Global number field search results

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Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying matches 1-50 of )

Label	Polynomial	Discriminant	Galois group	Class group
18.0.149385972680924763865244423159808.1	x^18 + 75x^16 + 2178x^14 + 32829x^12 + 283689x^10 + 1444041x^8 + 4240305x^6 + 6661035x^4 + 4752513x^2 + 1137267	\( -\,2^{18}\cdot 3^{27}\cdot 73^{3}\cdot 577^{3} \)	18T767	$[2, 4, 1548]$ (GRH)
18.0.350345670377968069507061800493571.1	x^18 + 72x^16 + 2160x^14 + 34944x^12 + 329472x^10 - 4693x^9 + 1824768x^8 - 168948x^7 + 5677056x^6 - 2027376x^5 + 8847360x^4 - 9010560x^3 + 5308416x^2 - 10812672x + 22810681	\( -\,3^{45}\cdot 17^{9} \)	$C_{18}$ (as 18T1)	$[2, 2, 2774]$ (GRH)
18.0.504202701918008951235072000000000.2	x^18 + 27x^16 + 495x^14 + 6219x^12 + 59292x^10 - 2x^9 + 430038x^8 + 378x^7 + 2361801x^6 - 8244x^5 + 9427185x^4 + 39510x^3 + 24883956x^2 - 34668x + 33385281	\( -\,2^{18}\cdot 3^{44}\cdot 5^{9} \)	$C_{18}$ (as 18T1)	$[24966]$ (GRH)
18.0.519527019723470744090368949777303.1	x^18 - 7x^17 + 58x^16 - 266x^15 + 1435x^14 - 5199x^13 + 21866x^12 - 64937x^11 + 227650x^10 - 559943x^9 + 1686287x^8 - 3386581x^7 + 8904619x^6 - 13996282x^5 + 32437184x^4 - 36161351x^3 + 74452082x^2 - 44882086x + 83092129	\( -\,19^{16}\cdot 23^{9} \)	$C_{18}$ (as 18T1)	$[13149]$ (GRH)
18.0.649907439846766024629709761975683.1	x^18 - x^17 + 77x^16 - 77x^15 + 2509x^14 - 2509x^13 + 45069x^12 - 45069x^11 + 487693x^10 - 487693x^9 + 3269901x^8 - 3269901x^7 + 13542669x^6 - 13542669x^5 + 34088205x^4 - 34088205x^3 + 52765965x^2 - 52765965x + 57746701	\( -\,17^{9}\cdot 19^{17} \)	$C_{18}$ (as 18T1)	$[38836]$ (GRH)
18.0.762006701275810777282417256300544.1	x^18 - 2x^17 + 39x^16 - 66x^15 + 860x^14 - 1276x^13 + 12807x^12 - 16470x^11 + 138889x^10 - 152462x^9 + 1120553x^8 - 1017454x^7 + 6677144x^6 - 4749676x^5 + 28239050x^4 - 14144668x^3 + 76910381x^2 - 20623090x + 103115431	\( -\,2^{27}\cdot 3^{9}\cdot 19^{16} \)	$C_{18}$ (as 18T1)	$[18506]$ (GRH)
18.0.869245000449362794439473301291008.1	x^18 + 66x^16 + 1747x^14 + 23660x^12 + 173859x^10 + 685517x^8 + 1396052x^6 + 1433185x^4 + 689767x^2 + 122317	\( -\,2^{18}\cdot 7^{16}\cdot 13^{9}\cdot 97^{2} \)	18T586	$[2, 4, 1584]$ (GRH)
18.0.1119284599813901503934006266380351.1	x^18 - 6x^17 + 57x^16 - 212x^15 + 1206x^14 - 2976x^13 + 12940x^12 - 17568x^11 + 83169x^10 - 40258x^9 + 573705x^8 - 365916x^7 + 4002937x^6 - 3216606x^5 + 17344149x^4 - 10599756x^3 + 31588815x^2 - 10143966x + 34082749	\( -\,3^{27}\cdot 7^{12}\cdot 13^{9} \)	$C_6 \times C_3$ (as 18T2)	$[2, 10, 1580]$ (GRH)
18.0.1261446981901370189638661902928499.8	x^18 - 9x^17 + 51x^16 - 196x^15 + 804x^14 - 3012x^13 + 12898x^12 - 46452x^11 + 170676x^10 - 511402x^9 + 1574124x^8 - 3865668x^7 + 9988128x^6 - 19346514x^5 + 40437777x^4 - 56155537x^3 + 89390700x^2 - 70039875x + 77095313	\( -\,3^{24}\cdot 7^{12}\cdot 19^{9} \)	$C_6 \times C_3$ (as 18T2)	$[18, 558]$ (GRH)
18.0.1773722731399331010404115847164903.2	x^18 - 9x^17 + 72x^16 - 372x^15 + 1908x^14 - 7560x^13 + 30192x^12 - 97146x^11 + 320526x^10 - 855266x^9 + 2391597x^8 - 5261490x^7 + 12570585x^6 - 22062519x^5 + 44899785x^4 - 57927960x^3 + 99243441x^2 - 73205505x + 103239849	\( -\,3^{44}\cdot 23^{9} \)	$C_{18}$ (as 18T1)	$[37449]$ (GRH)
18.0.2001504424181159874396672000000000.16	x^18 + 15x^16 - 8x^15 + 333x^14 + 24x^13 + 5655x^12 + 2670x^11 + 69687x^10 + 43582x^9 + 674097x^8 + 378498x^7 + 4862043x^6 + 2018526x^5 + 23403354x^4 + 6369416x^3 + 65929308x^2 + 9405912x + 82566296	\( -\,2^{18}\cdot 3^{24}\cdot 5^{9}\cdot 7^{12} \)	$C_6 \times C_3$ (as 18T2)	$[6, 6, 6, 6, 18]$ (GRH)
18.0.2939487800594529948360199110656000.1	x^18 + 68x^16 + 1627x^14 + 19505x^12 + 131697x^10 + 516410x^8 + 1146558x^6 + 1326597x^4 + 683179x^2 + 102185	\( -\,2^{30}\cdot 5^{3}\cdot 37^{6}\cdot 107^{3}\cdot 191^{3} \)	18T837	$[2, 2, 2, 1444]$ (GRH)
18.0.3192433564329392175935038228267008.1	x^18 + 93x^16 + 3519x^14 + 70211x^12 + 806046x^10 + 5497452x^8 + 22162597x^6 + 50450268x^4 + 57830979x^2 + 24303817	\( -\,2^{18}\cdot 3^{24}\cdot 73^{3}\cdot 577^{4} \)	18T765	$[2, 2, 10388]$ (GRH)
18.0.4352961928683212902721499543224559.1	x^18 - x^17 + 96x^16 - 96x^15 + 3896x^14 - 3896x^13 + 87021x^12 - 87021x^11 + 1167646x^10 - 1167646x^9 + 9658271x^8 - 9658271x^7 + 48845771x^6 - 48845771x^5 + 146814521x^4 - 146814521x^3 + 258142646x^2 - 258142646x + 295252021	\( -\,3^{9}\cdot 7^{9}\cdot 19^{17} \)	$C_{18}$ (as 18T1)	$[2, 2, 2, 6632]$ (GRH)
18.0.4859083482029548266268283212136448.1	x^18 + 84x^16 + 2772x^14 + 47040x^12 + 451584x^10 + 2540160x^8 + 8354304x^6 + 15410304x^4 + 14224896x^2 + 4741632	\( -\,2^{27}\cdot 3^{27}\cdot 7^{15} \)	$C_6 \times C_3$ (as 18T2)	$[2, 2, 28, 364]$ (GRH)
18.0.7041044961999737113734118289433303.2	x^18 - 9x^17 + 60x^16 - 268x^15 + 1272x^14 - 5004x^13 + 22294x^12 - 81192x^11 + 315630x^10 - 978324x^9 + 3218604x^8 - 8208228x^7 + 22683008x^6 - 45561114x^5 + 102647091x^4 - 147782137x^3 + 257711352x^2 - 208331724x + 258264152	\( -\,3^{24}\cdot 7^{12}\cdot 23^{9} \)	$C_6 \times C_3$ (as 18T2)	$[3, 6, 3942]$ (GRH)
18.0.7626281990217745472007517214473951.1	x^18 - 7x^17 + 76x^16 - 378x^15 + 2531x^14 - 9987x^13 + 50888x^12 - 164417x^11 + 687416x^10 - 1828199x^9 + 6495797x^8 - 13992021x^7 + 43041793x^6 - 71859458x^5 + 193370792x^4 - 226538639x^3 + 536835424x^2 - 336518414x + 707215681	\( -\,19^{16}\cdot 31^{9} \)	$C_{18}$ (as 18T1)	$[2, 39906]$ (GRH)
18.0.8610038236258048513179648000000000.2	x^18 + 9x^16 - 16x^15 + 360x^14 + 240x^13 + 3928x^12 - 1680x^11 + 49218x^10 + 47424x^9 + 559842x^8 + 375408x^7 + 3618320x^6 + 3283728x^5 + 27436416x^4 + 39093488x^3 + 139982661x^2 + 126029568x + 236250749	\( -\,2^{24}\cdot 3^{18}\cdot 5^{9}\cdot 7^{14} \)	$S_3 \times C_6$ (as 18T6)	$[6, 6, 378]$ (GRH)
18.0.12397041052269497924235545162109375.1	x^18 - 3x^17 - 2x^16 + 226x^14 - 314x^13 + 2056x^12 - 2712x^11 + 26144x^10 - 23076x^9 + 264952x^8 - 69734x^7 + 1914474x^6 - 24520x^5 + 9403275x^4 - 679057x^3 + 28645658x^2 - 1743720x + 39701416	\( -\,3^{9}\cdot 5^{9}\cdot 7^{12}\cdot 13^{12} \)	$C_6 \times C_3$ (as 18T2)	$[2, 2, 2, 20, 140]$ (GRH)
18.0.12516723252931349928823131701451339.1	x^18 - 6x^17 + 75x^16 - 299x^15 + 2178x^14 - 5913x^13 + 32653x^12 - 52812x^11 + 291324x^10 - 201688x^9 + 2166219x^8 - 907068x^7 + 15298582x^6 - 8508129x^5 + 75490509x^4 - 37914480x^3 + 173222787x^2 - 45736635x + 210280141	\( -\,3^{27}\cdot 7^{12}\cdot 17^{9} \)	$C_6 \times C_3$ (as 18T2)	$[2, 2, 13286]$ (GRH)
18.0.14219059916154378364791264791424459.2	x^18 - 3x^17 + 51x^16 - 145x^15 + 1377x^14 - 4017x^13 + 24968x^12 - 71760x^11 + 328884x^10 - 886259x^9 + 3240978x^8 - 7306587x^7 + 21644553x^6 - 36408891x^5 + 88661442x^4 - 102732573x^3 + 217719351x^2 - 173351430x + 337293181	\( -\,3^{24}\cdot 7^{15}\cdot 13^{9} \)	$C_6 \times C_3$ (as 18T2)	$[2, 2, 8246]$ (GRH)
18.0.14845701048926894165227270175719424.3	x^18 - 6x^17 + 33x^16 - 130x^15 + 633x^14 - 1870x^13 + 6342x^12 - 16970x^11 + 50908x^10 - 87252x^9 + 276223x^8 - 443116x^7 + 892387x^6 - 960518x^5 + 5324905x^4 + 4622682x^3 + 21350862x^2 + 11905764x + 19683833	\( -\,2^{27}\cdot 7^{15}\cdot 13^{12} \)	$C_6 \times C_3$ (as 18T2)	$[6, 6, 1092]$ (GRH)
18.0.21137726688804112981348984293163008.2	x^18 - 4x^17 + 20x^16 - 38x^15 - 56x^14 + 42x^13 - 1868x^12 - 2142x^11 - 766x^10 - 7126x^9 + 94236x^8 + 435918x^7 + 1272160x^6 + 4190046x^5 + 10123484x^4 + 18327094x^3 + 32238933x^2 + 42657746x + 24890048	\( -\,2^{18}\cdot 3^{6}\cdot 7^{15}\cdot 13^{12} \)	$S_3 \times C_6$ (as 18T6)	$[3, 3, 2184]$ (GRH)
18.0.23845365740806374055553449712418816.1	x^18 - 6x^17 + 27x^16 - 98x^15 + 441x^14 - 1194x^13 + 3092x^12 - 8442x^11 + 21552x^10 - 23424x^9 + 91239x^8 - 177996x^7 + 55755x^6 - 228654x^5 + 1834899x^4 + 3117170x^3 + 7609494x^2 + 4744224x + 4634713	\( -\,2^{27}\cdot 3^{27}\cdot 13^{12} \)	$C_6 \times C_3$ (as 18T2)	$[2, 2, 3458]$ (GRH)
18.0.26036970568557781217070611380223151.1	x^18 - 9x^17 + 90x^16 - 516x^15 + 3204x^14 - 14112x^13 + 66792x^12 - 238122x^11 + 919602x^10 - 2697362x^9 + 8749269x^8 - 20953674x^7 + 57705369x^6 - 108970803x^5 + 254607615x^4 - 347840628x^3 + 682386453x^2 - 523610901x + 844617131	\( -\,3^{44}\cdot 31^{9} \)	$C_{18}$ (as 18T1)	$[93339]$ (GRH)
18.0.29091207730813357496487416074727531.2	x^18 - 7x^17 + 15x^16 + 6x^15 + 41x^14 - 547x^13 + 2399x^12 - 6459x^11 + 19848x^10 - 51876x^9 + 153844x^8 - 309033x^7 + 710103x^6 - 1068295x^5 + 2318748x^4 - 2871539x^3 + 5252508x^2 - 3731965x + 4399861	\( -\,11^{9}\cdot 37^{16} \)	$C_{18}$ (as 18T1)	$[38, 342]$ (GRH)
18.0.29585973151813465955360437434322443.1	x^18 - 3x^17 + 60x^16 - 157x^15 + 1116x^14 - 1161x^13 + 3951x^12 + 16026x^11 + 7536x^10 - 5656x^9 + 654144x^8 + 635424x^7 + 1444480x^6 + 14185344x^5 + 24462336x^4 + 8265216x^3 + 41054208x^2 + 180725760x + 207974400	\( -\,3^{21}\cdot 521^{9} \)	$D_9$ (as 18T5)	$[85, 170]$ (GRH)
18.0.43398229994269610052656606538315887.1	x^18 + 70x^16 - 4x^15 + 1925x^14 - 210x^13 + 27573x^12 - 4025x^11 + 230055x^10 - 36104x^9 + 1167950x^8 - 164045x^7 + 3604930x^6 - 360675x^5 + 6472620x^4 - 293353x^3 + 6075300x^2 + 2299968	\( -\,7^{12}\cdot 17^{9}\cdot 31^{9} \)	$S_3 \times C_3$ (as 18T3)	$[3, 3, 9, 9, 18]$ (GRH)
18.0.61268774277068881806471520977944576.1	x^18 + 74x^16 + 2072x^14 + 28120x^12 + 196544x^10 + 710400x^8 + 1323712x^6 + 1188736x^4 + 407296x^2 + 18944	\( -\,2^{27}\cdot 37^{17} \)	$C_{18}$ (as 18T1)	$[17, 1190]$ (GRH)
18.0.74422866183848971206656000000000000.1	x^18 + 113x^16 + 4986x^14 + 109769x^12 + 1290015x^10 + 8207609x^8 + 29008613x^6 + 56338590x^4 + 55167918x^2 + 20511149	\( -\,2^{30}\cdot 5^{12}\cdot 7^{12}\cdot 29^{5} \)	18T176	$[2, 2, 6, 1536]$ (GRH)
18.0.74849463536141758591392983590109184.2	x^18 + 57x^16 + 1211x^14 + 12568x^12 + 72546x^10 + 245270x^8 + 483426x^6 + 518415x^4 + 248454x^2 + 26001	\( -\,2^{18}\cdot 3^{9}\cdot 53^{4}\cdot 107^{9} \)	18T781	$[2, 5006]$ (GRH)
18.0.78582417975702211875446018069790723.2	x^18 - x^17 + 47x^16 + 32x^15 + 1551x^14 + 1282x^13 + 23855x^12 + 46050x^11 + 258875x^10 + 362877x^9 + 1037476x^8 + 1297357x^7 + 2797383x^6 + 2663843x^5 + 3326344x^4 + 1462041x^3 + 1415022x^2 + 277585x + 519841	\( -\,3^{9}\cdot 7^{12}\cdot 19^{16} \)	$C_{18}$ (as 18T1)	$[3, 3, 3, 657]$ (GRH)
18.0.79892001943166438658690014520815616.1	x^18 - 3x^17 + 33x^16 - 91x^15 + 972x^14 - 3216x^13 + 17387x^12 - 47466x^11 + 246777x^10 - 744566x^9 + 2781420x^8 - 5768394x^7 + 20679591x^6 - 45616323x^5 + 134273652x^4 - 125897574x^3 + 462427464x^2 - 1117528098x + 2682840203	\( -\,2^{12}\cdot 3^{18}\cdot 7^{15}\cdot 13^{9} \)	$S_3 \times C_6$ (as 18T6)	$[2, 2, 2, 2, 4, 468]$ (GRH)
18.0.87039873532075611618416695574933504.1	x^18 - 7x^17 + 21x^16 - 10x^15 - 25x^14 - 337x^13 + 3019x^12 - 11321x^11 + 32356x^10 - 81340x^9 + 216453x^8 - 535373x^7 + 1224513x^6 - 2351635x^5 + 4043761x^4 - 5640557x^3 + 6680809x^2 - 5296030x + 2999263	\( -\,2^{12}\cdot 11^{9}\cdot 37^{14} \)	$S_3 \times C_6$ (as 18T6)	$[2, 6, 24, 72]$ (GRH)
18.0.95090394182193546591849307801911296.2	x^18 - 6x^17 + 81x^16 - 370x^15 + 2577x^14 - 9226x^13 + 39726x^12 - 107954x^11 + 304596x^10 - 615760x^9 + 1620055x^8 - 2975076x^7 + 6181459x^6 - 8245054x^5 + 15664617x^4 - 17759238x^3 + 36433958x^2 - 26053208x + 31314401	\( -\,2^{27}\cdot 7^{12}\cdot 13^{15} \)	$C_6 \times C_3$ (as 18T2)	$[2, 2, 6, 6, 378]$ (GRH)
18.0.104058872623657018481772248523222499.4	x^18 - 3x^17 + 7x^16 - 24x^15 + 322x^14 - 530x^13 + 4726x^12 - 6396x^11 + 62002x^10 - 59326x^9 + 668982x^8 - 297270x^7 + 5328864x^6 - 804120x^5 + 29142209x^4 - 3014537x^3 + 98419102x^2 - 6470051x + 152453839	\( -\,7^{12}\cdot 13^{12}\cdot 19^{9} \)	$C_6 \times C_3$ (as 18T2)	$[18, 1638]$ (GRH)
18.0.144702241276662140714874256260206223.2	x^18 - 3x^17 + 18x^16 - 147x^15 + 822x^14 - 1827x^13 - 99x^12 + 6528x^11 + 29988x^10 - 74840x^9 - 40512x^8 + 12960x^7 + 1123200x^6 - 1445376x^5 - 829440x^4 + 1155072x^3 + 3244032x^2 - 4718592x + 2097152	\( -\,3^{30}\cdot 7^{15}\cdot 23^{6} \)	$S_3 \times C_6$ (as 18T6)	$[2, 2, 3192]$ (GRH)
18.0.165107449555765648724828672000000000.4	x^18 + 5x^16 - 16x^15 + 306x^14 + 172x^13 + 5100x^12 + 4488x^11 + 75533x^10 + 72264x^9 + 817621x^8 + 822724x^7 + 6632797x^6 + 5813816x^5 + 37070685x^4 + 21380228x^3 + 129463023x^2 + 35149140x + 219558249	\( -\,2^{18}\cdot 5^{9}\cdot 7^{12}\cdot 13^{12} \)	$C_6 \times C_3$ (as 18T2)	$[2, 2, 2, 18, 558]$ (GRH)
18.0.179099310176045734691646526162025107.1	x^18 - 7x^17 + 60x^16 - 170x^15 + 1392x^14 - 4613x^13 + 24354x^12 - 23677x^11 + 48833x^10 - 35038x^9 + 59244x^8 - 39753x^7 + 33797x^6 - 10244x^5 + 1771x^4 - 295x^3 + 43x^2 - 8x + 1	\( -\,37^{12}\cdot 67^{9} \)	$S_3 \times C_3$ (as 18T3)	$[2, 2, 2, 2, 8, 344]$ (GRH)
18.0.210287410844167058761982755564945408.5	x^18 - 2x^17 + 19x^16 + 38x^15 + 81x^14 + 826x^13 + 3336x^12 + 3902x^11 + 45764x^10 - 17244x^9 + 40103x^8 - 540496x^7 - 196809x^6 - 1431434x^5 - 69861x^4 - 50646490x^3 + 64290142x^2 + 55016416x + 1769766817	\( -\,2^{18}\cdot 7^{12}\cdot 157^{9} \)	$S_3 \times C_3$ (as 18T3)	$[6, 18, 126]$ (GRH)
18.0.215154340657376220394997912000000000.1	x^18 - 3x^17 + 47x^16 - 172x^15 + 1517x^14 - 5332x^13 + 22374x^12 - 75980x^11 + 148668x^10 + 42506x^9 - 580776x^8 + 29214x^7 + 5997076x^6 - 20620332x^5 + 41420961x^4 - 55016363x^3 + 52690863x^2 - 31834602x + 13067109	\( -\,2^{12}\cdot 5^{9}\cdot 11^{6}\cdot 19^{15} \)	$S_3 \times C_6$ (as 18T6)	$[2, 2, 4, 4312]$ (GRH)
18.0.231020214178968501941151058507071488.1	x^18 + 76x^16 + 2166x^14 + 29716x^12 + 209741x^10 + 768208x^8 + 1451581x^6 + 1344364x^4 + 521284x^2 + 54872	\( -\,2^{33}\cdot 11^{6}\cdot 19^{15} \)	$S_3 \times C_6$ (as 18T6)	$[90, 180]$ (GRH)
18.0.243706199334710775656643000000000000.5	x^18 - 2375x^12 + 2291875x^6 + 421875	\( -\,2^{12}\cdot 3^{21}\cdot 5^{12}\cdot 13^{12} \)	$C_3^2 : C_2$ (as 18T4)	$[3, 3, 6, 6, 6, 6]$ (GRH)
18.0.295307224547164431964209152000000000.1	x^18 - 2x^17 + 20x^16 - 58x^15 + 421x^14 - 516x^13 + 6419x^12 - 2572x^11 + 71211x^10 + 17826x^9 + 639262x^8 + 466198x^7 + 4295158x^6 + 3906398x^5 + 19859011x^4 + 16508326x^3 + 53966797x^2 + 27726080x + 60112841	\( -\,2^{24}\cdot 5^{9}\cdot 37^{14} \)	$S_3 \times C_6$ (as 18T6)	$[2, 2, 2, 4238]$ (GRH)
18.0.308154864637927691969232913151717376.2	x^18 - 9x^17 + 96x^16 - 518x^15 + 3228x^14 - 10782x^13 + 42574x^12 - 97176x^11 + 161823x^10 - 297157x^9 - 55194x^8 + 410082x^7 + 2610916x^6 - 4401372x^5 + 87864060x^4 - 169850772x^3 + 539250456x^2 - 713931504x + 599486056	\( -\,2^{12}\cdot 3^{21}\cdot 7^{14}\cdot 13^{9} \)	$S_3 \times C_6$ (as 18T6)	$[2, 2, 2, 4, 4, 468]$ (GRH)
18.0.330204794362909836518332446749753344.1	x^18 - 2x^17 + 50x^16 + 26x^15 + 958x^14 + 606x^13 + 11197x^12 + 636x^11 + 68077x^10 - 139670x^9 + 170189x^8 - 1801562x^7 + 93271x^6 - 6155838x^5 + 11588776x^4 + 36901748x^3 + 100260832x^2 + 145398680x + 203590394	\( -\,2^{18}\cdot 13^{2}\cdot 193^{6}\cdot 229^{6} \)	18T769	$[2, 2, 2, 12460]$ (GRH)
18.0.347294177030908919809654319019700224.1	x^18 - 9x^17 + 45x^16 - 140x^15 + 600x^14 - 2856x^13 + 12354x^12 - 36498x^11 + 109749x^10 - 332479x^9 + 1175109x^8 - 3139962x^7 + 7914304x^6 - 16057650x^5 + 41336448x^4 - 89051570x^3 + 194857845x^2 - 245213451x + 260439319	\( -\,2^{12}\cdot 3^{18}\cdot 7^{14}\cdot 19^{9} \)	$S_3 \times C_6$ (as 18T6)	$[3, 15, 1260]$ (GRH)
18.0.410403006358127324860166545115234375.1	x^18 - 3x^17 + 52x^16 - 252x^15 + 1402x^14 - 7266x^13 + 25794x^12 - 86808x^11 + 256538x^10 - 407056x^9 + 647468x^8 - 1953586x^7 + 6247014x^6 - 12462682x^5 + 21097703x^4 - 27033887x^3 + 29682552x^2 - 16477776x + 14492736	\( -\,5^{9}\cdot 7^{12}\cdot 19^{15} \)	$C_6 \times C_3$ (as 18T2)	$[2, 26, 728]$ (GRH)
18.0.451985616395723240517472053274603584.1	x^18 + 81x^16 - 221x^15 + 2784x^14 - 10842x^13 + 57423x^12 - 210678x^11 + 718602x^10 - 2094040x^9 + 5830770x^8 - 15415413x^7 + 39375297x^6 - 88940514x^5 + 164458332x^4 - 232245897x^3 + 233241462x^2 - 147873180x + 45232552	\( -\,2^{6}\cdot 3^{24}\cdot 13^{12}\cdot 181^{4} \)	18T459	$[2, 2, 2, 7026]$ (GRH)
18.0.474295404311594698259070089068359375.1	x^18 - 7x^17 + 24x^16 - 50x^15 + 241x^14 - 1033x^13 + 4672x^12 - 14541x^11 + 52234x^10 - 139961x^9 + 445351x^8 - 952935x^7 + 2517118x^6 - 4112929x^5 + 9673910x^4 - 11979744x^3 + 23891131x^2 - 16951280x + 24056839	\( -\,3^{9}\cdot 5^{9}\cdot 37^{16} \)	$C_{18}$ (as 18T1)	$[37058]$ (GRH)

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