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Results (displaying matches 1-50 of at least 1000) Next
| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 18.0.55229672715150469850028716544000000000.1 | x18 + 285x16 + 34200x14 + 2244375x12 + 87530625x10 + 2063221875x8 + 28567687500x6 + 214257656250x4 + 730423828125x2 + 730423828125 | \( -\,2^{18}\cdot 3^{9}\cdot 5^{9}\cdot 19^{17} \) | $C_{18}$ (as 18T1) | $[2, 2, 2617972]$ (GRH) |
| 18.0.184093323834250344728515453895309591043.1 | x18 - 9x17 + 207x16 - 1452x15 + 18648x14 - 105840x13 + 976272x12 - 4545126x11 + 32991876x10 - 125652506x9 + 749248587x8 - 2289051090x7 + 11455485945x6 - 26836628409x5 + 113757248880x4 - 185230785420x3 + 665351396991x2 - 576856453545x + 1743009516489 | \( -\,3^{44}\cdot 83^{9} \) | $C_{18}$ (as 18T1) | $[10774323]$ (GRH) |
| 18.0.421412815345064168757967085957375942091.1 | x18 - 9x17 + 225x16 - 1596x15 + 22104x14 - 127512x13 + 1262352x12 - 5986422x11 + 46502352x10 - 180492362x9 + 1149875379x8 - 3577518954x7 + 19116861729x6 - 45526465413x5 + 206139713310x4 - 340247545008x3 + 1307472810363x2 - 1144383031881x + 3709960454951 | \( -\,3^{44}\cdot 7^{9}\cdot 13^{9} \) | $C_{18}$ (as 18T1) | $[7, 7, 249242]$ (GRH) |
| 18.0.620651279815192016958464288029880859375.1 | x18 - 9x17 + 234x16 - 1668x15 + 23940x14 - 139104x13 + 1424040x12 - 6809130x11 + 54623250x10 - 213823058x9 + 1405734741x8 - 4409563914x7 + 24309351321x6 - 58323184659x5 + 272500787439x4 - 452550480084x3 + 1795735413621x2 - 1578496430709x + 5291384827899 | \( -\,3^{44}\cdot 5^{9}\cdot 19^{9} \) | $C_{18}$ (as 18T1) | $[2, 2, 7697016]$ (GRH) |
| 18.0.828809655441826774321495340465219960832.1 | x18 + 213x16 - 6x15 + 20232x14 - 372x13 + 1112048x12 + 2232x11 + 38661657x10 + 1074518x9 + 878462091x8 + 49747296x7 + 13080744725x6 + 1198422450x5 + 126327354123x4 + 18837567282x3 + 761687723085x2 + 133856748120x + 2131852243753 | \( -\,2^{18}\cdot 3^{24}\cdot 7^{15}\cdot 11^{9} \) | $C_6 \times C_3$ (as 18T2) | $[2, 2, 2, 2, 630, 1260]$ (GRH) |
| 18.0.957193458914897226781087429876810532211.1 | x18 + 318x16 - x15 + 39447x14 - 321x13 + 2500302x12 - 133146x11 + 89391399x10 - 15798444x9 + 1882862586x8 - 809469819x7 + 23827510937x6 - 18496427643x5 + 185880800082x4 - 182182097162x3 + 930282815520x2 - 609765780432x + 2780371629001 | \( -\,3^{27}\cdot 7^{15}\cdot 31^{9} \) | $C_6 \times C_3$ (as 18T2) | $[2, 4, 76, 16492]$ (GRH) |
| 18.0.2967726843159493858840932623319995101863.7 | x18 - 93x16 - 48x15 + 4050x14 + 6240x13 - 91658x12 - 228384x11 + 1071381x10 + 4611968x9 - 823257x8 - 35960496x7 - 77344856x6 - 104708448x5 - 4174416x4 + 533722240x3 + 4177096704x2 + 12286132224x + 10835984384 | \( -\,3^{24}\cdot 7^{15}\cdot 19^{12} \) | $C_6 \times C_3$ (as 18T2) | $[4, 7372092]$ (GRH) |
| 18.0.3776542477491033702973795200304073601024.1 | x18 - 9x17 + 258x16 - 1706x15 + 25692x14 - 123246x13 + 1221682x12 - 4356336x11 + 28639551x10 - 81366637x9 + 336386712x8 - 771159882x7 + 2020760692x6 - 3333464652x5 + 16394855484x4 - 26333009892x3 + 201734400000x2 - 303589255200x + 486213973000 | \( -\,2^{12}\cdot 3^{21}\cdot 7^{14}\cdot 37^{9} \) | $S_3 \times C_6$ (as 18T6) | $[18, 54, 12312]$ (GRH) |
| 18.0.5402572979943138104302196852621075629959.7 | x18 - 3x16 - 102x15 + 306x14 - 2904x13 + 10306x12 - 25956x11 + 197229x10 - 685960x9 + 4076145x8 - 16235718x7 + 47843680x6 - 129191472x5 + 192346320x4 - 242786912x3 + 186484608x2 + 741275136x + 1196406784 | \( -\,3^{27}\cdot 7^{12}\cdot 13^{15} \) | $C_6 \times C_3$ (as 18T2) | $[19, 1639092]$ (GRH) |
| 18.0.46287577738090612111387516950954005968023.1 | x18 + 318x16 - 4x15 + 31761x14 - 5688x13 + 1346987x12 - 850383x11 + 29343633x10 - 33350634x9 + 387929952x8 - 516066921x7 + 3633489894x6 - 2896022691x5 + 22810900296x4 + 4904628409x3 + 82416559734x2 + 65824912344x + 283790949688 | \( -\,3^{27}\cdot 13^{15}\cdot 17^{9} \) | $C_6 \times C_3$ (as 18T2) | $[2, 14, 14, 70952]$ (GRH) |
| 18.0.46572979962512449327252831469568000000000.1 | x18 - 6x17 + 171x16 - 866x15 + 12825x14 - 53706x13 + 534596x12 - 1842426x11 + 13567536x10 - 37365600x9 + 219817671x8 - 463924236x7 + 2271460011x6 - 3413556846x5 + 15903607875x4 - 10762099726x3 + 82917294006x2 + 893627904x + 191108188441 | \( -\,2^{27}\cdot 3^{27}\cdot 5^{9}\cdot 13^{12} \) | $C_6 \times C_3$ (as 18T2) | $[2, 2, 2, 2, 90, 8190]$ (GRH) |
| 18.0.83965375312753658928066380894847299471799.1 | x18 - 9x17 + 60x16 - 262x15 + 1929x14 - 10053x13 + 71441x12 - 309315x11 + 1767420x10 - 6349626x9 + 33272703x8 - 106851099x7 + 497306862x6 - 1307684628x5 + 4889287872x4 - 9029732096x3 + 25896306432x2 - 25618016256x + 54730227712 | \( -\,3^{21}\cdot 13^{9}\cdot 31^{14} \) | $S_3 \times C_6$ (as 18T6) | $[20, 1491440]$ (GRH) |
| 18.0.86161979862499093345337569390232247250944.2 | x18 - 7x17 + 111x16 - 570x15 + 5575x14 - 24157x13 + 183489x12 - 702801x11 + 4348726x10 - 14614200x9 + 74356953x8 - 212878813x7 + 887867263x6 - 2056738955x5 + 6915161271x4 - 11750894177x3 + 30681517019x2 - 29651248130x + 55649538283 | \( -\,2^{12}\cdot 3^{9}\cdot 17^{9}\cdot 37^{14} \) | $S_3 \times C_6$ (as 18T6) | $[2, 2, 2, 1940166]$ (GRH) |
| 18.0.120092997667342126925823206694597892767744.2 | x18 - 2x17 + 164x16 - 314x15 + 13029x14 - 21092x13 + 651907x12 - 798220x11 + 22417227x10 - 18246558x9 + 545228110x8 - 241380330x7 + 9318786102x6 - 1404347650x5 + 107199772771x4 + 3474292326x3 + 747079319085x2 + 64419294176x + 2378782567897 | \( -\,2^{24}\cdot 3^{9}\cdot 7^{9}\cdot 37^{14} \) | $S_3 \times C_6$ (as 18T6) | $[2, 2, 18, 18, 36, 468]$ (GRH) |
| 18.0.169999752992335178942220108544792000000000.1 | x18 - 7x17 + 120x16 - 626x15 + 6531x14 - 28695x13 + 229872x12 - 888043x11 + 5767404x10 - 19494767x9 + 103972952x8 - 299009263x7 + 1307752076x6 - 3039956271x5 + 10743313753x4 - 18290873776x3 + 50489934410x2 - 48726323693x + 97992831511 | \( -\,2^{12}\cdot 5^{9}\cdot 11^{9}\cdot 37^{14} \) | $S_3 \times C_6$ (as 18T6) | $[2, 2, 2, 4, 28, 23436]$ (GRH) |
| 18.0.178541578852998866709992697969426969133056.1 | x18 - 6x17 + 105x16 - 470x15 + 5088x14 - 19992x13 + 150340x12 - 481404x11 + 2729481x10 - 7706476x9 + 37870875x8 - 94591272x7 + 340487281x6 - 646277772x5 + 2508975903x4 - 6699277158x3 + 23166778845x2 - 36740356506x + 47051159113 | \( -\,2^{18}\cdot 3^{27}\cdot 7^{9}\cdot 19^{12} \) | $C_6 \times C_3$ (as 18T2) | $[2, 2, 2, 42, 84, 588]$ (GRH) |
| 18.0.182535844857539433056785809958362947780608.1 | x18 - 2x17 + 173x16 - 330x15 + 14429x14 - 23330x13 + 755082x12 - 929854x11 + 27080080x10 - 22449952x9 + 685380987x8 - 317287568x7 + 12167724659x6 - 2095429314x5 + 145194850029x4 + 2023454274x3 + 1048817590026x2 + 78764845432x + 3461536818169 | \( -\,2^{33}\cdot 11^{9}\cdot 37^{14} \) | $S_3 \times C_6$ (as 18T6) | $[2, 2, 2, 14, 270774]$ (GRH) |
| 18.0.319780656433835079525248091919941689225216.1 | x18 - 7x17 + 129x16 - 682x15 + 7559x14 - 33625x13 + 283423x12 - 1103801x11 + 7509688x10 - 25521676x9 + 142410717x8 - 411169037x7 + 1882145661x6 - 4387355467x5 + 16263505093x4 - 27720649061x3 + 80685361261x2 - 77705750398x + 166746964831 | \( -\,2^{12}\cdot 37^{14}\cdot 59^{9} \) | $S_3 \times C_6$ (as 18T6) | $[6, 6, 649404]$ (GRH) |
| 18.0.474797564089947061005643868926528923561984.2 | x18 - 6x17 + 117x16 - 432x15 + 7029x14 - 4380x13 + 269520x12 + 360156x11 + 6871230x10 + 13600116x9 + 121388427x8 + 236256312x7 + 1453703763x6 + 2285310216x5 + 11313506295x4 + 12526883586x3 + 52656339330x2 + 33634384392x + 143873586899 | \( -\,2^{12}\cdot 3^{30}\cdot 7^{15}\cdot 17^{9} \) | $S_3 \times C_6$ (as 18T6) | $[3, 6, 126, 4410]$ (GRH) |
| 18.0.1004285770264603077807571330317567473594368.1 | x18 - 7x17 + 147x16 - 794x15 + 9831x14 - 44661x13 + 414045x12 - 1636273x11 + 12151554x10 - 41702360x9 + 253396625x8 - 736480093x7 + 3673658915x6 - 8598059427x5 + 34867471171x4 - 59468160457x3 + 191099338775x2 - 183041086898x + 442378829803 | \( -\,2^{12}\cdot 37^{14}\cdot 67^{9} \) | $S_3 \times C_6$ (as 18T6) | $[2, 6, 18, 211302]$ (GRH) |
| 18.0.1030197932390779328264996615851405379432448.1 | x18 - 3x17 + 6x16 + 90x15 - 39x14 - 1401x13 + 20406x12 - 100113x11 + 481848x10 - 1697075x9 + 6375792x8 - 19367253x7 + 59042850x6 - 141091389x5 + 317659023x4 - 527232024x3 + 800021124x2 - 738392301x + 619938747 | \( -\,2^{12}\cdot 3^{30}\cdot 7^{14}\cdot 23^{9} \) | $S_3 \times C_6$ (as 18T6) | $[2, 6, 6, 18, 11718]$ (GRH) |
| 18.0.1056138901279026047519828726794817132040663.9 | x18 - 6x17 - 45x16 + 286x15 + 1074x14 - 8460x13 + 3702x12 + 21564x11 + 216501x10 - 1108894x9 + 2166711x8 - 741978x7 + 5953192x6 - 49153200x5 + 88036464x4 - 8290208x3 - 445115136x2 + 498077184x + 921751552 | \( -\,3^{24}\cdot 7^{15}\cdot 31^{12} \) | $C_6 \times C_3$ (as 18T2) | $[15926169]$ (GRH) |
| 18.0.1245190474036783044610867207005696000000000.3 | x18 - 3x17 - 60x16 + 60x15 + 1944x14 + 1116x13 - 22314x12 - 19494x11 + 210087x10 + 301551x9 + 816822x8 + 5088618x7 + 20836656x6 + 36778968x5 + 128208960x4 + 167694048x3 + 625363200x2 + 242697600x + 1721055744 | \( -\,2^{18}\cdot 3^{31}\cdot 5^{9}\cdot 13^{14} \) | $S_3 \times C_6$ (as 18T6) | $[14, 2754192]$ (GRH) |
| 18.0.1692424187101732222765092905977936491966464.1 | x18 - 7x17 + 156x16 - 850x15 + 11075x14 - 50767x13 + 492124x12 - 1957691x11 + 15151936x10 - 52229455x9 + 330391428x8 - 962984783x7 + 5002295088x6 - 11724742015x5 + 49602460501x4 - 84577334312x3 + 284676104674x2 - 271819124605x + 693932370643 | \( -\,2^{12}\cdot 37^{14}\cdot 71^{9} \) | $S_3 \times C_6$ (as 18T6) | $[6, 42, 42, 7686]$ (GRH) |
| 18.0.1882508498699710301766760487236393418883072.1 | x18 + 252x16 + 26460x14 + 1498224x12 + 49441392x10 + 958402368x8 + 10435936896x6 + 56923292160x4 + 119538913536x2 + 54965524992 | \( -\,2^{27}\cdot 3^{45}\cdot 7^{15} \) | $C_{18}$ (as 18T1) | $[2, 5642754]$ (GRH) |
| 18.0.2342772393121389342665065120137216000000000.1 | x18 - 6x17 + 57x16 - 342x15 + 2397x14 - 8274x13 + 73002x12 - 114570x11 + 1570920x10 - 636788x9 + 24975411x8 + 9022440x7 + 286583163x6 + 206392410x5 + 2169968997x4 + 1548565326x3 + 9411997182x2 + 4225615884x + 17320048361 | \( -\,2^{33}\cdot 3^{30}\cdot 5^{9}\cdot 7^{14} \) | $S_3 \times C_6$ (as 18T6) | $[2, 2, 6, 6, 219198]$ (GRH) |
| 18.0.3003823256884925694987438506048666589724672.1 | x18 - 7x17 - 50x16 + 520x15 + 296x14 - 14596x13 + 31102x12 + 144874x11 - 651061x10 - 156909x9 + 5579540x8 - 10349906x7 - 6028004x6 + 37023896x5 + 14364176x4 - 242844992x3 + 517853824x2 - 521534464x + 242280448 | \( -\,2^{18}\cdot 7^{9}\cdot 127^{14} \) | $S_3 \times C_6$ (as 18T6) | $[6, 6, 648144]$ (GRH) |
| 18.0.3870328444867146736146206444709275111784448.1 | x18 + 221x16 + 18798x14 + 773383x12 + 15825836x10 + 146193112x8 + 451182511x6 + 175757803x4 + 11193715x2 + 107653 | \( -\,2^{18}\cdot 13^{15}\cdot 19^{16} \) | $C_{18}$ (as 18T1) | $[3, 9, 909594]$ (GRH) |
| 18.0.5062090151414178056069202621780473318873407.1 | x18 - x17 + 95x16 - 786x15 - 3197x14 + 39408x13 - 47312x12 - 130372x11 - 88308x10 - 3107148x9 + 43928444x8 - 130864084x7 + 152081560x6 - 646274448x5 + 2209461811x4 - 1564440675x3 - 1350313403x2 - 452031866x + 2852917793 | \( -\,19^{15}\cdot 37^{15} \) | $C_6 \times C_3$ (as 18T2) | $[2, 2, 2, 28, 67564]$ (GRH) |
| 18.0.6978814404767355448133435215913472000000000.2 | x18 - 81x16 + 3735x14 - 95193x12 + 1676052x10 - 25382x9 - 15545754x8 + 6167826x7 + 129779769x6 - 281435616x5 + 167351805x4 + 3605893830x3 + 7379910756x2 - 10205696088x + 65865831261 | \( -\,2^{18}\cdot 3^{44}\cdot 5^{9}\cdot 7^{12} \) | $C_{18}$ (as 18T1) | $[3, 3, 1858158]$ (GRH) |
| 18.0.7028317179364168027995195360411648000000000.3 | x18 - 6x17 + 237x16 - 1302x15 + 27597x14 - 124314x13 + 2042502x12 - 6836730x11 + 104127960x10 - 234474428x9 + 3743115171x8 - 4993969080x7 + 93909017643x6 - 60571863750x5 + 1569548611977x4 - 315811185954x3 + 15683707815702x2 + 81200252004x + 70597462733281 | \( -\,2^{33}\cdot 3^{31}\cdot 5^{9}\cdot 7^{14} \) | $S_3 \times C_6$ (as 18T6) | $[2, 2, 2, 2, 304, 10032]$ (GRH) |
| 18.0.7065768916593110856047783889584316216508416.1 | x18 - 2x17 + 98x16 - 230x15 + 7698x14 - 11158x13 + 451361x12 - 483714x11 + 19896362x10 - 12565692x9 + 686399371x8 - 27166024x7 + 17905672065x6 + 7923669502x5 + 323641640959x4 + 201391197924x3 + 3528664372527x2 + 1687026042884x + 17172029521969 | \( -\,2^{18}\cdot 3^{9}\cdot 7^{15}\cdot 19^{16} \) | $C_{18}$ (as 18T1) | $[2, 2, 12, 598788]$ (GRH) |
| 18.0.7065768916593110856047783889584316216508416.2 | x18 - 2x17 + 98x16 - 230x15 + 7698x14 - 12222x13 + 450829x12 - 294056x11 + 20316110x10 - 1036720x9 + 691813801x8 + 163570074x7 + 17189420781x6 + 4958427054x5 + 301709383024x4 + 51432868270x3 + 3384649707670x2 + 106026030264x + 17934199170349 | \( -\,2^{18}\cdot 3^{9}\cdot 7^{15}\cdot 19^{16} \) | $C_{18}$ (as 18T1) | $[2, 2, 228, 74556]$ (GRH) |
| 18.0.7220738962643911588750494056035314570262659.1 | x18 + 294x16 - 161x15 + 32481x14 - 21558x13 + 1885484x12 - 473373x11 + 63962538x10 + 40776861x9 + 1386184545x8 + 1712290440x7 + 23514110103x6 + 23995814184x5 + 285834467088x4 + 213915299096x3 + 1630678178304x2 + 1262975131200x + 3320473161664 | \( -\,3^{27}\cdot 7^{9}\cdot 31^{15} \) | $C_6 \times C_3$ (as 18T2) | $[2, 4, 28, 58156]$ (GRH) |
| 18.0.8575646213021703940521028812918699203493888.3 | x18 - 3x17 - 78x16 + 108x15 + 2664x14 - 12x13 - 41898x12 - 26646x11 + 339819x10 + 315807x9 - 1018584x8 + 613290x7 + 6179676x6 + 3729264x5 + 5211552x4 + 12964608x3 + 42863616x2 + 761856x + 107610112 | \( -\,2^{18}\cdot 3^{30}\cdot 7^{9}\cdot 13^{14} \) | $S_3 \times C_6$ (as 18T6) | $[5, 30, 442890]$ (GRH) |
| 18.0.8826761707820991064360908575466167817698823.10 | x18 - 201x16 - 324x15 + 17658x14 + 54144x13 - 814130x12 - 3918456x11 + 18110517x10 + 145388304x9 - 29319813x8 - 2622648420x7 - 6893038592x6 + 11462360976x5 + 109788683088x4 + 298107348480x3 + 389859017472x2 + 168742637568x + 25516048384 | \( -\,3^{24}\cdot 7^{15}\cdot 37^{12} \) | $C_6 \times C_3$ (as 18T2) | $[3, 693, 9009]$ (GRH) |
| 18.0.11464615459611696074365702834006806143172608.1 | x18 - 4x17 + 73x16 - 30x15 + 3926x14 - 2892x13 + 101877x12 + 389884x11 + 727903x10 + 6714132x9 + 19205829x8 + 49846322x7 + 310395661x6 + 187135216x5 + 1909020302x4 + 450056094x3 + 3062291750x2 + 337394588x + 3057477097 | \( -\,2^{18}\cdot 17^{9}\cdot 79^{14} \) | $S_3 \times C_6$ (as 18T6) | $[2, 2, 2, 4, 84, 5460]$ (GRH) |
| 18.0.12639964587166968704098411698997775327821824.1 | x18 + 204x16 - 6x15 + 14787x14 - 354x13 + 387161x12 - 51156x11 + 863727x10 - 952408x9 + 18104562x8 + 12264582x7 + 50853848x6 - 22106286x5 + 191128917x4 + 248399886x3 + 1056948351x2 + 752535174x + 1084437811 | \( -\,2^{27}\cdot 3^{24}\cdot 37^{15} \) | $C_6 \times C_3$ (as 18T2) | $[2, 2, 2, 234, 8190]$ (GRH) |
| 18.0.14952227306849866974860634662963099734114304.1 | x18 + 434x16 + 74648x14 + 6681864x12 + 343561344x10 + 10535881216x8 + 192490790912x6 + 2009002082304x4 + 10714677772288x2 + 21429355544576 | \( -\,2^{27}\cdot 7^{15}\cdot 31^{15} \) | $C_6 \times C_3$ (as 18T2) | $[2, 18, 126, 16884]$ (GRH) |
| 18.0.15122562715473759157739145863562318625468416.2 | x18 - 3x17 + 24x16 + 42x15 + 393x14 - 1725x13 + 32856x12 - 157041x11 + 983802x10 - 3697991x9 + 16474170x8 - 51892869x7 + 180078636x6 - 449775009x5 + 1169945709x4 - 2071336188x3 + 3760200192x2 - 3727057221x + 4059023093 | \( -\,2^{12}\cdot 3^{30}\cdot 7^{14}\cdot 31^{9} \) | $S_3 \times C_6$ (as 18T6) | $[3, 12, 12, 137592]$ (GRH) |
| 18.0.16413889305350509964853040604122672586106807.2 | x18 - 3x17 + 66x16 - 8x15 + 7548x14 + 51456x13 + 277369x12 + 1401495x11 - 2483370x10 - 5227070x9 + 207680922x8 - 291557100x7 + 233470852x6 - 171617115x5 + 16443414363x4 - 51037054889x3 + 121351374567x2 - 143569732788x + 176288881193 | \( -\,3^{24}\cdot 13^{9}\cdot 19^{17} \) | $C_{18}$ (as 18T1) | $[3, 4280742]$ (GRH) |
| 18.0.16572404264697372849747294259176558211104768.1 | x18 - 6x17 + 264x16 - 1446x15 + 33861x14 - 153312x13 + 2737851x12 - 9357396x11 + 151699395x10 - 356745098x9 + 5906580054x8 - 8515724286x7 + 160131076710x6 - 118816855266x5 + 2888612355147x4 - 789904049838x3 + 31158412601505x2 - 1029715188852x + 151614141291361 | \( -\,2^{24}\cdot 3^{31}\cdot 7^{14}\cdot 11^{9} \) | $S_3 \times C_6$ (as 18T6) | $[2, 2, 6, 6, 6, 12, 7884]$ (GRH) |
| 18.0.23325000591813882581633268226911166306572831.2 | x18 - 9x17 + 12x16 + 32x15 + 1686x14 - 9846x13 + 49286x12 - 22440x11 + 1331088x10 - 4191132x9 + 33730047x8 - 34322004x7 + 527869077x6 - 1067345487x5 + 7933667079x4 - 8669431748x3 + 68468181699x2 - 104866576881x + 427034554111 | \( -\,3^{27}\cdot 13^{9}\cdot 19^{16} \) | $C_{18}$ (as 18T1) | $[19, 1323084]$ (GRH) |
| 18.0.24016469656532628829808489513181922235252736.1 | x18 + 372x16 + 52452x14 + 3732648x12 + 148347648x10 + 3427494912x8 + 45983342592x6 + 342643212288x4 + 1265144168448x2 + 1686858891264 | \( -\,2^{27}\cdot 3^{27}\cdot 31^{15} \) | $C_6 \times C_3$ (as 18T2) | $[2, 6, 342, 7182]$ (GRH) |
| 18.0.33072058616555172267704055543460613736681159.1 | x18 + 315x16 + 42903x14 + 3235470x12 + 145272897x10 - 2063929x9 + 3893509620x8 - 888655572x7 + 59407364016x6 - 73024540848x5 + 455759740800x4 - 1761607827840x3 + 1421970391296x2 - 9636571236096x + 18040528188928 | \( -\,3^{45}\cdot 7^{15}\cdot 11^{9} \) | $C_{18}$ (as 18T1) | $[3, 18, 1084806]$ (GRH) |
| 18.0.33072058616555172267704055543460613736681159.2 | x18 + 315x16 + 42903x14 + 3235470x12 + 145272897x10 - 6297529x9 + 3893509620x8 - 600770772x7 + 59407364016x6 - 1188816048x5 + 455759740800x4 + 682703468160x3 + 1421970391296x2 + 7312629429504x + 18089129916928 | \( -\,3^{45}\cdot 7^{15}\cdot 11^{9} \) | $C_{18}$ (as 18T1) | $[3, 18, 721278]$ (GRH) |
| 18.0.33471151027064787570494624202065583768076288.1 | x18 - 4x17 + 139x16 - 352x15 + 7335x14 + 12684x13 + 272213x12 + 487528x11 + 6703724x10 - 8055840x9 - 83825356x8 + 137544224x7 + 858619904x6 - 759789312x5 - 2724186624x4 + 5673216000x3 + 6471729152x2 - 14371176448x + 8569634816 | \( -\,2^{18}\cdot 7^{15}\cdot 11^{6}\cdot 19^{15} \) | $S_3 \times C_6$ (as 18T6) | $[2, 2, 2, 2, 4, 28, 15288]$ (GRH) |
| 18.0.33703610765963698533467381091270298700673024.1 | x18 + 474x16 + 80343x14 + 6224884x12 + 246937647x10 + 5138452458x8 + 53819444489x6 + 260620415400x4 + 463401439632x2 + 2019487744 | \( -\,2^{12}\cdot 3^{24}\cdot 79^{15} \) | $S_3 \times C_6$ (as 18T6) | $[2, 2, 28, 169260]$ (GRH) |
| 18.0.39938750212536083623342446592174713370832896.1 | x18 - 5x17 + 26x16 - 98x15 + 1015x14 - 3133x13 + 22318x12 - 56341x11 + 448088x10 - 819803x9 + 6431560x8 - 9409373x7 + 73631164x6 - 71250155x5 + 603793415x4 - 329016700x3 + 3333390128x2 - 293112723x + 9397502237 | \( -\,2^{12}\cdot 31^{9}\cdot 79^{14} \) | $S_3 \times C_6$ (as 18T6) | $[3, 8628984]$ (GRH) |
| 18.0.41709759864743767520229789527327232000000000.1 | x18 - 69x16 - 76x15 + 2439x14 + 5700x13 - 26645x12 - 162564x11 + 240744x10 + 2377242x9 + 7371690x8 - 2498994x7 - 10081135x6 + 63660336x5 + 1018042977x4 + 3360208862x3 + 8852161824x2 + 11377676520x + 13658762789 | \( -\,2^{18}\cdot 3^{24}\cdot 5^{9}\cdot 19^{16} \) | $C_{18}$ (as 18T1) | $[57, 1667022]$ (GRH) |
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