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 61)

Label	Polynomial	Discriminant	Galois group	Class group
18.0.382767468601979969221900924428079566404384980992.2	x^18 - 3x^17 - 42x^16 + 12x^15 + 1512x^14 + 1572x^13 - 5418x^12 - 3414x^11 + 258483x^10 + 481455x^9 + 4287204x^8 + 13613802x^7 + 73994292x^6 + 146257296x^5 + 667973280x^4 + 855399936x^3 + 3840924672x^2 + 1876512768x + 11595603968	\( -\,2^{18}\cdot 3^{30}\cdot 13^{14}\cdot 23^{9} \)	$S_3 \times C_6$ (as 18T6)	$[3, 3, 3, 6, 236316906]$ (GRH)
18.0.1348608123969580736044287667264238937751275533631.6	x^18 - 666x^15 + 10989x^14 - 132534x^13 + 504828x^12 + 267732x^11 - 2869461x^10 - 2521772x^9 + 77298624x^8 + 21004974x^7 - 459144729x^6 + 1801890306x^5 + 9112996548x^4 - 24669932040x^3 + 41395363200x^2 + 65283984000x + 33270400000	\( -\,3^{45}\cdot 37^{17} \)	$C_{18}$ (as 18T1)	$[14802753096]$ (GRH)
18.0.1968100446373322200925262150357418865721092079616.1	x^18 - 7x^17 + 4x^16 + 184x^15 + 128x^14 - 8092x^13 + 51598x^12 - 134342x^11 + 478943x^10 - 3007341x^9 + 21773822x^8 - 92692658x^7 + 352111696x^6 - 1127712400x^5 + 4235753024x^4 - 12494373536x^3 + 32946159232x^2 - 50298266368x + 59975185408	\( -\,2^{18}\cdot 31^{9}\cdot 127^{14} \)	$S_3 \times C_6$ (as 18T6)	$[9, 9, 244021806]$ (GRH)
18.0.15537225845019417529672325781592151434950300401664.2	x^18 - 7x^17 + 22x^16 + 72x^15 + 648x^14 - 9060x^13 + 72318x^12 - 272982x^11 + 1442715x^10 - 7028429x^9 + 45186124x^8 - 191602578x^7 + 838542252x^6 - 2810738664x^5 + 10903299792x^4 - 31071279168x^3 + 87450314880x^2 - 137349245952x + 194888648704	\( -\,2^{18}\cdot 3^{9}\cdot 13^{9}\cdot 127^{14} \)	$S_3 \times C_6$ (as 18T6)	$[2, 84, 357158172]$ (GRH)
18.0.17215978016843899580835684099700667905564175265792.1	x^18 - 9x^17 - 420x^16 + 1984x^15 + 73770x^14 - 37218x^13 - 6149376x^12 - 16784976x^11 + 237244221x^10 + 1419179555x^9 - 2094160692x^8 - 40253540568x^7 - 102727801808x^6 + 224932172208x^5 + 2034413940288x^4 + 5797665555712x^3 + 9183109401600x^2 + 8595850543104x + 4021085863936	\( -\,2^{12}\cdot 3^{24}\cdot 7^{9}\cdot 79^{14} \)	$S_3 \times C_6$ (as 18T6)	$[2, 2, 4, 12, 84, 1009932]$ (GRH)
18.0.22497960113751479934820492718164014658776000000000.1	x^18 - 9x^17 - 402x^16 + 1840x^15 + 69018x^14 - 10914x^13 - 5537100x^12 - 17815248x^11 + 205547661x^10 + 1433969187x^9 - 1050471018x^8 - 39884181384x^7 - 128655698368x^6 + 185836782000x^5 + 2638164247776x^4 + 9516122868224x^3 + 19470659444736x^2 + 24153643711488x + 15157286557696	\( -\,2^{12}\cdot 3^{27}\cdot 5^{9}\cdot 79^{14} \)	$S_3 \times C_6$ (as 18T6)	$[6, 84, 45051972]$ (GRH)
18.0.147244256784536162442327315331004890491666009075712.1	x^18 - 2x^17 - 127x^16 - 1370x^15 + 1071x^14 + 162946x^13 + 2249906x^12 + 19230652x^11 + 121957908x^10 + 608611962x^9 + 2449633407x^8 + 8020398008x^7 + 21278039105x^6 + 45104419528x^5 + 74302857419x^4 + 90626337302x^3 + 75780975570x^2 + 38197162944x + 8660565481	\( -\,2^{12}\cdot 7^{15}\cdot 19^{9}\cdot 31^{15} \)	$S_3 \times C_3$ (as 18T3)	$[2, 2, 2, 4, 4, 4, 4, 12, 156, 9516]$ (GRH)
18.0.1235093905746889405718571099119702734980596317089792.1	x^18 - 9x^17 + 384x^16 - 2272x^15 + 88605x^14 - 658197x^13 + 12846028x^12 - 64843719x^11 + 865327146x^10 - 5579169113x^9 + 77246982246x^8 - 512686378569x^7 + 3789040141804x^6 - 15288000079185x^5 + 92885783574705x^4 - 423518882731740x^3 + 2727446539429518x^2 - 8733433478069253x + 23845975839012979	\( -\,2^{12}\cdot 3^{27}\cdot 17^{9}\cdot 37^{15} \)	$S_3 \times C_6$ (as 18T6)	$[2, 78, 70196490]$ (GRH)
18.0.2173089240515381294985625698929389621300732316614656.6	x^18 + 684x^16 + 145692x^14 + 10824528x^12 + 377384688x^10 + 6981100992x^8 + 70338466944x^6 + 363270583296x^4 + 755493868800x^2 + 40292160000	\( -\,2^{27}\cdot 3^{45}\cdot 19^{17} \)	$C_{18}$ (as 18T1)	$[2, 14851834524]$ (GRH)
18.0.2718642342706308433638679144477426237858460895019008.1	x^18 + 75x^16 - 518x^15 + 14895x^14 + 38628x^13 + 1453312x^12 + 695970x^11 + 97733346x^10 + 422945816x^9 + 8555002947x^8 + 33622267188x^7 + 365903950891x^6 + 1580920554276x^5 + 17528600923959x^4 + 88916584556742x^3 + 542518369755228x^2 + 1475998825390308x + 4052214442111177	\( -\,2^{24}\cdot 3^{27}\cdot 11^{9}\cdot 37^{14} \)	$S_3 \times C_6$ (as 18T6)	$[2, 6, 210, 4951590]$ (GRH)
18.0.3266961213891533812087277880596312351679162976508187.2	x^18 + 109359x^12 + 354417390x^6 + 291038813883	\( -\,3^{27}\cdot 1657^{12} \)	$S_3 \times C_3$ (as 18T3)	$[2, 2, 1050, 2470650]$ (GRH)
18.0.4083569424758367433043797712456360033585527698911232.1	x^18 - 9x^17 + 12x^16 - 410x^15 + 10995x^14 - 9861x^13 + 162726x^12 - 3204009x^11 + 24015348x^10 + 104943021x^9 + 1568694924x^8 - 152631309x^7 + 19476958064x^6 + 109343418069x^5 + 2476828380501x^4 + 13611173843684x^3 + 68512294190292x^2 + 162135328484937x + 329489799094441	\( -\,2^{12}\cdot 3^{27}\cdot 29^{9}\cdot 37^{14} \)	$S_3 \times C_6$ (as 18T6)	$[3, 3, 378, 4455864]$ (GRH)
18.0.8880520706942285236653498213029984177183105373284187.2	x^18 + 118863x^12 + 418673070x^6 + 373714754427	\( -\,3^{27}\cdot 1801^{12} \)	$S_3 \times C_3$ (as 18T3)	$[26, 26, 312, 67704]$ (GRH)
18.0.21156460455554157443184358692743823704081665160523776.1	x^18 - 388x^16 - 1770x^15 + 79167x^14 + 461226x^13 - 7119103x^12 - 69040572x^11 + 412426863x^10 + 4399169196x^9 - 18676098374x^8 - 265581279066x^7 + 550446017812x^6 + 17062555046622x^5 + 128931293649937x^4 + 697432636061526x^3 + 2270159537466107x^2 + 2634341655131550x + 6328125825565187	\( -\,2^{12}\cdot 7^{12}\cdot 37^{15}\cdot 47^{9} \)	$S_3 \times C_3$ (as 18T3)	$[3, 3, 3, 3, 3, 3, 777, 46620]$ (GRH)
18.0.76610513899544453304430517636008399400337408000000000.1	x^18 - 4x^17 - 161x^16 + 122x^15 + 12163x^14 + 26048x^13 - 396092x^12 - 1847422x^11 + 4445026x^10 + 49750964x^9 + 101924407x^8 - 223146292x^7 - 1210841585x^6 + 1527209132x^5 + 28187586667x^4 + 108856477778x^3 + 256578470140x^2 + 342514005968x + 299674652229	\( -\,2^{30}\cdot 3^{6}\cdot 5^{9}\cdot 7^{14}\cdot 43^{14} \)	$S_3 \times C_6$ (as 18T6)	$[3, 3, 6, 12, 252, 212688]$ (GRH)
18.0.125658219152626752999993187563351622531489799076360192.1	x^18 + 242604x^12 + 14701076640x^6 + 1728	\( -\,2^{12}\cdot 3^{27}\cdot 1123^{12} \)	$S_3 \times C_3$ (as 18T3)	$[301, 4515, 58695]$ (GRH)
18.0.844516909583529949970724206594089321365947904000000000.1	x^18 - 3x^17 - 552x^16 + 6240x^15 + 53364x^14 - 1530168x^13 + 13275402x^12 - 60135330x^11 + 149804439x^10 - 232194769x^9 + 966780294x^8 - 7176130086x^7 + 33707047332x^6 - 107168086212x^5 + 257696335560x^4 - 491003942664x^3 + 736717649280x^2 - 788668438368x + 499240711936	\( -\,2^{18}\cdot 3^{31}\cdot 5^{9}\cdot 7^{14}\cdot 13^{14} \)	$S_3 \times C_6$ (as 18T6)	$[2, 2, 2, 2, 30, 154037940]$ (GRH)
18.0.987529472131924046848116539449875888434135640677420907.4	x^18 - 9x^17 + 45x^16 + 36x^15 - 1026x^14 + 4590x^13 - 12816x^12 + 26028x^11 + 90828x^10 - 1489446x^9 + 5627718x^8 - 12557430x^7 + 49427415x^6 - 103026411x^5 + 91894095x^4 - 352468422x^3 + 573552900x^2 + 396747072x + 780420096	\( -\,3^{39}\cdot 7^{12}\cdot 127^{12} \)	$S_3 \times C_3$ (as 18T3)	$[3, 18, 18, 18, 18, 252, 252]$ (GRH)
18.0.1162725121036380649066150832445210229839758684897673216.1	x^18 + 762x^16 + 218313x^14 + 30376749x^12 + 2249058240x^10 + 89192075616x^8 + 1757405549952x^6 + 14140144366848x^4 + 39992306079744x^2 + 9792653414400	\( -\,2^{18}\cdot 3^{27}\cdot 127^{17} \)	$C_{18}$ (as 18T1)	$[2, 2, 2, 2217190170]$ (GRH)
18.0.2013844958403898050255539081540690226371968347203186688.1	x^18 - 9x^17 + 45x^16 + 636x^15 - 5526x^14 + 21690x^13 - 29010x^12 - 57708x^11 + 2184723x^10 - 57195115x^9 + 237549663x^8 - 590965020x^7 + 7075342842x^6 - 18851833098x^5 + 11484916434x^4 - 293292196752x^3 + 462523978377x^2 + 433013473827x + 4995175830121	\( -\,2^{12}\cdot 3^{33}\cdot 19^{12}\cdot 43^{12} \)	$S_3 \times C_3$ (as 18T3)	$[3, 9, 9, 9, 1386, 26334]$ (GRH)
18.0.2677761276299797163442203648730856426156058904000000000.1	x^18 - 3x^17 - 807x^16 + 1005x^15 + 269049x^14 + 73797x^13 - 46410555x^12 - 66738279x^11 + 4474849215x^10 + 10471753955x^9 - 240910122405x^8 - 759018551721x^7 + 6760093363683x^6 + 26905061270919x^5 - 81820212046617x^4 - 419376128500893x^3 + 286839979293732x^2 + 2932106044957716x + 3159025422781024	\( -\,2^{12}\cdot 3^{31}\cdot 5^{9}\cdot 7^{14}\cdot 19^{14} \)	$S_3 \times C_6$ (as 18T6)	$[3, 6, 12, 220646244]$ (GRH)
18.0.5217281166509238670480233915527947833639206912000000000.1	x^18 - 8x^17 - 517x^16 + 1678x^15 + 96179x^14 + 34920x^13 - 5376324x^12 + 5188354x^11 + 148150274x^10 - 258684356x^9 - 628744217x^8 - 3685397192x^7 + 30254061027x^6 - 6887580648x^5 + 43144941139x^4 - 488373903890x^3 + 1226187715060x^2 + 1982246556352x + 9154324841549	\( -\,2^{24}\cdot 5^{9}\cdot 877^{14} \)	$S_3 \times C_6$ (as 18T6)	$[2, 2, 54, 61400052]$ (GRH)
18.0.8580431183528775336283156521153602102325171937488142336.1	x^18 - 8x^17 - 172x^16 - 1382x^15 + 11784x^14 + 353158x^13 + 4437353x^12 + 37700470x^11 + 245003955x^10 + 1270005030x^9 + 5351249319x^8 + 18426951344x^7 + 51518737541x^6 + 115116872056x^5 + 199374151874x^4 + 253917378998x^3 + 219504667881x^2 + 113162419542x + 25987884553	\( -\,2^{27}\cdot 11^{9}\cdot 313^{15} \)	$S_3 \times C_3$ (as 18T3)	$[9, 9, 27, 54, 151956]$ (GRH)
18.0.22126735189344705358145337335147732804466351023987884032.1	x^18 - 2x^17 - 475x^16 - 2764x^15 + 35862x^14 + 811404x^13 + 11671470x^12 + 80449872x^11 + 381518397x^10 + 414420542x^9 + 1059157049x^8 + 62716099132x^7 + 708210563500x^6 + 5574455143176x^5 + 57576694070148x^4 + 257270466657168x^3 + 1724517820231056x^2 + 176904804349440x + 19989274074918912	\( -\,2^{27}\cdot 3^{9}\cdot 727^{15} \)	$S_3 \times C_3$ (as 18T3)	$[2, 2, 6, 6, 2922, 61362]$ (GRH)
18.0.32944359581476773238038574207216434174814161602181070848.2	x^18 - 6x^17 - 588x^16 + 2730x^15 + 140388x^14 - 535026x^13 - 15515850x^12 + 66139470x^11 + 839143659x^10 - 4277544184x^9 - 17718435114x^8 + 79245803352x^7 + 350741017488x^6 - 605392710048x^5 - 6069527174496x^4 - 1091786217216x^3 + 57382505628672x^2 + 110075105415168x + 64478748483584	\( -\,2^{18}\cdot 3^{30}\cdot 7^{9}\cdot 103^{14} \)	$S_3 \times C_6$ (as 18T6)	$[2, 6, 1010271384]$ (GRH)
18.0.51620863001368675404465326891529689310638927567087468544.1	x^18 - x^17 - 339x^16 - 46x^15 + 47557x^14 + 56007x^13 - 3490681x^12 - 7365053x^11 + 144682296x^10 + 437794222x^9 - 3261383845x^8 - 13326944589x^7 + 32763269619x^6 + 195609354075x^5 - 27367760547x^4 - 1043363367495x^3 + 187960310919x^2 + 6621321395790x + 10883991773043	\( -\,2^{18}\cdot 3^{6}\cdot 11^{9}\cdot 523^{14} \)	$S_3 \times C_6$ (as 18T6)	$[2, 7931527162]$ (GRH)
18.0.317180535547366983497681454181403157145875143430046117888.1	x^18 - x^17 - 984x^16 + 2510x^15 + 399126x^14 - 1518902x^13 - 79528672x^12 + 365710044x^11 + 8041909773x^10 - 37726851253x^9 - 388634200160x^8 + 1634195356934x^7 + 9217764115764x^6 - 27873163776444x^5 - 74670398987968x^4 - 46074585055336x^3 + 719202938309504x^2 + 674017524612704x + 783773403510784	\( -\,2^{12}\cdot 7^{15}\cdot 19^{6}\cdot 211^{14} \)	$S_3 \times C_6$ (as 18T6)	$[3, 3, 3, 9, 9, 6906690]$ (GRH)
18.0.924932277939078761663470646803127775979456162566125826048.1	x^18 - x^17 + 470x^16 + 2513x^15 + 149163x^14 + 956039x^13 + 28464247x^12 + 225068368x^11 + 3988265085x^10 + 28542470943x^9 + 336726026476x^8 + 2290282965516x^7 + 19375023447318x^6 + 96784777040119x^5 + 380485121195032x^4 + 969083882090814x^3 + 1861722334970505x^2 + 2126907556454464x + 1628413597910449	\( -\,2^{12}\cdot 3^{9}\cdot 7^{6}\cdot 19^{14}\cdot 73^{14} \)	$S_3 \times C_6$ (as 18T6)	$[3, 3, 3, 12, 12, 5992980]$ (GRH)
18.0.2432575246331888759197234289996630135894514528681984000000.1	x^18 + 1302x^16 + 537075x^14 + 87091648x^12 + 7014895419x^10 + 308465253054x^8 + 7475073472013x^6 + 92453456727660x^4 + 451572633759492x^2 + 194277433462336	\( -\,2^{30}\cdot 3^{24}\cdot 5^{6}\cdot 7^{14}\cdot 31^{14} \)	$S_3 \times C_6$ (as 18T6)	$[2, 2, 4, 12, 77921736]$ (GRH)
18.0.7339058714058696548373894733037168312034761402182635301443.1	x^18 - 9x^17 + 45x^16 + 1902x^15 - 15021x^14 + 57771x^13 - 5041232x^12 + 29633925x^11 - 22759602x^10 - 6203302885x^9 + 27813323421x^8 - 57748921875x^7 + 9019520363287x^6 - 26874825967038x^5 + 52528838073972x^4 - 300600540176057x^3 + 412931389362222x^2 + 333613339887189x + 1397069806495609	\( -\,3^{21}\cdot 7^{12}\cdot 19^{12}\cdot 73^{12} \)	$S_3 \times C_3$ (as 18T3)	$[3, 3, 3, 3, 3, 3, 3, 9, 9, 36, 2052]$ (GRH)
18.0.7959340260508580929689411840109697873368492825644925717707.3	x^18 + 248166x^12 + 3825681705x^6 + 1855425871872	\( -\,3^{31}\cdot 7^{12}\cdot 13^{12}\cdot 43^{12} \)	$S_3 \times C_3$ (as 18T3)	$[3, 3, 3, 9, 9, 18, 18, 126, 126]$ (GRH)
18.0.61964593082726514847228199844585196138864186652205647474688.1	x^18 + 51576x^12 + 306516240x^6 + 5159780352	\( -\,2^{12}\cdot 3^{33}\cdot 1933^{12} \)	$S_3 \times C_3$ (as 18T3)	$[3, 6, 6, 54, 54, 108, 1404]$ (GRH)
18.0.66305754614937078316581682973174263499455978739075060969472.1	x^18 - 3024x^15 + 1165924x^12 + 2022824160x^9 + 951986143216x^6 + 208357877056896x^3 + 19780262567688384	\( -\,2^{12}\cdot 3^{27}\cdot 7^{12}\cdot 13^{12}\cdot 37^{12} \)	$S_3 \times C_3$ (as 18T3)	$[3, 3, 3, 3, 3, 3, 9, 117, 15561]$ (GRH)
18.0.69192308370830114650627499075939863765733769216000000000000.1	x^18 - 126x^16 - 1506x^15 + 13413x^14 + 94968x^13 + 606345x^12 + 23306106x^11 + 362900991x^10 + 207124472x^9 - 20638244151x^8 - 55026746730x^7 + 964213213642x^6 + 1142790467772x^5 - 26838014382981x^4 + 4275378675392x^3 + 597733410996390x^2 - 2203214877726000x + 2708125245357200	\( -\,2^{27}\cdot 3^{18}\cdot 5^{12}\cdot 11^{15}\cdot 103^{9} \)	$S_3^2$ (as 18T11)	$[3, 3, 6, 18, 18, 18, 234, 702]$ (GRH)
18.0.75333124892092297262992244259187556332425903757023354560191.1	x^18 - 6x^17 - 1527x^16 + 8808x^15 + 927642x^14 - 5120388x^13 - 288098278x^12 + 1510843992x^11 + 49548274205x^10 - 244055933606x^9 - 4575731495955x^8 + 20737038801648x^7 + 221396206694440x^6 - 911575249761792x^5 - 3926480656027888x^4 + 16967797388265088x^3 - 74294080126316288x^2 - 74967510509588480x + 3741267643296382976	\( -\,7^{12}\cdot 97^{15}\cdot 127^{9} \)	$S_3 \times C_3$ (as 18T3)	$[3, 3, 3, 3, 42, 84, 86268]$ (GRH)
18.0.91418944539476011360498909897881806021621599527281394659328.1	x^18 - 9x^17 + 255x^16 - 1824x^15 + 24423x^14 - 137697x^13 + 1727788x^12 - 8466441x^11 - 43796637x^10 + 269577198x^9 + 5420996661x^8 - 22405758879x^7 + 238912851253x^6 - 660557469432x^5 - 10676966704536x^4 + 23268587608140x^3 + 505306443813876x^2 - 547038123493644x + 948137416523604	\( -\,2^{12}\cdot 3^{21}\cdot 7^{14}\cdot 13^{14}\cdot 19^{14} \)	$S_3^2$ (as 18T11)	$[3, 3, 3, 3, 9, 9, 18, 54, 54, 54]$ (GRH)
18.0.262152748150496553757816558021167153326662254632938777325568.1	x^18 - 2x^17 + 501x^16 + 14648x^15 + 272582x^14 + 3144591x^13 + 27063010x^12 + 177529456x^11 + 942236178x^10 + 4085550909x^9 + 15020023463x^8 + 47124023126x^7 + 130555515789x^6 + 316870835959x^5 + 684237290359x^4 + 1237214238291x^3 + 1844496811058x^2 + 1914036738569x + 1310138919769	\( -\,2^{12}\cdot 3^{9}\cdot 29^{6}\cdot 1129^{14} \)	$S_3 \times C_6$ (as 18T6)	$[5, 105, 86358510]$ (GRH)
18.0.335985111257225502524094185723848201140371850113581056000000.1	x^18 + 912x^16 + 310692x^14 + 52656708x^12 + 4846114662x^10 + 244755477132x^8 + 6554580709188x^6 + 88881650645340x^4 + 561033372337329x^2 + 1286936844705604	\( -\,2^{30}\cdot 3^{6}\cdot 5^{6}\cdot 7^{14}\cdot 181^{14} \)	$S_3 \times C_6$ (as 18T6)	$[2, 6, 12, 12, 12, 12, 391740]$ (GRH)
18.0.490669523847518219543603050415476754595311155180270121791488.1	x^18 + 3x^16 + 1008x^14 + 195268x^12 - 268014x^10 - 64460646x^8 + 2448021928x^6 + 5576982228x^4 - 170682814251x^2 + 832184947467	\( -\,2^{12}\cdot 3^{9}\cdot 7^{12}\cdot 2953^{12} \)	$S_3 \times C_3$ (as 18T3)	$[2, 6, 6, 18, 36, 36, 36, 468]$ (GRH)
18.0.490742062616166373662983522813549807415554217709176000000000.1	x^18 - 6x^17 - 687x^16 + 5406x^15 + 272031x^14 - 1075578x^13 - 45303006x^12 + 153139332x^11 + 4227681804x^10 - 17494139554x^9 - 302274108753x^8 + 1253829209316x^7 + 18917369006865x^6 - 93984714115572x^5 - 281050838668113x^4 + 2951327570583606x^3 + 17012485372731978x^2 - 151213514911900860x + 463589489758381849	\( -\,2^{12}\cdot 3^{31}\cdot 5^{9}\cdot 7^{9}\cdot 67^{15} \)	$S_3 \times C_3$ (as 18T3)	$[6, 6, 6, 378, 145908]$ (GRH)
18.0.679431909497141409089207993258291620226476010831347538702336.1	x^18 - 8x^17 - 404x^16 + 10918x^15 + 91669x^14 - 3015554x^13 + 1101203x^12 + 468459422x^11 - 1783988569x^10 - 51385464532x^9 + 77131235840x^8 + 3937918314038x^7 + 16704551289024x^6 - 53767855256436x^5 - 391238980093323x^4 + 512206086889224x^3 + 9961068503950641x^2 + 26421806277378576x + 22113695846279691	\( -\,2^{12}\cdot 23^{9}\cdot 853^{15} \)	$S_3 \times C_3$ (as 18T3)	$[2, 2, 42, 294, 328104]$ (GRH)
18.0.733114560372703860308311985400170653539593347139329480594827.1	x^18 + 530694x^12 + 13431802185x^6 + 23917744283328	\( -\,3^{27}\cdot 19^{12}\cdot 433^{12} \)	$S_3 \times C_3$ (as 18T3)	$[3, 3, 3, 3, 3, 3, 21, 63, 126, 378]$ (GRH)
18.0.1389021752112961964809440433226376447489723810648175849165227.1	x^18 + 485982x^12 + 46823693841x^6 + 195920474112	\( -\,3^{27}\cdot 8677^{12} \)	$S_3 \times C_3$ (as 18T3)	$[3, 3, 3, 9, 9, 1386, 18018]$ (GRH)
18.0.2094561035195319823494242687991631414291476262838089296768483.1	x^18 - 3x^17 - 416x^16 + 1257x^15 + 288337x^14 - 10786920x^13 + 157669824x^12 - 1816888320x^11 + 30380700672x^10 - 623446253568x^9 + 11510437699584x^8 - 113780248805376x^7 + 677775794503680x^6 - 3079806388273152x^5 + 18983977004040192x^4 - 90314630466895872x^3 + 453434281285386240x^2 - 722517043735166976x + 436217609315155968	\( -\,3^{9}\cdot 13^{12}\cdot 37^{12}\cdot 97^{12} \)	$S_3 \times C_3$ (as 18T3)	$[2, 2, 2, 6, 18, 18, 396, 8316]$ (GRH)
18.0.2270120800429981380726586184495439361286008707872399584386003.1	x^18 + 27592275x^12 + 25321119032448x^6 + 1418640313495891968	\( -\,3^{33}\cdot 17^{12}\cdot 307^{12} \)	$S_3 \times C_3$ (as 18T3)	$[2, 2, 6, 6, 12, 12, 12, 36, 36, 36]$ (GRH)
18.0.6916534707190682077071725436128319105898712657538875913221307.2	x^18 - 9919x^15 + 103266244x^12 + 25079348385x^9 + 2032589480652x^6 - 3842823830391x^3 + 7625597484987	\( -\,3^{27}\cdot 7^{12}\cdot 13^{12}\cdot 109^{12} \)	$S_3 \times C_3$ (as 18T3)	$[3, 3, 3, 3, 3, 6, 18, 990, 2970]$ (GRH)
18.0.13052029345071760863843934415776181167639406996071732693359375.1	x^18 + 606x^16 - 42x^15 + 153015x^14 - 8484x^13 + 22856695x^12 - 428442x^11 + 2469822387x^10 + 729775284x^9 + 200774929287x^8 + 139597980018x^7 + 12034816391578x^6 + 8756629556136x^5 + 575675484948417x^4 + 8578727481828x^3 + 17233229874363636x^2 - 6266059191729120x + 421748783514829120	\( -\,3^{18}\cdot 5^{9}\cdot 7^{15}\cdot 11^{9}\cdot 487^{9} \)	$S_3^2$ (as 18T11)	$[2, 2, 2, 6, 6, 6, 246, 64944]$ (GRH)
18.0.14752461749278147190952026748722919230164585269517740875639283.1	x^18 - 3x^17 - 440x^16 + 437x^15 - 337117x^14 + 23671983x^13 - 368833646x^12 - 6602474036x^11 + 387409454753x^10 - 8399255282261x^9 + 115084114183121x^8 - 1118467036430126x^7 + 8043217290890512x^6 - 43369484085540759x^5 + 174370588263468377x^4 - 510173162432207521x^3 + 1031399763020665000x^2 - 1294085044187005725x + 762516782753267677	\( -\,3^{9}\cdot 13^{12}\cdot 41^{12}\cdot 103^{12} \)	$S_3 \times C_3$ (as 18T3)	$[3, 63, 6867, 20601]$ (GRH)
18.0.26735514947708767000623460382175089698901347865969225007869952.1	x^18 + 1465272x^12 + 63795390480x^6 + 699092182315008	\( -\,2^{12}\cdot 3^{27}\cdot 7^{12}\cdot 13^{12}\cdot 61^{12} \)	$S_3 \times C_3$ (as 18T3)	$[3, 3, 3, 3, 3, 3, 3, 3, 3, 57, 15561]$ (GRH)
18.0.48015245256971127697547575538546724520114168666540072247586816.1	x^18 + 141x^16 - 360x^15 + 13683x^14 - 71064x^13 + 1291103x^12 - 11920464x^11 + 77297904x^10 - 445448336x^9 + 1752021792x^8 - 13129615872x^7 + 55401409440x^6 - 99026005248x^5 + 847107279360x^4 - 3040844951808x^3 + 2031770407680x^2 - 19444819046400x + 63555755265792	\( -\,2^{12}\cdot 3^{18}\cdot 17^{12}\cdot 23^{9}\cdot 313^{9} \)	$S_3^2$ (as 18T11)	$[2, 6, 6, 6, 6, 6, 36, 36, 3420]$ (GRH)