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Label Polynomial Discriminant Galois group Class group
18.0.571037074156239243011.1 x18 + 3x16 - 6x15 + 5x14 - 15x13 + 20x12 - 20x11 + 35x10 - 35x9 + 33x8 - 40x7 + 31x6 - 23x5 + 20x4 - 11x3 + 5x2 - 3x + 1 \( -\,23^{10}\cdot 13784339 \) 18T874 Trivial
18.10.1394653473478634087010304.1 x18 - 3x16 - 6x15 - 2x14 + 15x13 + 24x12 + 8x11 - 30x10 - 47x9 - 17x8 + 30x7 + 43x6 + 13x5 - 15x4 - 15x3 - 2x2 + 3x + 1 \( 2^{12}\cdot 37^{9}\cdot 2619937 \) 18T874 Trivial (GRH)
18.6.701843953894492563948261376.1 x18 + 3x16 - 6x15 - 2x14 - 15x13 + 6x12 + 8x11 + 30x10 + 7x9 - 7x8 - 30x7 - 11x6 + 3x5 + 15x4 + 3x3 - 2x2 - 3x + 1 \( 2^{12}\cdot 37^{9}\cdot 34807\cdot 37879 \) 18T874 Trivial (GRH)
18.14.19881090465606192610226262016.1 x18 - 15x16 - 6x15 + 88x14 + 75x13 - 240x12 - 352x11 + 228x10 + 745x9 + 263x8 - 606x7 - 683x6 - 87x5 + 303x4 + 249x3 + 88x2 + 15x + 1 \( 2^{12}\cdot 37^{9}\cdot 233\cdot 941\cdot 170341 \) 18T874 Trivial (GRH)
18.16.350896807924550394793668620288.1 x18 - 21x16 - 6x15 + 178x14 + 105x13 - 762x12 - 712x11 + 1626x10 + 2311x9 - 1151x8 - 3462x7 - 1247x6 + 1507x5 + 1731x4 + 771x3 + 178x2 + 21x + 1 \( -\,2^{12}\cdot 37^{9}\cdot 4799\cdot 137357761 \) 18T874 Trivial (GRH)
18.8.1757222112441619456947647290259.1 x18 - 8x16 - 6x15 + 11x14 + 40x13 + 31x12 - 44x11 - 115x10 - 68x9 + 76x8 + 150x7 + 67x6 - 54x5 - 75x4 - 22x3 + 11x2 + 8x + 1 \( -\,229^{9}\cdot 1014629111 \) 18T874 Trivial (GRH)
18.12.10225694911036350424496141344627.1 x18 - 14x16 - 6x15 + 66x14 + 70x13 - 113x12 - 264x11 - 62x10 + 364x9 + 434x8 - 16x7 - 406x6 - 302x5 + 8x4 + 122x3 + 66x2 + 14x + 1 \( -\,229^{9}\cdot 5904368983 \) 18T874 Trivial (GRH)
18.14.165902599539004537536552000000000.1 x18 - 3x17 - 24x16 + 28x15 + 282x14 + 126x13 - 1271x12 - 1818x11 + 456x10 + 553x9 - 2481x8 + 762x7 + 6836x6 + 3381x5 - 3087x4 - 2907x3 - 636x2 - 48x - 1 \( 2^{12}\cdot 3^{24}\cdot 5^{9}\cdot 79^{2}\cdot 149\cdot 281^{2} \) 18T874 Trivial (GRH)
18.18.185796054149506881407493212819456.1 x18 - 27x16 - 6x15 + 298x14 + 135x13 - 1704x12 - 1192x11 + 5190x10 + 5137x9 - 7257x8 - 10650x7 + 959x6 + 7853x5 + 5325x4 + 1713x3 + 298x2 + 27x + 1 \( 2^{12}\cdot 37^{9}\cdot 349028605296593 \) 18T874 Trivial (GRH)
18.10.2759811760383335787070730320809984.1 x18 - 3x17 - 12x16 + 2x15 + 30x14 + 72x13 + 77x12 - 24x11 + 144x10 + 199x9 - 417x8 - 54x7 + 688x6 - 387x5 - 747x4 + 429x3 + 492x2 - 21 \( 2^{12}\cdot 3^{21}\cdot 7^{10}\cdot 67\cdot 227^{2}\cdot 257^{2} \) 18T874 Trivial (GRH)
18.6.492055314924578283041666849832960000.1 x18 - 12x16 - 8x15 - 180x14 - 240x13 - 412x12 + 1512x11 - 1512x10 + 28352x9 - 19008x8 + 55968x7 - 59324x6 - 295920x5 - 149760x4 - 769280x3 - 403200x2 + 384000x - 25600 \( 2^{26}\cdot 3^{18}\cdot 5^{4}\cdot 37^{9}\cdot 233 \) 18T874 Trivial (GRH)
18.14.119896077691376921345726910546792000000000.1 x18 - 3x17 - 132x16 + 222x15 + 7479x14 - 1860x13 - 226799x12 - 273006x11 + 3594435x10 + 10055456x9 - 19549308x8 - 125806305x7 - 160347317x6 + 261301800x5 + 1510844220x4 + 3698753736x3 + 5719657296x2 + 5068342260x + 1914919780 \( 2^{12}\cdot 3^{24}\cdot 5^{9}\cdot 79^{2}\cdot 149\cdot 7554091^{2} \) 18T874 $[3]$ (GRH)
18.12.227214842256824958738151908292991724285952.1 x18 - 9x17 - 90x16 + 704x15 + 4725x14 - 21032x13 - 164531x12 + 177232x11 + 3317873x10 + 4709032x9 - 28617940x8 - 115852927x7 - 65900133x6 + 565616724x5 + 1823754372x4 + 2727089468x3 + 2288404092x2 + 1035235308x + 196195508 \( -\,2^{12}\cdot 37^{9}\cdot 139\cdot 89959^{2}\cdot 615997^{2} \) 18T874 $[3]$ (GRH)
18.12.1019443660108235620242452440038509695664128.1 x18 - 2x17 - 131x16 + 396x15 + 6435x14 - 28474x13 - 135655x12 + 949740x11 + 491516x10 - 15086532x9 + 26645874x8 + 86724264x7 - 390842556x6 + 310262532x5 + 1202258516x4 - 3689296500x3 + 4580574604x2 - 2812072848x + 698831764 \( -\,2^{16}\cdot 37^{9}\cdot 67^{2}\cdot 139\cdot 4999^{2}\cdot 87613^{2} \) 18T874 $[3]$ (GRH)
18.16.13204805800957263883631911003213434716160000.1 x18 - 186x16 - 124x15 + 13527x14 + 18036x13 - 500656x12 - 982368x11 + 10023315x10 + 25851304x9 - 103411782x8 - 343327668x7 + 427284889x6 + 2106458820x5 + 175340160x4 - 4295389120x3 - 1947556800x2 + 1854816000x - 123654400 \( -\,2^{24}\cdot 3^{18}\cdot 5^{4}\cdot 37^{9}\cdot 67\cdot 139^{4} \) 18T874 Trivial (GRH)
18.10.1015246136759185261931525913402896014260965376.1 x18 - 3x17 - 120x16 + 176x15 + 6219x14 + 1740x13 - 172753x12 - 355296x11 + 2354379x10 + 10209556x9 - 4482066x8 - 109929465x7 - 236404637x6 + 121228032x5 + 1585023144x4 + 3670192968x3 + 4492843728x2 + 3028832352x + 894791184 \( 2^{12}\cdot 3^{21}\cdot 7^{10}\cdot 11^{4}\cdot 67\cdot 487^{2}\cdot 600469^{2} \) 18T874 $[3]$ (GRH)
18.12.20524932102406811680483147938644837890889150464.1 x18 - 187x16 - 637x15 + 11530x14 + 69505x13 - 247265x12 - 2795555x11 - 1605105x10 + 48261988x9 + 142692310x8 - 231443086x7 - 1876953056x6 - 2556688578x5 + 5013215707x4 + 22086498934x3 + 32390759770x2 + 22594393249x + 6276416863 \( -\,2^{12}\cdot 37^{2}\cdot 43^{2}\cdot 101^{9}\cdot 179\cdot 100558321^{2} \) 18T874 $[3]$ (GRH)
18.0.68031822397385704323327440417682068561570555605549056.1 x18 - 666x16 - 836x15 - 5121x14 + 693540x13 + 78880376x12 - 120805560x11 - 11196401241x10 - 26465161176x9 - 1243428132186x8 + 10179941498940x7 + 426471361916601x6 - 1193247825135372x5 - 38890024289693124x4 + 79282594732523072x3 + 1276967763570965616x2 - 3861937353596896320x + 8332747069445731648 \( -\,2^{24}\cdot 3^{24}\cdot 11^{10}\cdot 862559^{4} \) 18T874 Trivial (GRH)
18.18.206965120322023780883776584258126018307696157475694936129536.1 x18 - 2826x16 - 1884x15 + 3191535x14 + 4255380x13 - 1889868432x12 - 3677605848x11 + 640037186847x10 + 1566545909384x9 - 126008992005570x8 - 348984105127020x7 + 13983683787376737x6 + 39378422425826340x5 - 809958483143306820x4 - 1982681218316985312x3 + 21225806692214506992x2 + 29997087058481564736x - 203877935399756689856 \( 2^{16}\cdot 3^{24}\cdot 37^{9}\cdot 179^{4}\cdot 1433\cdot 15551^{4} \) 18T874 Trivial (GRH)


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