as 28T1854) trivial (GRH)
28.2.444...808.1 x28 - 2 \( -\,2^{83}\cdot 7^{28} \) $D_4\times F_7$ (as 28T41) trivial (GRH)
28.0.444...808.1 x28 + 2 \( 2^{83}\cdot 7^{28} \) $D_4\times F_7$ (as 28T41) trivial (GRH)
28.2.456...976.1 x28 - 2x - 2 \( -\,2^{28}\cdot 29\cdot 2411\cdot 243370014514934784554049882825862109 \) $S_{28}$ (as 28T1854) trivial (GRH)
28.2.557...571.1 x28 - 20x26 + 294x24 - 3361x22 + 28147x20 - 154673x18 + 536790x16 - 1083403x14 + 980940x12 + 64462x10 - 677733x8 - 44521x6 + 115444x4 + 5415x2 - 6859 \( -\,19^{13}\cdot 197^{14} \) $D_{28}$ (as 28T10) $[29]$ (GRH)
28.0.860...281.1 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)
28.0.141...481.1 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)
28.0.186...125.1 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)
28.0.596...125.1 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)
28.0.714...129.1 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)
28.0.160...384.1 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)
28.2.295...963.1 x28 - 14x27 + 80x26 - 221x25 + 397x24 - 1904x23 + 10213x22 - 26576x21 + 32909x20 - 65079x19 + 350623x18 - 1046531x17 + 1678487x16 - 1771438x15 + 2670493x14 - 7195176x13 + 14367013x12 - 15585945x11 + 7205726x10 - 3208396x9 + 37523327x8 - 120026000x7 + 201372903x6 - 215912334x5 + 156455683x4 - 76691304x3 + 25200801x2 - 5337738x + 544563 \( -\,7^{13}\cdot 29^{27} \) $D_{28}$ (as 28T10) $[7]$ (GRH)
28.0.463...984.1 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)
28.28.463...984.1 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)
28.0.482...544.1 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)
28.0.792...344.1 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)
28.2.919...000.1 x28 - 5 \( -\,2^{28}\cdot 5^{27}\cdot 7^{28} \) $D_4\times F_7$ (as 28T41) trivial (GRH)
28.28.207...741.1 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)
28.2.244...000.1 x28 + 10x26 - 280x24 - 2600x22 + 24800x20 + 288000x18 - 1128000x16 - 72400000x14 - 791360000x12 - 3704000000x10 - 17401600000x8 - 19584000000x6 - 96256000000x4 - 10240000000x2 - 90880000000 \( -\,2^{42}\cdot 5^{21}\cdot 71^{13} \) $D_{28}$ (as 28T10) n/a
28.2.271...000.1 x28 - 15x26 - 390x24 + 2850x22 + 49825x20 + 260250x18 + 737875x16 + 549375x14 - 1364375x12 + 4565625x10 + 13346875x8 - 16781250x6 + 7031250x4 + 128437500x2 - 11796875 \( -\,2^{28}\cdot 5^{21}\cdot 151^{13} \) $D_{28}$ (as 28T10) n/a
28.2.320...672.1 x28 - 24x24 - 160x22 - 1656x20 + 35040x18 - 27616x16 - 906528x14 + 2661648x12 + 11464832x10 - 75391104x8 + 141558144x6 - 105026816x4 + 23099904x2 - 1565568 \( -\,2^{77}\cdot 151^{13} \) $D_{28}$ (as 28T10) n/a
28.2.335...384.1 x28 - 29x26 + 319x24 - 928x22 - 2494x20 - 21982x18 + 156890x16 - 105676x14 - 41383x12 - 3321805x10 + 13163303x8 - 22596220x6 + 20965492x4 - 8196560x2 - 1114064 \( -\,2^{40}\cdot 29^{27} \) $D_{28}$ (as 28T10) $[7]$ (GRH)
28.0.365...625.1 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)
28.0.902...416.1 x28 + 197x24 + 9834x20 + 111451x16 + 395946x12 + 345566x8 + 1437x4 + 1 \( 2^{56}\cdot 29^{24} \) $C_2\times C_{14}$ (as 28T2) $[4, 4, 1204]$ (GRH)
28.2.101...947.1 x28 - 3x + 1 \( -\,11\cdot 13\cdot 23\cdot 47\cdot 47470777\cdot 1382383981477549009491771296663714047117 \) $S_{28}$ (as 28T1854) trivial (GRH)
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