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Label Polynomial Discriminant Galois group Class group
18.0.168...552.1 x18 - 4x17 + 8x16 - 11x15 + 16x14 - 20x13 + 14x12 - 8x10 + 13x9 - 20x8 + 18x7 - 2x6 - 14x5 + 20x4 - 17x3 + 10x2 - 4x + 1 \( -\,2^{12}\cdot 3^{9}\cdot 7^{6}\cdot 11^{6} \) $C_3\times S_3^2$ (as 18T46) trivial
18.0.137...747.1 x18 - x17 + x16 + 2x15 - 9x14 + 6x13 + 3x12 - 21x11 + 32x10 - 24x9 + 14x8 - 5x7 + 13x6 - 14x5 + 6x4 - 3x3 - x2 + 1 \( -\,3^{9}\cdot 19^{6}\cdot 23^{6} \) $C_3\times S_3^2$ (as 18T46) trivial
18.0.494...968.1 x18 - 3x17 + 7x16 - 9x15 + 6x14 + 4x13 + 11x12 - 54x11 + 121x10 - 152x9 + 100x8 + 14x7 - 89x6 + 83x5 - 4x4 - 50x3 + 36x2 - 10x + 1 \( -\,2^{12}\cdot 3^{9}\cdot 19^{10} \) $C_3\times S_3^2$ (as 18T46) trivial
18.0.316...952.1 x18 - 4x17 + 20x15 - 29x14 + 37x13 - 145x12 + 234x11 + 137x10 - 1107x9 + 2430x8 - 4388x7 + 7497x6 - 10621x5 + 11285x4 - 8627x3 + 4555x2 - 1479x + 223 \( -\,2^{18}\cdot 3^{9}\cdot 19^{10} \) $C_3\times S_3^2$ (as 18T46) trivial (GRH)
18.0.414...208.1 x18 - 3x17 - 6x16 + 27x15 + 18x14 - 129x13 - 3x12 + 354x11 - 162x10 - 464x9 + 426x8 + 150x7 - 390x6 + 252x5 + 84x4 - 216x3 + 132x2 - 36x + 4 \( -\,2^{26}\cdot 3^{31} \) $C_3\times S_3^2$ (as 18T46) trivial
18.6.490...000.1 x18 - 2x17 - 6x16 + 17x15 + 30x14 - 76x13 - 72x12 + 210x11 + 106x10 - 303x9 - 118x8 + 262x7 + 102x6 - 142x5 - 68x4 + 25x3 + 16x2 - 1 \( 2^{12}\cdot 5^{9}\cdot 19^{10} \) $C_3\times S_3^2$ (as 18T46) trivial
18.0.182...088.1 x18 - 7x17 + 23x16 - 58x15 + 132x14 - 232x13 + 286x12 - 260x11 + 147x10 + 123x9 - 425x8 + 390x7 - 314x5 + 322x4 - 174x3 + 57x2 - 11x + 1 \( -\,2^{26}\cdot 3^{9}\cdot 13^{10} \) $C_3\times S_3^2$ (as 18T46) trivial
18.0.297...888.1 x18 - 9x17 + 42x16 - 129x15 + 264x14 - 324x13 + 126x12 + 369x11 - 819x10 + 711x9 + 162x8 - 1215x7 + 1608x6 - 1269x5 + 729x4 - 333x3 + 117x2 - 27x + 3 \( -\,2^{12}\cdot 3^{31}\cdot 7^{6} \) $C_3\times S_3^2$ (as 18T46) trivial
18.0.355...000.1 x18 - 3x17 + 15x16 - 18x15 + 33x14 - 21x13 + 75x12 + 69x11 + 132x10 + 214x9 + 309x8 + 507x7 + 567x6 + 543x5 + 381x4 + 195x3 + 75x2 + 12x + 1 \( -\,2^{12}\cdot 3^{33}\cdot 5^{6} \) $C_3\times S_3^2$ (as 18T46) trivial
18.0.387...232.1 x18 - 3x17 + x16 + 9x15 - 22x14 - 20x13 + 45x12 + 16x11 + 73x10 + 70x9 + 20x8 + 50x7 + 25x6 + 23x5 + 122x4 + 138x3 + 68x2 + 14x + 1 \( -\,2^{12}\cdot 3^{9}\cdot 37^{10} \) $C_3\times S_3^2$ (as 18T46) trivial
18.6.666...000.1 x18 - 2x17 + 10x16 - 15x15 + 26x14 - 34x13 - 10x12 + 14x11 - 112x10 + 111x9 - 70x8 + 88x7 + 28x6 + 10x5 + 16x4 - 19x3 - 8x2 - 4x - 1 \( 2^{12}\cdot 5^{9}\cdot 11^{6}\cdot 19^{6} \) $C_3\times S_3^2$ (as 18T46) trivial (GRH)
18.0.138...000.1 x18 - 4x17 + 5x16 - 16x15 + 69x14 - 82x13 - 86x12 + 196x11 + 72x10 - 294x9 + 127x8 - 204x7 + 759x6 - 1052x5 + 769x4 - 336x3 + 90x2 - 14x + 1 \( -\,2^{12}\cdot 3^{9}\cdot 5^{14}\cdot 7^{10} \) $C_3\times S_3^2$ (as 18T46) $[3]$ (GRH)
18.0.303...000.1 x18 - 2x17 + 8x16 - x15 + 58x14 - 55x13 + 123x12 + 9x11 + 70x10 - 12x9 + 49x8 + 204x7 + 37x6 + 175x5 + 118x4 + 90x3 + 264x2 + 208x + 64 \( -\,2^{18}\cdot 5^{12}\cdot 7^{15} \) $C_3\times S_3^2$ (as 18T46) $[18]$ (GRH)
18.0.714...088.1 x18 - 3x17 - 6x16 + 3x15 + 90x14 - 66x13 - 198x12 - 231x11 + 891x10 + 55x9 - 276x8 - 1461x7 + 2190x6 - 1323x5 + 21x4 - 2289x3 + 3759x2 - 1449x + 1393 \( -\,2^{12}\cdot 3^{31}\cdot 7^{10} \) $C_3\times S_3^2$ (as 18T46) $[3]$ (GRH)
18.0.781...712.1 x18 + 6x16 - 24x15 - 72x14 + 132x13 + 774x12 + 828x11 - 102x10 - 416x9 - 324x8 - 1752x7 - 1515x6 + 1476x5 + 1632x4 - 576x3 - 288x2 + 192x + 64 \( -\,2^{18}\cdot 3^{31}\cdot 13^{6} \) $C_3\times S_3^2$ (as 18T46) trivial (GRH)
18.18.965...000.1 x18 - 2x17 - 22x16 + 35x15 + 174x14 - 218x13 - 650x12 + 630x11 + 1268x10 - 931x9 - 1322x8 + 732x7 + 728x6 - 302x5 - 200x4 + 59x3 + 24x2 - 4x - 1 \( 2^{12}\cdot 5^{9}\cdot 19^{6}\cdot 37^{6} \) $C_3\times S_3^2$ (as 18T46) trivial (GRH)
18.0.360...312.1 x18 - 6x17 + 15x16 + 21x15 - 189x14 + 447x13 - 277x12 - 819x11 + 2771x10 - 6116x9 + 8916x8 - 5025x7 + 13003x6 - 24345x5 + 9437x4 - 22214x3 + 36967x2 + 19033x + 93919 \( -\,2^{12}\cdot 3^{9}\cdot 7^{6}\cdot 11^{14} \) $C_3\times S_3^2$ (as 18T46) $[3]$ (GRH)
18.0.650...928.1 x18 - 25x15 + 252x12 - 1245x9 + 2786x6 - 1715x3 + 343 \( -\,2^{12}\cdot 3^{27}\cdot 7^{6}\cdot 11^{6} \) $C_3\times S_3^2$ (as 18T46) $[3]$ (GRH)
18.0.214...112.1 x18 - 6x17 + 3x16 + 36x15 - 72x14 + 24x13 + 677x12 - 2154x11 + 650x10 - 12520x9 + 93111x8 - 184794x7 + 51751x6 + 253950x5 - 276628x4 - 32494x3 + 217588x2 - 143080x + 34300 \( -\,2^{26}\cdot 3^{9}\cdot 7^{6}\cdot 13^{10} \) $C_3\times S_3^2$ (as 18T46) $[3]$ (GRH)
18.0.376...192.1 x18 - 5x16 - 16x15 - 20x14 + 152x13 + 370x12 + 32x11 - 2786x10 - 3960x9 + 13300x8 + 14472x7 - 12096x6 - 79632x5 + 22194x4 + 192240x3 - 108675x2 - 139320x + 106677 \( -\,2^{20}\cdot 3^{9}\cdot 67^{10} \) $C_3\times S_3^2$ (as 18T46) $[3]$ (GRH)
18.0.457...632.1 x18 - 3x17 + 21x16 - 42x15 + 189x14 - 237x13 + 963x12 - 438x11 + 3060x10 + 1234x9 + 7878x8 + 8448x7 + 16185x6 + 21609x5 + 25599x4 + 24864x3 + 19005x2 + 10773x + 2779 \( -\,2^{18}\cdot 3^{31}\cdot 7^{10} \) $C_3\times S_3^2$ (as 18T46) trivial (GRH)
18.0.137...000.1 x18 - 5x15 + 76x12 - 715x9 + 2632x6 - 1785x3 + 343 \( -\,2^{12}\cdot 3^{27}\cdot 5^{6}\cdot 7^{10} \) $C_3\times S_3^2$ (as 18T46) $[3]$ (GRH)
18.0.182...528.1 x18 - 6x17 + 6x16 + 78x15 - 48x14 - 720x13 + 27x12 + 3312x11 + 2754x10 - 7740x9 - 13158x8 - 5742x7 + 11037x6 + 43218x5 + 76230x4 + 77742x3 + 51030x2 + 21546x + 5061 \( -\,2^{20}\cdot 3^{31}\cdot 7^{10} \) $C_3\times S_3^2$ (as 18T46) $[3, 3]$ (GRH)
18.0.191...352.1 x18 - 5x15 + 40x12 + x9 + 608x6 + 3819x3 + 6859 \( -\,2^{12}\cdot 3^{27}\cdot 19^{10} \) $C_3\times S_3^2$ (as 18T46) $[3]$ (GRH)
18.0.195...008.1 x18 - 3x17 - 21x16 + 54x15 + 228x14 - 504x13 - 1012x12 + 2040x11 + 4523x10 - 6703x9 - 1497x8 + 252x7 + 34702x6 - 21324x5 + 57104x4 - 90118x3 + 127507x2 + 22997x + 160003 \( -\,2^{20}\cdot 3^{9}\cdot 79^{10} \) $C_3\times S_3^2$ (as 18T46) $[3]$ (GRH)
18.0.200...152.1 x18 - 3x17 - 25x16 + 97x15 + 324x14 - 1424x13 - 2893x12 + 12134x11 + 25059x10 - 36958x9 - 87068x8 + 95416x7 + 313237x6 + 151945x5 - 220562x4 - 362142x3 - 140268x2 + 158994x + 138087 \( -\,2^{18}\cdot 3^{9}\cdot 7^{10}\cdot 13^{10} \) $C_3\times S_3^2$ (as 18T46) trivial (GRH)
18.0.200...152.2 x18 - 3x17 + 10x16 - 9x15 - 7x14 + 118x13 + 42x12 - 536x11 + 2032x10 - 3800x9 + 4088x8 + 1616x7 - 9680x6 + 16256x5 - 2176x4 - 33024x3 + 44288x2 - 22528x + 4096 \( -\,2^{18}\cdot 3^{9}\cdot 7^{10}\cdot 13^{10} \) $C_3\times S_3^2$ (as 18T46) trivial (GRH)
18.0.204...368.1 x18 - 3x17 + 9x16 - 57x15 + 143x14 - 3x13 + 1674x12 + 1233x11 + 5724x10 + 2007x9 + 10875x8 + 1305x7 + 10340x6 + 858x5 + 5358x4 + 381x3 + 1558x2 + 165x + 183 \( -\,2^{12}\cdot 3^{9}\cdot 7^{6}\cdot 43^{10} \) $C_3\times S_3^2$ (as 18T46) $[3]$ (GRH)
18.0.217...368.1 x18 + 11x16 - 18x15 + 68x14 + 70x13 + 533x12 + 1100x11 + 580x10 + 7210x9 + 16613x8 + 59948x7 + 60667x6 + 137522x5 + 142906x4 + 494826x3 + 675168x2 - 1634408x + 1185076 \( -\,2^{12}\cdot 3^{9}\cdot 139^{10} \) $C_3\times S_3^2$ (as 18T46) $[3, 3]$ (GRH)
18.0.275...672.1 x18 - 8x15 + 43x12 - 148x9 + 559x6 + 2652x3 + 2197 \( -\,2^{18}\cdot 3^{27}\cdot 13^{10} \) $C_3\times S_3^2$ (as 18T46) trivial (GRH)
18.0.520...152.1 x18 - 30x15 + 360x12 - 1672x9 + 6720x6 - 6048x3 + 21952 \( -\,2^{12}\cdot 3^{37}\cdot 7^{10} \) $C_3\times S_3^2$ (as 18T46) $[3]$ (GRH)
18.0.520...152.2 x18 - 12x15 + 87x12 - 848x9 + 7392x6 - 18816x3 + 21952 \( -\,2^{12}\cdot 3^{37}\cdot 7^{10} \) $C_3\times S_3^2$ (as 18T46) $[3]$ (GRH)
18.0.569...048.2 x18 - 57x15 + 954x12 - 3931x9 + 6396x6 - 4563x3 + 2197 \( -\,2^{18}\cdot 3^{37}\cdot 13^{6} \) $C_3\times S_3^2$ (as 18T46) trivial (GRH)
18.0.143...392.1 x18 - 9x17 + 63x16 - 279x15 + 1026x14 - 3024x13 + 8037x12 - 18900x11 + 38367x10 - 63180x9 + 86670x8 - 99792x7 + 70551x6 + 84807x5 - 319788x4 + 302292x3 + 122472x2 - 418446x + 226233 \( -\,2^{12}\cdot 3^{31}\cdot 7^{6}\cdot 13^{6} \) $C_3\times S_3^2$ (as 18T46) $[3]$ (GRH)
18.0.297...003.1 x18 - 6x17 + 39x16 - 150x15 + 669x14 - 1584x13 + 4191x12 - 10746x11 + 16053x10 - 31018x9 + 54399x8 - 57408x7 + 104028x6 - 119904x5 + 49968x4 - 132864x3 + 112896x2 + 43008x + 4096 \( -\,3^{31}\cdot 37^{10} \) $C_3\times S_3^2$ (as 18T46) $[3]$ (GRH)
18.18.445...000.1 x18 - 42x16 - 6x15 + 621x14 + 174x13 - 4243x12 - 1224x11 + 14907x10 + 2716x9 - 27504x8 - 90x7 + 24358x6 - 4302x5 - 7317x4 + 1174x3 + 657x2 + 42x - 1 \( 2^{33}\cdot 3^{24}\cdot 5^{6}\cdot 7^{6} \) $C_3\times S_3^2$ (as 18T46) trivial (GRH)
18.0.521...000.1 x18 - 9x17 + 33x16 - 27x15 - 189x14 + 717x13 - 1142x12 + 597x11 + 1758x10 - 7263x9 + 16119x8 - 23991x7 + 28780x6 - 25590x5 + 9324x4 - 4725x3 + 8820x2 + 17199x + 9261 \( -\,2^{12}\cdot 3^{9}\cdot 5^{6}\cdot 7^{6}\cdot 181^{6} \) $C_3\times S_3^2$ (as 18T46) trivial (GRH)
18.0.563...448.1 x18 - 3x17 - 2x16 + 27x15 - 63x14 - 182x13 + 326x12 + 24x11 + 1072x10 + 3160x9 + 1576x8 + 3344x7 + 7792x6 + 7808x5 + 30080x4 + 60160x3 + 60672x2 + 26624x + 4096 \( -\,2^{18}\cdot 3^{9}\cdot 127^{10} \) $C_3\times S_3^2$ (as 18T46) $[2]$ (GRH)
18.0.753...968.1 x18 - 2x17 + 3x16 - 58x15 + 197x14 - 42x13 - 644x12 + 370x11 + 2172x10 - 4392x9 + 3635x8 - 2080x7 + 1995x6 - 2114x5 + 1387x4 - 534x3 + 122x2 - 16x + 1 \( -\,2^{12}\cdot 3^{9}\cdot 7^{14}\cdot 13^{10} \) $C_3\times S_3^2$ (as 18T46) $[3, 3]$ (GRH)
18.0.101...083.1 x18 - 3x17 - 27x16 + 54x15 + 354x14 - 426x13 - 2956x12 + 1716x11 + 18452x10 + 7658x9 - 32814x8 - 114078x7 + 30115x6 + 394695x5 + 97727x4 - 771736x3 + 26068x2 + 309680x + 134848 \( -\,3^{9}\cdot 7^{10}\cdot 67^{10} \) $C_3\times S_3^2$ (as 18T46) $[9]$ (GRH)
18.0.122...528.1 x18 - 16x15 + 649x12 + 5872x9 + 19627x6 - 1824x3 + 6859 \( -\,2^{18}\cdot 3^{27}\cdot 19^{10} \) $C_3\times S_3^2$ (as 18T46) $[3]$ (GRH)
18.0.186...032.1 x18 - 2x17 + 16x16 - 114x15 + 486x14 - 1617x13 + 5983x12 - 21824x11 + 61120x10 - 124458x9 + 193737x8 - 252336x7 + 307981x6 - 344420x5 + 321958x4 - 236085x3 + 139299x2 - 130761x + 126963 \( -\,2^{12}\cdot 3^{9}\cdot 7^{10}\cdot 31^{10} \) $C_3\times S_3^2$ (as 18T46) $[3]$ (GRH)
18.0.517...288.1 x18 - 6x17 + 24x16 - 78x15 + 216x14 - 714x13 + 2135x12 - 5022x11 + 7298x10 - 686x9 - 15438x8 + 30174x7 + 19897x6 - 100260x5 + 3110x4 + 71956x3 + 25906x2 + 1900x + 703 \( -\,2^{26}\cdot 3^{9}\cdot 19^{6}\cdot 97^{6} \) $C_3\times S_3^2$ (as 18T46) $[3]$ (GRH)
18.0.683...848.1 x18 - 6x17 + 7x16 + 5x15 - 123x14 + 2007x13 - 10303x12 + 16857x11 + 45543x10 - 311864x9 + 844354x8 - 1438355x7 + 1685627x6 - 1365187x5 + 739367x4 - 280422x3 + 121521x2 - 68391x + 19363 \( -\,2^{18}\cdot 3^{9}\cdot 163^{10} \) $C_3\times S_3^2$ (as 18T46) $[2]$ (GRH)
18.0.761...000.1 x18 - 6x16 - 12x15 - 45x14 - 48x13 + 660x12 + 6267x10 - 1024x9 + 19710x8 - 9060x7 + 11553x6 - 13680x5 - 65244x4 + 29136x3 - 73008x2 + 32448x + 140608 \( -\,2^{26}\cdot 3^{31}\cdot 5^{6}\cdot 7^{6} \) $C_3\times S_3^2$ (as 18T46) $[3, 3]$ (GRH)
18.0.126...512.1 x18 - 6x17 + 26x16 - 82x15 + 172x14 - 156x13 - 2102x12 + 10416x11 - 12604x10 - 17892x9 + 56416x8 - 53392x7 + 52964x6 - 115936x5 + 291840x4 - 625664x3 + 892928x2 - 655360x + 262144 \( -\,2^{20}\cdot 3^{9}\cdot 7^{6}\cdot 13^{6}\cdot 47^{6} \) $C_3\times S_3^2$ (as 18T46) $[3]$ (GRH)
18.0.127...408.1 x18 - 3x17 + 10x16 + 91x15 + 151x14 + 34x13 + 3415x12 + 14395x11 + 29125x10 - 21192x9 - 97073x8 - 90513x7 + 153009x6 + 344700x5 - 49059x4 - 421497x3 - 92718x2 + 222021x + 111051 \( -\,2^{20}\cdot 3^{9}\cdot 151^{10} \) $C_3\times S_3^2$ (as 18T46) trivial (GRH)
18.0.150...448.1 x18 - 7x15 + 226x12 + 445x9 + 7252x6 + 17427x3 + 50653 \( -\,2^{12}\cdot 3^{27}\cdot 37^{10} \) $C_3\times S_3^2$ (as 18T46) $[3]$ (GRH)
18.0.154...000.1 x18 - 11x16 - 75x15 + 321x14 + 147x13 + 641x12 - 11589x11 + 15447x10 + 30186x9 - 55196x8 - 52869x7 + 188785x6 + 172251x5 + 49959x4 + 210708x3 + 285795x2 + 30537x + 1161 \( -\,2^{12}\cdot 3^{9}\cdot 5^{6}\cdot 13^{10}\cdot 31^{6} \) $C_3\times S_3^2$ (as 18T46) $[3]$ (GRH)
18.0.172...168.1 x18 - 3x17 - 5x16 + 51x15 - 122x14 - 612x13 + 1167x12 - 306x11 + 4617x10 + 27540x9 + 20628x8 + 39366x7 + 164835x6 + 227691x5 + 857304x4 + 2226366x3 + 3332988x2 + 2243862x + 531441 \( -\,2^{12}\cdot 3^{9}\cdot 271^{10} \) $C_3\times S_3^2$ (as 18T46) trivial (GRH)
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