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Label Polynomial Discriminant Galois group Class group
27.1.437270368662830612637452956330749689027.1 x27 - x - 1 \( -\,23\cdot 3539\cdot 535391\cdot 10033918834509020645502251401 \) $S_{27}$ (as 27T2392) Trivial (GRH)
27.1.449582607823244927259046304907550096579.1 x27 + x - 1 \( -\,151\cdot 144512650291622071\cdot 20602820982951053299 \) $S_{27}$ (as 27T2392) Trivial (GRH)
27.27.706965049015104706497203195837614914543357369.1 x27 - 27x25 + 324x23 - 2277x21 + 10395x19 - 32319x17 + 69768x15 - 104652x13 + 107406x11 - 72930x9 + 30888x7 - 7371x5 + 819x3 - 27x - 1 \( 3^{94} \) $C_{27}$ (as 27T1) Trivial (GRH)
27.1.826260826778206666631489441194722724701633731.1 x27 + 2x - 1 \( -\,229351\cdot 3602603985935124183594095692605319901381 \) $S_{27}$ (as 27T2392) Trivial (GRH)
27.27.7977212169716289044333767743376433611324896529.1 x27 - x26 - 42x25 + 37x24 + 728x23 - 564x22 - 6817x21 + 4664x20 + 37948x19 - 23103x18 - 130429x17 + 71289x16 + 279661x15 - 138143x14 - 372684x13 + 166778x12 + 305327x11 - 124486x10 - 150120x9 + 56020x8 + 42107x7 - 14253x6 - 6122x5 + 1790x4 + 395x3 - 85x2 - 10x + 1 \( 7^{18}\cdot 19^{24} \) $C_3\times C_9$ (as 27T2) Trivial (GRH)
27.1.28105327126796183803132932513380581740627623936.1 x27 - 4x - 4 \( -\,2^{26}\cdot 263\cdot 1592403079552126010285410393405129573 \) $S_{27}$ (as 27T2392) Trivial (GRH)
27.1.28931587510147902226726652006325673846179364864.1 x27 - 2x - 2 \( -\,2^{26}\cdot 239\cdot 911\cdot 1492637\cdot 10924843\cdot 125481509\cdot 967669291801 \) $S_{27}$ (as 27T2392) Trivial (GRH)
27.1.29757847887343501070113214188474091663330902016.1 x27 - x - 2 \( -\,2^{27}\cdot 47\cdot 4717303065439408933563627808093088051 \) $S_{27}$ (as 27T2392) Trivial (GRH)
27.1.29757847893499620558587041306002149293331489783.1 x27 - x - 4 \( -\,167\cdot 359\cdot 10245289151\cdot 48446943180119740684317685671961 \) $S_{27}$ (as 27T2392) Trivial (GRH)
27.1.29757847893499620650320371499270765951731105792.1 x27 - 2 \( -\,2^{26}\cdot 3^{81} \) $C_9.(C_9\times S_3)$ (as 27T176) Trivial (GRH)
27.1.30584108276851339073914090992215858057282846720.1 x27 + 2x - 2 \( -\,2^{26}\cdot 5\cdot 7\cdot 11\cdot 80071\cdot 14783591491235038142928766927013 \) $S_{27}$ (as 27T2392) Trivial (GRH)
27.1.31410368660203057497507810485160950162834587648.1 x27 + 4x - 4 \( -\,2^{26}\cdot 1831\cdot 255625869232040633091991440618651397 \) $S_{27}$ (as 27T2392) Trivial (GRH)
27.27.50323116815004832630295337440131512593194174521.1 x27 - 45x25 + 837x23 - 8430x21 + 50652x19 - 193x18 - 188811x17 + 2934x16 + 441720x15 - 15822x14 - 646731x13 + 37506x12 + 585063x11 - 42453x10 - 319331x9 + 24462x8 + 99963x7 - 7245x6 - 16119x5 + 1080x4 + 1059x3 - 81x2 - 18x + 1 \( 3^{66}\cdot 7^{18} \) $C_3\times C_9$ (as 27T2) Trivial (GRH)
27.27.735278035529026786878794063569162978753987707441.1 x27 - 51x25 - 4x24 + 1080x23 + 156x22 - 12356x21 - 2448x20 + 83283x19 + 19984x18 - 339003x17 - 91596x16 + 825846x15 + 238428x14 - 1168977x13 - 344712x12 + 930681x11 + 259620x10 - 414755x9 - 102465x8 + 101628x7 + 20920x6 - 12933x5 - 2085x4 + 755x3 + 90x2 - 15x - 1 \( 3^{36}\cdot 19^{24} \) $C_3\times C_9$ (as 27T2) Trivial (GRH)
27.1.43207461914112074238522908041698612863100209996211.1 x27 - 3x - 3 \( -\,3^{27}\cdot 71\cdot 337\cdot 14619373\cdot 78563389\cdot 206180539890995287 \) $S_{27}$ (as 27T2392) Trivial (GRH)
27.3.46944089987663498525424751985000152191384750818109.1 x27 - 3x - 1 \( 3^{27}\cdot 11\cdot 29\cdot 318911\cdot 7780103222533\cdot 7777884788734331 \) $S_{27}$ (as 27T2392) $[2]$ (GRH)
27.1.46944089988550351501910827524896651452623050603715.1 x27 + 3x - 1 \( -\,3^{27}\cdot 5\cdot 29573\cdot 718375177076041\cdot 57954924238599673 \) $S_{27}$ (as 27T2392) Trivial (GRH)
27.1.46973847836000424634318110126447672587955631816704.1 x27 + 3x - 2 \( -\,2^{27}\cdot 3^{27}\cdot 1592729\cdot 28815787221263522142841 \) $S_{27}$ (as 27T2392) Trivial (GRH)
27.27.550892378962365588304561118053988796799287710804809.1 x27 - 6x26 - 47x25 + 302x24 + 943x23 - 6448x22 - 10567x21 + 76481x20 + 71695x19 - 556066x18 - 291044x17 + 2587104x16 + 603975x15 - 7811439x14 - 35156x13 + 15161145x12 - 2848142x11 - 18230502x10 + 6439289x9 + 12558384x8 - 6282221x7 - 4210683x6 + 2778704x5 + 421825x4 - 457387x3 + 20126x2 + 21522x - 2699 \( 13^{18}\cdot 19^{24} \) $C_3\times C_9$ (as 27T2) Trivial (GRH)
27.1.1127129811580525429258316897077920778307403598875259.1 x27 - 2x - 3 \( -\,2833\cdot 233083\cdot 3093889\cdot 426423967391\cdot 1293809775098462396398319 \) $S_{27}$ (as 27T2392) Trivial (GRH)
27.1.1127130637840902624857160283640102926725220750412411.1 x27 - x - 3 \( -\,5388993289\cdot 58684642644166161743\cdot 3564036539687671224493 \) $S_{27}$ (as 27T2392) Trivial (GRH)
27.1.1127130637840908780976740490797413723399509150616187.1 x27 - 3 \( -\,3^{107} \) $C_9.(C_9\times S_3)$ (as 27T176) Trivial (GRH)
27.1.1127130637840914937096320697954724520073797550819963.1 x27 + x - 3 \( -\,991\cdot 43499487821953\cdot 240698508804661\cdot 108628318596533067121 \) $S_{27}$ (as 27T2392) Trivial (GRH)
27.1.1174074727829015705990408280552362125221513051327099.1 x27 + 3x - 3 \( -\,3^{27}\cdot 11083579402853\cdot 13891265934804536061236909 \) $S_{27}$ (as 27T2392) Trivial (GRH)
27.27.3475226802198116057554377769989579566636047832552241.1 x27 - 9x26 - 27x25 + 420x24 + 9x23 - 8244x22 + 7758x21 + 88713x20 - 125694x19 - 570907x18 + 991197x17 + 2239173x16 - 4595436x15 - 5142816x14 + 13108698x13 + 5797086x12 - 22773501x11 - 112752x10 + 22776726x9 - 6585183x8 - 11690658x7 + 5812863x6 + 2561958x5 - 1837044x4 - 142095x3 + 213804x2 - 7074x - 7019 \( 3^{66}\cdot 13^{18} \) $C_3\times C_9$ (as 27T2) Trivial (GRH)
27.27.27485917061841905258715957728464424188465393850574441.1 x27 - 9x26 - 45x25 + 558x24 + 564x23 - 14325x22 + 3278x21 + 200187x20 - 152250x19 - 1689790x18 + 1662003x17 + 9058716x16 - 9244050x15 - 31587348x14 + 28970679x13 + 71864499x12 - 50585529x11 - 103930188x10 + 44676536x9 + 88142967x8 - 15697422x7 - 37059379x6 + 2104236x5 + 7157724x4 - 134797x3 - 528300x2 + 16716x + 7064 \( 3^{36}\cdot 7^{18}\cdot 13^{18} \) $C_3^3$ (as 27T4) Trivial (GRH)
27.27.70567721948812723604880306782225092911730957083793489.1 x27 - 6x26 - 53x25 + 366x24 + 982x23 - 8844x22 - 6757x21 + 112446x20 - 14683x19 - 834075x18 + 521672x17 + 3777786x16 - 3504440x15 - 10646520x14 + 12070299x13 + 18475792x12 - 24076806x11 - 18615256x10 + 28010042x9 + 9025037x8 - 17745073x7 - 453885x6 + 4979339x5 - 862152x4 - 251138x3 + 61524x2 - 1124x - 223 \( 7^{18}\cdot 37^{24} \) $C_3\times C_9$ (as 27T2) Trivial (GRH)
27.27.93991579198394673195940551085616659931617170424829641.1 x27 - x26 - 52x25 + 47x24 + 1128x23 - 914x22 - 13369x21 + 9612x20 + 95357x19 - 60102x18 - 425693x17 + 231576x16 + 1201391x15 - 553157x14 - 2121177x13 + 810403x12 + 2271851x11 - 706862x10 - 1399735x9 + 342875x8 + 461618x7 - 78149x6 - 74294x5 + 4948x4 + 4861x3 + 271x2 - 34x - 1 \( 109^{26} \) $C_{27}$ (as 27T1) Trivial (GRH)
27.3.110898761632028778210869975092030791887124902069665792.1 x27 - 4x - 2 \( 2^{26}\cdot 555937897\cdot 70012520507\cdot 42456561322999590418419407 \) $S_{27}$ (as 27T2392) Trivial (GRH)
27.3.110898791389876228284002382374632342908260234650878781.1 x27 - 4x - 1 \( 241\cdot 3119\cdot 12228551\cdot 12064779711493270243744089382808808946789 \) $S_{27}$ (as 27T2392) Trivial (GRH)
27.1.110898791389877115136978868450172239407521472950664387.1 x27 + 4x - 1 \( -\,937\cdot 1655257\cdot 4229767\cdot 92058643\cdot 183628791318117083204427628903 \) $S_{27}$ (as 27T2392) $[2]$ (GRH)
27.1.110898821147724565210111275732773790428656805531877376.1 x27 + 4x - 2 \( -\,2^{26}\cdot 7\cdot 211\cdot 277\cdot 9820621\cdot 411289693845079379557406117008951 \) $S_{27}$ (as 27T2392) Trivial (GRH)
27.1.112025922027717580491467365903199704881290362951387771.1 x27 + 4x - 3 \( -\,11854057\cdot 9450428830207040550882062225886015638467940803 \) $S_{27}$ (as 27T2392) Trivial (GRH)
27.1.499253841597823035730555735945079609621365309403299840.1 x27 - 2x - 4 \( -\,2^{50}\cdot 5\cdot 139\cdot 42307\cdot 361717434139\cdot 41692232937963286631 \) $S_{27}$ (as 27T2392) Trivial (GRH)
27.1.499253842010953227406414947741939356093911362179170304.1 x27 + 2x - 4 \( -\,2^{50}\cdot 61379\cdot 35649361663\cdot 202651613609462963242873 \) $S_{27}$ (as 27T2392) Trivial (GRH)
27.1.1996968423127564419348927699584282983028731339264229376.1 x27 - 3x - 4 \( -\,2^{26}\cdot 3^{27}\cdot 41\cdot 1531018773258677\cdot 62166019490421251 \) $S_{27}$ (as 27T2392) Trivial (GRH)
27.1.1997015367217552532430060947581195242227227631565144064.1 x27 + x - 4 \( -\,2^{26}\cdot 97\cdot 739\cdot 7753\cdot 53544585743558317501712559568164689899 \) $S_{27}$ (as 27T2392) Trivial (GRH)
27.27.3217863581710817038235175421508758764893959268723195889.1 x27 - 9x26 - 45x25 + 636x24 + 27x23 - 17460x22 + 31872x21 + 229473x20 - 738450x19 - 1345159x18 + 7506369x17 + 647631x16 - 38801514x15 + 30109320x14 + 100880532x13 - 138866430x12 - 120638421x11 + 261338922x10 + 44503222x9 - 240759207x8 + 22047264x7 + 115889073x6 - 21421602x5 - 28758384x4 + 5399355x3 + 3255948x2 - 411264x - 105461 \( 3^{66}\cdot 19^{18} \) $C_3\times C_9$ (as 27T2) Trivial (GRH)
27.27.6504389611606252637488188857147585077648657433962663281.1 x27 - 3x26 - 72x25 + 194x24 + 2136x23 - 5166x22 - 34511x21 + 74439x20 + 337788x19 - 642199x18 - 2109834x17 + 3469977x16 + 8634362x15 - 11919870x14 - 23358597x13 + 25816709x12 + 41360031x11 - 34011447x10 - 46156293x9 + 25045044x8 + 29760855x7 - 8403372x6 - 9106128x5 + 587949x4 + 751973x3 + 31935x2 - 14445x - 1153 \( 3^{36}\cdot 37^{24} \) $C_3\times C_9$ (as 27T2) Trivial (GRH)
27.1.11466666281598039055674857163705092874817691487932776448.1 x27 + 5x - 2 \( -\,2^{27}\cdot 102533\cdot 472897035109621\cdot 1761964015755790324648349537 \) $S_{27}$ (as 27T2392) Trivial (GRH)
27.27.25450405558360134867067668541820239712260815470994619689.1 x27 - 9x26 - 63x25 + 774x24 + 834x23 - 26013x22 + 24482x21 + 438771x20 - 917742x19 - 3954764x18 + 12493773x17 + 17637390x16 - 89943576x15 - 16499340x14 + 367102377x13 - 183437513x12 - 838172511x11 + 827108970x10 + 967374964x9 - 1484013339x8 - 364627638x7 + 1223353523x6 - 171844968x5 - 419177382x4 + 123185675x3 + 52146132x2 - 17057376x - 1145024 \( 3^{36}\cdot 7^{18}\cdot 19^{18} \) $C_3^3$ (as 27T4) $[2, 2]$ (GRH)
27.3.45865537965996467420418831264009202586276600490849383813.1 x27 - 5x - 3 \( 17\cdot 359\cdot 5984861568115119773\cdot 1255709015602496871819754676848927 \) $S_{27}$ (as 27T2392) Trivial (GRH)
27.3.45866665066876460435700187354179628500729234048268894208.1 x27 - 5x - 2 \( 2^{27}\cdot 7\cdot 12805208083\cdot 398913576491\cdot 9557048364382464605843591 \) $S_{27}$ (as 27T2392) Trivial (GRH)
27.3.45866665096634307885773319761462230051750369380850107197.1 x27 - 5x - 1 \( 191\cdot 180797\cdot 135031817\cdot 9836406442864970501664393432790394942983 \) $S_{27}$ (as 27T2392) Trivial (GRH)
27.1.45866665096634308772626296247537769948249630619149892803.1 x27 + 5x - 1 \( -\,83\cdot 563\cdot 796853\cdot 1231778062127328031049100178271442365420402719 \) $S_{27}$ (as 27T2392) Trivial (GRH)
27.1.45867792227272149237980784744990797413723399509150616187.1 x27 + 5x - 3 \( -\,26784394391927\cdot 906908513152058455369\cdot 1888263188591623325749 \) $S_{27}$ (as 27T2392) Trivial (GRH)
27.1.47863680463851860855473749371874037931430553343164940288.1 x27 + 5x - 4 \( -\,2^{26}\cdot 23\cdot 4591\cdot 1054203587\cdot 40409162693929\cdot 158557479410628355703 \) $S_{27}$ (as 27T2392) Trivial (GRH)
27.1.73417444981913314280334795949102827452496728781547778643.1 x27 + 3x - 5 \( -\,3^{25}\cdot 41\cdot 181\cdot 3917\cdot 23593\cdot 985450601\cdot 128213533389611086945001 \) $S_{27}$ (as 27T2392) Trivial (GRH)
27.1.614890292796495532086888341869635692124068737030029296875.1 x27 - 5x - 5 \( -\,5^{26}\cdot 7\cdot 769\cdot 76657233947984763773781582607681381 \) $S_{27}$ (as 27T2392) Trivial (GRH)
27.1.660646059101739963744377659248723289832910846176228525291.1 x27 - 4x - 5 \( -\,75879359\cdot 6952540213\cdot 1353159565227731\cdot 925449390832864291185083 \) $S_{27}$ (as 27T2392) Trivial (GRH)

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