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Results (displaying matches 1-50 of at least 1000) Next
| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 18.0.1102087125658583523206929858282481727.1 | x18 - 9x17 + 126x16 - 804x15 + 6660x14 - 33264x13 + 204504x12 - 828522x11 + 4088970x10 - 13554338x9 + 55596501x8 - 148974714x7 + 515548185x6 - 1074264939x5 + 3146390811x4 - 4653356364x3 + 11461225869x2 - 9291550797x + 18936946911 | \( -\,3^{44}\cdot 47^{9} \) | $C_{18}$ (as 18T1) | $[9, 139365]$ (GRH) |
| 18.0.2737570425013469092239722803000246272.1 | x18 + 99x16 + 4815x14 + 148083x12 + 3144492x10 - 2x9 + 47554038x8 + 954x7 + 510655881x6 - 47556x5 + 3750130377x4 + 482646x3 + 17095168548x2 - 838908x + 36926027009 | \( -\,2^{18}\cdot 3^{44}\cdot 13^{9} \) | $C_{18}$ (as 18T1) | $[1163474]$ (GRH) |
| 18.0.3387546805757652419012622474765664256.1 | x18 + 209x16 + 18392x14 + 885115x12 + 25314289x10 + 437575567x8 + 4443074988x6 + 24436912434x4 + 61092281085x2 + 44801006129 | \( -\,2^{18}\cdot 11^{9}\cdot 19^{17} \) | $C_{18}$ (as 18T1) | $[2, 2, 4, 75620]$ (GRH) |
| 18.0.5333686073828961010482481752887525376.1 | x18 + 108x16 + 5679x14 + 187740x12 + 4265379x10 - 2x9 + 68738148x8 + 1026x7 + 783654186x6 - 54738x5 + 6087814200x4 + 592092x3 + 29249550873x2 - 1092690x + 66331746447 | \( -\,2^{27}\cdot 3^{44}\cdot 7^{9} \) | $C_{18}$ (as 18T1) | $[9, 185364]$ (GRH) |
| 18.0.8531066207949676048491159248909849259.1 | x18 - 9x17 + 153x16 - 1020x15 + 10008x14 - 52920x13 + 380112x12 - 1636470x11 + 9357696x10 - 32934506x9 + 155739987x8 - 441398538x7 + 1756678785x6 - 3847455189x5 + 12957858630x4 - 19961087904x3 + 56678803083x2 - 47273111433x + 111738707823 | \( -\,3^{44}\cdot 59^{9} \) | $C_{18}$ (as 18T1) | $[4140423]$ (GRH) |
| 18.0.9748533507874859943721777394206605519.1 | x18 + 234x16 + 22815x14 + 1199562x12 + 36758007x10 - 327640x9 + 661644126x8 - 38333880x7 + 6689957274x6 - 1495021320x5 + 33884199180x4 - 21594752400x3 + 66074188401x2 - 84219534360x + 139161467719 | \( -\,3^{45}\cdot 53^{9} \) | $C_{18}$ (as 18T1) | $[2, 2, 2, 2, 2, 2, 2, 2, 8110]$ (GRH) |
| 18.0.10867175634578347994343560692370767872.1 | x18 + 87x16 - 8x15 + 4077x14 - 168x13 + 130959x12 + 10734x11 + 3060519x10 + 599534x9 + 52558377x8 + 13346178x7 + 650424667x6 + 161406414x5 + 5488830594x4 + 1059399976x3 + 28151284764x2 + 3006290520x + 65914946488 | \( -\,2^{18}\cdot 3^{24}\cdot 7^{12}\cdot 13^{9} \) | $C_6 \times C_3$ (as 18T2) | $[2, 2, 2, 18, 13338]$ (GRH) |
| 18.0.11682260499388589326243647883020829239.1 | x18 + 192x16 - x15 + 14310x14 - 195x13 + 542514x12 - 36945x11 + 11578902x10 - 2483709x9 + 146318868x8 - 75110319x7 + 1138108250x6 - 1005798375x5 + 5915118711x4 - 5625118235x3 + 22625119512x2 - 9990904116x + 55442113336 | \( -\,3^{27}\cdot 7^{15}\cdot 19^{9} \) | $C_6 \times C_3$ (as 18T2) | $[2, 4, 4, 103208]$ (GRH) |
| 18.0.13717212741604370463308637102507521799.1 | x18 - 6x17 + 165x16 - 734x15 + 11088x14 - 35448x13 + 395818x12 - 823572x11 + 8360469x10 - 9040888x9 + 116128899x8 - 40385748x7 + 1169457127x6 - 76884324x5 + 8399149179x4 - 863213550x3 + 34192143147x2 - 2336691090x + 64238725531 | \( -\,3^{27}\cdot 7^{12}\cdot 37^{9} \) | $C_6 \times C_3$ (as 18T2) | $[2, 18, 91656]$ (GRH) |
| 18.0.16001058221486883031447445258662576128.1 | x18 + 252x16 + 26460x14 + 1498224x12 + 49441392x10 + 958402368x8 + 10435936896x6 + 56923292160x4 + 119538913536x2 + 61983140352 | \( -\,2^{27}\cdot 3^{45}\cdot 7^{9} \) | $C_{18}$ (as 18T1) | $[2, 1472822]$ (GRH) |
| 18.0.18535932472341721596787579392000000000.1 | x18 + 210x16 + 17325x14 + 735000x12 + 17640000x10 + 248062500x8 + 2039625000x6 + 9405703125x4 + 21705468750x2 + 18087890625 | \( -\,2^{18}\cdot 3^{27}\cdot 5^{9}\cdot 7^{15} \) | $C_6 \times C_3$ (as 18T2) | $[2, 2, 2, 2, 2, 14, 5642]$ (GRH) |
| 18.0.19451929844843151808873875967466301627.1 | x18 - 3x17 + 135x16 - 397x15 + 8433x14 - 24849x13 + 317736x12 - 929568x11 + 7949448x10 - 22276859x9 + 136802574x8 - 340709811x7 + 1588480509x6 - 3151773927x5 + 11675224038x4 - 16134045101x3 + 49541028015x2 - 40252088898x + 105164497817 | \( -\,3^{24}\cdot 7^{15}\cdot 29^{9} \) | $C_6 \times C_3$ (as 18T2) | $[2, 18, 51948]$ (GRH) |
| 18.0.26792203422728825738155242257180552307.1 | x18 - 9x17 + 171x16 - 1164x15 + 12600x14 - 68544x13 + 539184x12 - 2394342x11 + 14927580x10 - 54191978x9 + 278675451x8 - 813324834x7 + 3515927145x6 - 7905023649x5 + 28924863876x4 - 45528034884x3 + 140699400039x2 - 119129457897x + 307625764301 | \( -\,3^{44}\cdot 67^{9} \) | $C_{18}$ (as 18T1) | $[2206717]$ (GRH) |
| 18.0.27668797159880354103659593728000000000.1 | x18 - 6x17 + 183x16 - 914x15 + 14145x14 - 58926x13 + 598896x12 - 2062338x11 + 15170424x10 - 42497460x9 + 238717983x8 - 530370468x7 + 2338835099x6 - 3934442502x5 + 14201203935x4 - 16785090334x3 + 54409682934x2 - 36356971812x + 95320292761 | \( -\,2^{27}\cdot 3^{27}\cdot 5^{9}\cdot 7^{12} \) | $C_6 \times C_3$ (as 18T2) | $[2, 2, 2, 2, 38, 3458]$ (GRH) |
| 18.0.30613671805187353870953069542862225408.1 | x18 + 135x16 + 8703x14 + 348039x12 + 9461124x10 - 2x9 + 180682038x8 + 1242x7 + 2419311081x6 - 79308x5 + 21883306869x4 + 1016694x3 + 121352263884x2 - 2203524x + 314709501201 | \( -\,2^{18}\cdot 3^{44}\cdot 17^{9} \) | $C_{18}$ (as 18T1) | $[2, 2, 1949868]$ (GRH) |
| 18.0.31239274635791169267446408746759536423.4 | x18 - 57x16 - 132x15 + 1674x14 + 6144x13 - 22610x12 - 158904x11 + 27669x10 + 1925200x9 + 3409803x8 - 11455716x7 - 37749104x6 + 56153808x5 + 521121744x4 + 1197861632x3 + 1296838656x2 + 671416320x + 134217728 | \( -\,3^{24}\cdot 7^{15}\cdot 13^{12} \) | $C_6 \times C_3$ (as 18T2) | $[7, 223041]$ (GRH) |
| 18.0.34087453954147523343197977587258425847.1 | x18 - 3x17 + 87x16 - 256x15 + 3117x14 - 8670x13 + 53789x12 - 105270x11 + 427959x10 - 112362x9 + 3866553x8 - 5879268x7 + 40584179x6 - 51988584x5 + 239214930x4 - 215794195x3 + 606840420x2 - 268220532x + 707555512 | \( -\,3^{24}\cdot 11^{9}\cdot 13^{15} \) | $C_6 \times C_3$ (as 18T2) | $[2, 36, 16380]$ (GRH) |
| 18.0.45150269416273000041555802844069788311.1 | x18 - 9x17 + 180x16 - 1236x15 + 14004x14 - 77112x13 + 632832x12 - 2848122x11 + 18488502x10 - 68032562x9 + 363852909x8 - 1075648194x7 + 4833747609x6 - 10993834143x5 + 41823565245x4 - 66458281248x3 + 213718242393x2 - 182157522921x + 490347077061 | \( -\,3^{44}\cdot 71^{9} \) | $C_{18}$ (as 18T1) | $[2, 3406662]$ (GRH) |
| 18.0.60058044833301692798474988224160989184.1 | x18 - 2x17 + 174x16 - 306x15 + 14120x14 - 21646x13 + 698247x12 - 919080x11 + 23121289x10 - 25526162x9 + 530650253x8 - 473795224x7 + 8430968114x6 - 5731976716x5 + 89361791435x4 - 41302878778x3 + 573297458501x2 - 135741604120x + 1696770051481 | \( -\,2^{18}\cdot 3^{9}\cdot 7^{9}\cdot 19^{16} \) | $C_{18}$ (as 18T1) | $[2, 2, 4, 568332]$ (GRH) |
| 18.0.65207117393079565410291669478441819083.1 | x18 + 234x16 - x15 + 21303x14 - 237x13 + 988554x12 - 60570x11 + 25847919x10 - 5091888x9 + 399193434x8 - 189463887x7 + 3750828353x6 - 3134543427x5 + 22666724232x4 - 22003449974x3 + 95124963726x2 - 50842837434x + 251122682539 | \( -\,3^{27}\cdot 7^{15}\cdot 23^{9} \) | $C_6 \times C_3$ (as 18T2) | $[2, 2, 26, 24206]$ (GRH) |
| 18.0.65241576375887238794986513680935682048.1 | x18 - 6x17 + 201x16 - 1010x15 + 17052x14 - 71736x13 + 791808x12 - 2760612x11 + 21979977x10 - 62431200x9 + 378327639x8 - 852307704x7 + 4043926949x6 - 6889678704x5 + 26626577955x4 - 31704369010x3 + 108873336285x2 - 72603966546x + 203458741597 | \( -\,2^{18}\cdot 3^{27}\cdot 7^{12}\cdot 11^{9} \) | $C_6 \times C_3$ (as 18T2) | $[2, 2, 2, 2, 36, 9828]$ (GRH) |
| 18.0.85141600462656403601383898181048991744.2 | x18 - 3x17 - 43x16 + 29x15 + 1049x14 + 1445x13 - 10513x12 - 31897x11 + 39670x10 + 406326x9 + 1397556x8 + 3675820x7 + 6943544x6 + 7108056x5 + 3205568x4 + 6357024x3 + 30682880x2 + 46538240x + 30224384 | \( -\,2^{18}\cdot 7^{12}\cdot 31^{15} \) | $S_3 \times C_6$ (as 18T6) | $[3, 3, 3, 38934]$ (GRH) |
| 18.0.106457240281657124613827288017419894784.1 | x18 - 9x17 + 183x16 - 1197x15 + 12952x14 - 66141x13 + 492684x12 - 2013565x11 + 11334053x10 - 35236854x9 + 157899241x8 - 312205750x7 + 1218166350x6 - 884685172x5 + 4598843440x4 + 907163984x3 + 8815673936x2 - 7949622416x + 5480201264 | \( -\,2^{18}\cdot 13^{2}\cdot 193^{4}\cdot 229^{9} \) | 18T782 | $[2, 2, 277500]$ (GRH) |
| 18.0.118026364303948717624477794198045747039.1 | x18 - 9x17 + 198x16 - 1380x15 + 17028x14 - 95760x13 + 850872x12 - 3920490x11 + 27457146x10 - 103473026x9 + 595838997x8 - 1802014938x7 + 8711912985x6 - 20223847899x5 + 82799864595x4 - 133810000764x3 + 463870664253x2 - 400059814653x + 1164793689863 | \( -\,3^{44}\cdot 79^{9} \) | $C_{18}$ (as 18T1) | $[4980185]$ (GRH) |
| 18.0.119025168578031262646195453952000000000.1 | x18 + 240x16 + 20700x14 + 871500x12 + 19687500x10 + 240975000x8 + 1508062500x6 + 4083750000x4 + 3206250000x2 + 421875000 | \( -\,2^{33}\cdot 3^{21}\cdot 5^{9}\cdot 7^{14} \) | $S_3 \times C_6$ (as 18T6) | $[2, 2, 2, 153406]$ (GRH) |
| 18.0.121525329645053177620052260620194807808.1 | x18 + 123x16 - 8x15 + 7677x14 - 264x13 + 314571x12 + 15918x11 + 9143631x10 + 1266502x9 + 192211413x8 + 37069122x7 + 2881098747x6 + 575805318x5 + 29298758262x4 + 4777613720x3 + 181053453228x2 + 16896372024x + 512126566568 | \( -\,2^{18}\cdot 3^{24}\cdot 7^{12}\cdot 17^{9} \) | $C_6 \times C_3$ (as 18T2) | $[2, 18, 18, 18, 468]$ (GRH) |
| 18.0.147303042689029667841882658956210597343.1 | x18 - x17 + 168x16 - 169x15 + 10480x14 - 10650x13 + 308310x12 - 300446x11 + 4450991x10 - 4301040x9 + 31097213x8 - 46920758x7 + 129371239x6 - 333953027x5 + 309774585x4 - 942303485x3 + 910645155x2 - 551296124x + 3387073609 | \( -\,19^{9}\cdot 37^{17} \) | $C_{18}$ (as 18T1) | $[1154174]$ (GRH) |
| 18.0.174259406310011076626476389857780739891.1 | x18 - 3x17 + 177x16 - 523x15 + 14229x14 - 42069x13 + 678152x12 - 1990740x11 + 21090282x10 - 59533211x9 + 443405220x8 - 1125215883x7 + 6227964435x6 - 12797520429x5 + 55287846336x4 - 79873197249x3 + 281667595275x2 - 233842540932x + 688036194091 | \( -\,3^{24}\cdot 7^{15}\cdot 37^{9} \) | $C_6 \times C_3$ (as 18T2) | $[38, 266, 532]$ (GRH) |
| 18.0.179124115636167311134377199898019495936.5 | x18 - 4x17 - 40x16 + 248x15 + 1161x14 - 9892x13 + 23362x12 + 72448x11 - 374940x10 + 317616x9 + 3876760x8 - 20356032x7 + 62210208x6 - 129573632x5 + 211472512x4 - 254183424x3 + 245058048x2 - 152907776x + 74063872 | \( -\,2^{18}\cdot 3^{9}\cdot 7^{14}\cdot 13^{15} \) | $S_3 \times C_6$ (as 18T6) | $[12, 86868]$ (GRH) |
| 18.0.233721825702929999566923221504000000000.1 | x18 + 185x16 + 12950x14 + 439375x12 + 7677500x10 + 69375000x8 + 323171875x6 + 725546875x4 + 621484375x2 + 72265625 | \( -\,2^{18}\cdot 5^{9}\cdot 37^{17} \) | $C_{18}$ (as 18T1) | $[2, 613928]$ (GRH) |
| 18.0.280655121419454569082411120580815224832.3 | x18 + 246x16 - 460x15 + 22707x14 - 56064x13 + 1082299x12 - 2735124x11 + 29051985x10 - 64909088x9 + 417136110x8 - 698258490x7 + 2860912354x6 - 2285780196x5 + 5662902273x4 + 10833272058x3 - 10099126569x2 + 5908781970x + 37617238057 | \( -\,2^{24}\cdot 3^{21}\cdot 7^{14}\cdot 11^{9} \) | $S_3 \times C_6$ (as 18T6) | $[3, 3, 18, 18, 1026]$ (GRH) |
| 18.0.311658701595221813593917258627482124288.1 | x18 + 180x16 + 15183x14 + 783204x12 + 27134019x10 - 2x9 + 653310108x8 + 1602x7 + 10917716106x6 - 130338x5 + 122042249064x4 + 2105724x3 + 828116450649x2 - 5692914x + 2600743873751 | \( -\,2^{27}\cdot 3^{44}\cdot 11^{9} \) | $C_{18}$ (as 18T1) | $[8732666]$ (GRH) |
| 18.0.421561400235330951371150243189110960128.1 | x18 - 9x17 + 204x16 - 1310x15 + 15900x14 - 72270x13 + 579766x12 - 1932168x11 + 10057503x10 - 26756821x9 + 84214434x8 - 179179878x7 + 372512932x6 - 539106924x5 + 4016812476x4 - 7029585108x3 + 46526330856x2 - 69223313904x + 93654474472 | \( -\,2^{12}\cdot 3^{21}\cdot 7^{14}\cdot 29^{9} \) | $S_3 \times C_6$ (as 18T6) | $[2, 2, 2, 18, 18, 1890]$ (GRH) |
| 18.0.540917700754627690421790767951711121408.1 | x18 - 9x17 + 99x16 - 572x15 + 4272x14 - 20712x13 + 124098x12 - 504282x11 + 2517105x10 - 8744095x9 + 37842855x8 - 111524946x7 + 414527356x6 - 998800626x5 + 3196420548x4 - 6011436698x3 + 15888370065x2 - 18328267323x + 33569437537 | \( -\,2^{12}\cdot 3^{18}\cdot 7^{14}\cdot 43^{9} \) | $S_3 \times C_6$ (as 18T6) | $[4, 527148]$ (GRH) |
| 18.0.822204469544577674838182026941616159571.1 | x18 - x17 + 205x16 - 206x15 + 15660x14 - 15867x13 + 567199x12 - 549752x11 + 10183475x10 - 9611761x9 + 89713575x8 - 122956128x7 + 446565912x6 - 1040646774x5 + 1226326338x4 - 3721651392x3 + 3392343195x2 - 3279342495x + 13375615217 | \( -\,23^{9}\cdot 37^{17} \) | $C_{18}$ (as 18T1) | $[2, 4, 276860]$ (GRH) |
| 18.0.975976429792931978524482994492749082624.1 | x18 - 7x17 + 66x16 - 290x15 + 1875x14 - 7347x13 + 41454x12 - 152011x11 + 715866x10 - 2313995x9 + 8987378x8 - 24753343x7 + 78686738x6 - 175507995x5 + 442941691x4 - 728414092x3 + 1370146814x2 - 1302399605x + 1581654073 | \( -\,2^{12}\cdot 31^{9}\cdot 37^{14} \) | $S_3 \times C_6$ (as 18T6) | $[2, 2, 6, 6, 8532]$ (GRH) |
| 18.0.1084205756727498980519837945309853646848.1 | x18 - 6x17 + 174x16 - 866x15 + 11382x14 - 46410x13 + 331962x12 - 1061466x11 + 4133913x10 - 9597594x9 + 31604088x8 - 62180514x7 + 165055169x6 - 244964646x5 + 562163766x4 - 638296924x3 + 1429338096x2 - 994714992x + 1562155624 | \( -\,2^{18}\cdot 3^{9}\cdot 7^{12}\cdot 19^{15} \) | $C_6 \times C_3$ (as 18T2) | $[2, 2, 2, 2, 14, 6734]$ (GRH) |
| 18.0.1205953284095546800596778947408883089408.1 | x18 + 222x16 + 18648x14 + 759240x12 + 15920064x10 + 172627200x8 + 964986048x6 + 2599765632x4 + 2672269056x2 + 372874752 | \( -\,2^{27}\cdot 3^{9}\cdot 37^{17} \) | $C_{18}$ (as 18T1) | $[2, 1402002]$ (GRH) |
| 18.0.1253868809453171177940640399286136471552.1 | x18 + 273x16 + 26208x14 + 1142505x12 + 26159679x10 + 336051261x8 + 2456997543x6 + 9888358662x4 + 19776717324x2 + 14832537993 | \( -\,2^{18}\cdot 3^{9}\cdot 7^{15}\cdot 13^{15} \) | $C_6 \times C_3$ (as 18T2) | $[2, 2, 2, 2, 2, 2, 2, 14, 3458]$ (GRH) |
| 18.0.1598763077775622674562101105291264000000.1 | x18 - 9x17 + 48x16 - 156x15 + 2478x14 - 25134x13 + 162220x12 - 616548x11 + 1597149x10 - 2510485x9 + 2463540x8 - 753984x7 + 1476580x6 - 2969220x5 + 2376000x4 + 8830864x3 - 3165888x2 - 7825920x + 4077568 | \( -\,2^{18}\cdot 3^{27}\cdot 5^{6}\cdot 13^{15} \) | $S_3 \times C_6$ (as 18T6) | $[2, 2, 2, 391092]$ (GRH) |
| 18.0.1603371662107021018978486840742329188352.1 | x18 - 2x17 + 92x16 - 186x15 + 4421x14 - 7220x13 + 141003x12 - 156556x11 + 3197563x10 - 1924606x9 + 52668918x8 - 9253226x7 + 622617494x6 + 75541038x5 + 5024127315x4 + 1294777734x3 + 24679661181x2 + 5368141552x + 54985356817 | \( -\,2^{24}\cdot 13^{9}\cdot 37^{14} \) | $S_3 \times C_6$ (as 18T6) | $[2, 2, 2, 196664]$ (GRH) |
| 18.0.1724925183796757382490845609984000000000.1 | x18 - 6x17 + 63x16 - 284x15 + 2382x14 - 8964x13 + 66460x12 - 209784x11 + 1383909x10 - 3584354x9 + 21853467x8 - 44268360x7 + 254826777x6 - 377964774x5 + 2043736503x4 - 2009879192x3 + 9908381091x2 - 4973847282x + 21442432211 | \( -\,2^{27}\cdot 3^{24}\cdot 5^{9}\cdot 13^{12} \) | $C_6 \times C_3$ (as 18T2) | $[2, 2, 2, 126, 2646]$ (GRH) |
| 18.0.1829454323323333626595491241240421203968.1 | x18 - 108x16 + 5247x14 - 143388x12 + 2370627x10 - 11662x9 - 23508324x8 + 1574370x7 + 135435594x6 - 52164126x5 - 366226488x4 + 539274204x3 + 798965721x2 - 1323415422x + 4642192563 | \( -\,2^{27}\cdot 3^{44}\cdot 7^{12} \) | $C_{18}$ (as 18T1) | $[3, 425907]$ (GRH) |
| 18.0.1879387730226102112759375150760179531776.1 | x18 - 6x17 + 117x16 - 578x15 + 6156x14 - 24564x13 + 180572x12 - 588492x11 + 3260457x10 - 8367384x9 + 38364819x8 - 74876916x7 + 289649625x6 - 402034464x5 + 1622202279x4 - 656223070x3 + 7631428449x2 + 1517303154x + 14079582973 | \( -\,2^{18}\cdot 3^{27}\cdot 7^{9}\cdot 13^{12} \) | $C_6 \times C_3$ (as 18T2) | $[2, 2, 2, 2, 8, 22568]$ (GRH) |
| 18.0.2471908731721405920557482056194302734375.1 | x18 - 3x17 - 90x16 + 105x15 + 4146x14 + 3969x13 - 66495x12 - 104844x11 + 645948x10 + 1440664x9 - 394080x8 - 17911008x7 + 10282368x6 + 42470400x5 + 17473536x4 + 29097984x3 + 767557632x2 + 905969664x + 1073741824 | \( -\,3^{31}\cdot 5^{9}\cdot 7^{12}\cdot 23^{6} \) | $S_3 \times C_6$ (as 18T6) | $[6, 6, 63270]$ (GRH) |
| 18.0.2909353438387945911099105025784000000000.1 | x18 - 7x17 + 75x16 - 346x15 + 2471x14 - 9925x13 + 59557x12 - 219953x11 + 1098634x10 - 3586552x9 + 14782497x8 - 41171933x7 + 138893691x6 - 313467091x5 + 842632363x4 - 1401562361x3 + 2837225215x2 - 2720012338x + 3659949451 | \( -\,2^{12}\cdot 5^{9}\cdot 7^{9}\cdot 37^{14} \) | $S_3 \times C_6$ (as 18T6) | $[2, 2, 6, 88578]$ (GRH) |
| 18.0.3123894467595344662196894875152879190016.1 | x18 - 2x17 + 101x16 - 202x15 + 5245x14 - 8562x13 + 178994x12 - 203038x11 + 4318608x10 - 2774640x9 + 75342043x8 - 16921424x7 + 940014547x6 + 68658878x5 + 7988920261x4 + 1747923682x3 + 41322035770x2 + 8074688936x + 97158937289 | \( -\,2^{33}\cdot 7^{9}\cdot 37^{14} \) | $S_3 \times C_6$ (as 18T6) | $[2, 2, 753844]$ (GRH) |
| 18.0.3676774411522871683138204076633580896256.2 | x18 + 126x16 + 6615x14 + 187278x12 + 3090087x10 + 29950074x8 + 163061514x6 + 444713220x4 + 466948881x2 + 107354541 | \( -\,2^{18}\cdot 3^{45}\cdot 7^{15} \) | $C_{18}$ (as 18T1) | $[2, 604086]$ (GRH) |
| 18.0.4575727330315213559892705312768000000000.1 | x18 - 6x17 + 12x16 - 102x15 + 597x14 - 264x13 + 11127x12 + 2220x11 + 139035x10 + 135622x9 + 1595346x8 + 2445570x7 + 13116918x6 + 19084950x5 + 64200627x4 + 70378146x3 + 164145177x2 + 100403604x + 163257381 | \( -\,2^{24}\cdot 3^{30}\cdot 5^{9}\cdot 7^{14} \) | $S_3 \times C_6$ (as 18T6) | $[6, 6, 6, 12, 756]$ (GRH) |
| 18.0.4664905028044379350971453203047862914143.1 | x18 - 3x17 + 165x16 - 490x15 + 10839x14 - 30510x13 + 345457x12 - 776070x11 + 5556303x10 - 6413124x9 + 64492053x8 - 64188012x7 + 669977697x6 - 651424590x5 + 5007118512x4 - 3879890761x3 + 19161182850x2 - 7873833456x + 31296928456 | \( -\,3^{24}\cdot 13^{15}\cdot 19^{9} \) | $C_6 \times C_3$ (as 18T2) | $[6, 108, 9828]$ (GRH) |
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