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
18.0.680129765110548404696137774571.1	x^18 - 7x^17 + 31x^16 - 98x^15 + 331x^14 - 957x^13 + 2693x^12 - 6227x^11 + 15226x^10 - 30674x^9 + 66392x^8 - 111391x^7 + 216508x^6 - 293668x^5 + 517517x^4 - 511304x^3 + 833369x^2 - 453934x + 713641	\( -\,11^{9}\cdot 19^{16} \)	$C_{18}$ (as 18T1)	$[2, 542]$ (GRH)
18.0.735565072612935262326166126592.1	x^18 + 38x^16 + 608x^14 + 5320x^12 + 27664x^10 + 86944x^8 + 160512x^6 + 160512x^4 + 72960x^2 + 9728	\( -\,2^{27}\cdot 19^{17} \)	$C_{18}$ (as 18T1)	$[1026]$ (GRH)
18.0.2322038274967832964613417227771.2	x^18 - 9x^17 + 45x^16 - 156x^15 + 504x^14 - 1512x^13 + 4272x^12 - 10422x^11 + 24552x^10 - 51962x^9 + 108099x^8 - 193914x^7 + 351249x^6 - 518733x^5 + 814050x^4 - 933768x^3 + 1272483x^2 - 860841x + 992091	\( -\,3^{44}\cdot 11^{9} \)	$C_{18}$ (as 18T1)	$[1791]$ (GRH)
18.0.3830034706318154794675914145792.1	x^18 - 2x^17 + 36x^16 - 124x^15 + 667x^14 - 2334x^13 + 8164x^12 - 20338x^11 + 54321x^10 - 96972x^9 + 150518x^8 - 244982x^7 + 834376x^6 - 2158328x^5 + 4885022x^4 - 8338866x^3 + 13279313x^2 - 14690014x + 10525279	\( -\,2^{18}\cdot 19^{16}\cdot 37^{3} \)	$C_2\times C_2^2:C_9$ (as 18T26)	$[2, 2, 570]$ (GRH)
18.0.3830034706318154794675914145792.2	x^18 + 46x^16 + 875x^14 + 8918x^12 + 52728x^10 + 183435x^8 + 367668x^6 + 408591x^4 + 229992x^2 + 50653	\( -\,2^{18}\cdot 19^{16}\cdot 37^{3} \)	18T264	$[2, 2, 468]$ (GRH)
18.0.5165866906776180186538815258624.1	x^18 + 36x^16 + 525x^14 + 4014x^12 + 17550x^10 + 45426x^8 + 69728x^6 + 61395x^4 + 28116x^2 + 5041	\( -\,2^{18}\cdot 3^{24}\cdot 7^{12}\cdot 71^{2} \)	18T263	$[2, 2, 2, 160]$ (GRH)
18.0.5532813802997213476490534191104.1	x^18 + 48x^16 + 867x^14 + 8006x^12 + 42207x^10 + 132831x^8 + 251956x^6 + 280899x^4 + 168873x^2 + 42121	\( -\,2^{18}\cdot 3^{24}\cdot 73^{3}\cdot 577^{3} \)	18T767	$[2, 1252]$ (GRH)
18.0.7053072320828130442597556717031.1	x^18 - 3x^17 + 45x^16 - 70x^15 + 768x^14 - 195x^13 + 7003x^12 + 6999x^11 + 44889x^10 + 82138x^9 + 231111x^8 + 417480x^7 + 847530x^6 + 1108374x^5 + 1683297x^4 + 1332753x^3 + 931392x^2 - 168924x + 112589	\( -\,3^{24}\cdot 7^{12}\cdot 71^{5} \)	$C_2\times A_4^2$ (as 18T109)	$[2, 2, 2, 170]$ (GRH)
18.0.7521294167081161111736000000000.1	x^18 - 3x^17 - 9x^16 + 46x^15 + 39x^14 - 449x^13 + 87x^12 + 3323x^11 - 5496x^10 - 10508x^9 + 47263x^8 - 31209x^7 - 119189x^6 + 233575x^5 - 20211x^4 - 344955x^3 + 416495x^2 - 217450x + 52025	\( -\,2^{12}\cdot 5^{9}\cdot 7^{9}\cdot 13^{12} \)	$S_3 \times C_3$ (as 18T3)	$[2, 14, 42]$ (GRH)
18.0.9217661592820801741280239766571.4	x^18 - 9x^17 + 33x^16 - 52x^15 + 84x^14 - 540x^13 + 3178x^12 - 11892x^11 + 36576x^10 - 94398x^9 + 242916x^8 - 534324x^7 + 1183880x^6 - 2079090x^5 + 3606933x^4 - 4490689x^3 + 5618562x^2 - 3981963x + 3180563	\( -\,3^{24}\cdot 7^{12}\cdot 11^{9} \)	$C_6 \times C_3$ (as 18T2)	$[36, 36]$ (GRH)
18.0.9490397425838961457555240648704.1	x^18 + 42x^16 + 693x^14 + 5880x^12 + 28224x^10 + 79380x^8 + 130536x^6 + 120393x^4 + 55566x^2 + 9261	\( -\,2^{18}\cdot 3^{27}\cdot 7^{15} \)	$C_6 \times C_3$ (as 18T2)	$[2, 2, 2, 182]$ (GRH)
18.0.11088656920413061413017818359375.2	x^18 - 7x^17 + 40x^16 - 154x^15 + 627x^14 - 1979x^13 + 6508x^12 - 16865x^11 + 47380x^10 - 103535x^9 + 254065x^8 - 459765x^7 + 999805x^6 - 1439914x^5 + 2800752x^4 - 2907231x^3 + 5123532x^2 - 2913750x + 4775041	\( -\,3^{9}\cdot 5^{9}\cdot 19^{16} \)	$C_{18}$ (as 18T1)	$[3258]$ (GRH)
18.0.12065345096686615429034956292096.1	x^18 + 48x^16 + 873x^14 + 8175x^12 + 43777x^10 + 137970x^8 + 250326x^6 + 242159x^4 + 106935x^2 + 16361	\( -\,2^{30}\cdot 37^{6}\cdot 16361^{3} \)	18T837	$[4, 560]$ (GRH)
18.0.13944985186220076513047292273231.1	x^18 - 3x^17 + 13x^16 - 14x^15 + 49x^14 - 22x^13 - 184x^12 - 344x^11 + 2538x^10 - 15190x^9 + 54562x^8 - 33440x^7 + 69570x^6 - 112288x^5 + 224883x^4 - 115871x^3 + 162369x^2 - 11584x + 215851	\( -\,3^{9}\cdot 7^{12}\cdot 13^{15} \)	$C_6 \times C_3$ (as 18T2)	$[2, 2, 2, 2, 76]$ (GRH)
18.0.14166424145858741301073711988736.4	x^18 - 6x^17 + 39x^16 - 146x^15 + 609x^14 - 1806x^13 + 5568x^12 - 12930x^11 + 30840x^10 - 58068x^9 + 121791x^8 - 196452x^7 + 321467x^6 - 380358x^5 + 651183x^4 - 775582x^3 + 1625814x^2 - 1190916x + 1075033	\( -\,2^{27}\cdot 3^{27}\cdot 7^{12} \)	$C_6 \times C_3$ (as 18T2)	$[2, 18, 54]$ (GRH)
18.0.16528519607100378938441688416256.1	x^18 + 57x^16 + 1314x^14 + 15789x^12 + 106527x^10 + 406209x^8 + 836429x^6 + 820710x^4 + 272034x^2 + 16129	\( -\,2^{18}\cdot 3^{24}\cdot 7^{12}\cdot 127^{2} \)	18T263	$[2, 2, 2, 252]$ (GRH)
18.0.17656106622712745392937787195392.1	x^18 + 61x^16 + 1420x^14 + 16587x^12 + 107327x^10 + 402576x^8 + 882073x^6 + 1091004x^4 + 689157x^2 + 169457	\( -\,2^{18}\cdot 7^{12}\cdot 169457^{3} \)	18T765	$[2, 2176]$ (GRH)
18.0.26953746805951287370186752000000.1	x^18 + 24x^16 + 243x^14 + 1359x^12 + 4617x^10 + 9864x^8 + 13230x^6 + 10719x^4 + 4743x^2 + 867	\( -\,2^{30}\cdot 3^{33}\cdot 5^{6}\cdot 17^{2} \)	18T366	$[2, 2, 340]$ (GRH)
18.0.28277592430157040563214702870528.1	x^18 + 57x^16 + 1368x^14 + 17955x^12 + 140049x^10 + 660231x^8 + 1828332x^6 + 2742498x^4 + 1869885x^2 + 373977	\( -\,2^{18}\cdot 3^{9}\cdot 19^{17} \)	$C_{18}$ (as 18T1)	$[2, 2786]$ (GRH)
18.0.31329007244264248949886964450839.1	x^18 + 54x^16 + 1215x^14 + 14742x^12 + 104247x^10 - 1810x^9 + 433026x^8 - 48870x^7 + 1010394x^6 - 439830x^5 + 1180980x^4 - 1466100x^3 + 531441x^2 - 1319490x + 3335149	\( -\,3^{45}\cdot 13^{9} \)	$C_{18}$ (as 18T1)	$[2524]$ (GRH)
18.0.31616164379840194492072800177879.3	x^18 - 15x^16 - 6x^15 + 162x^14 + 192x^13 - 1032x^12 - 3222x^11 + 2442x^10 + 28042x^9 + 34182x^8 - 85296x^7 - 251841x^6 - 140562x^5 + 260853x^4 + 730068x^3 + 946224x^2 + 563136x + 123904	\( -\,3^{31}\cdot 13^{15} \)	$S_3 \times C_6$ (as 18T6)	$[3, 468]$ (GRH)
18.0.42902765942005709994121149284352.1	x^18 + 36x^16 + 484x^14 + 3305x^12 + 12769x^10 + 28966x^8 + 38380x^6 + 28335x^4 + 10332x^2 + 1323	\( -\,2^{18}\cdot 3^{9}\cdot 7^{6}\cdot 643^{6} \)	18T632	$[2, 2, 2, 240]$ (GRH)
18.0.43281927256346630219321487392768.1	x^18 - 6x^17 + 21x^16 - 66x^15 + 297x^14 - 742x^13 + 1346x^12 - 4058x^11 + 9676x^10 - 2428x^9 + 22175x^8 - 86316x^7 - 133405x^6 - 23318x^5 + 742493x^4 + 1890250x^3 + 3195846x^2 + 1805644x + 966337	\( -\,2^{27}\cdot 7^{12}\cdot 13^{12} \)	$C_6 \times C_3$ (as 18T2)	$[4, 268]$ (GRH)
18.0.51906361512443096981169273175191.1	x^18 - 3x^17 + 8x^16 + 12x^15 + 181x^14 - 201x^13 + 554x^12 + 4448x^11 + 1722x^10 - 19194x^9 + 21415x^8 + 61786x^7 - 43679x^6 - 81955x^5 + 216263x^4 + 55577x^3 - 55738x^2 - 11032x + 352312	\( -\,3^{9}\cdot 13^{15}\cdot 61^{6} \)	$S_3 \times C_6$ (as 18T6)	$[2, 2, 2, 140]$ (GRH)
18.0.58116758997176374949719154916247.1	x^18 - x^17 + 58x^16 - 58x^15 + 1426x^14 - 1426x^13 + 19381x^12 - 19381x^11 + 159430x^10 - 159430x^9 + 819661x^8 - 819661x^7 + 2647993x^6 - 2647993x^5 + 5390491x^4 - 5390491x^3 + 7260376x^2 - 7260376x + 7634353	\( -\,13^{9}\cdot 19^{17} \)	$C_{18}$ (as 18T1)	$[9774]$ (GRH)
18.0.60940886311952006474852072423424.2	x^18 + 48x^16 + 828x^14 + 6972x^12 + 31500x^10 + 77112x^8 + 96516x^6 + 52272x^4 + 8208x^2 + 216	\( -\,2^{33}\cdot 3^{21}\cdot 7^{14} \)	$S_3 \times C_6$ (as 18T6)	$[3, 3, 126]$ (GRH)
18.0.89156963198142398832050176000000.1	x^18 + 38x^16 + 609x^14 + 5357x^12 + 28133x^10 + 89540x^8 + 166180x^6 + 159887x^4 + 57967x^2 + 2401	\( -\,2^{30}\cdot 5^{6}\cdot 7^{4}\cdot 19^{12} \)	18T175	$[2, 1120]$ (GRH)
18.0.119665574759900159778264689410048.1	x^18 + 37x^16 + 518x^14 + 3515x^12 + 12284x^10 + 22200x^8 + 20683x^6 + 9287x^4 + 1591x^2 + 37	\( -\,2^{18}\cdot 37^{17} \)	$C_{18}$ (as 18T1)	$[1526]$ (GRH)
18.0.147682003746622037852672000000000.1	x^18 - 2x^17 + 30x^16 - 50x^15 + 552x^14 - 814x^13 + 6983x^12 - 8936x^11 + 65641x^10 - 72082x^9 + 465597x^8 - 424984x^7 + 2471666x^6 - 1778572x^5 + 9429355x^4 - 4814010x^3 + 23461605x^2 - 6474360x + 29134601	\( -\,2^{18}\cdot 5^{9}\cdot 19^{16} \)	$C_{18}$ (as 18T1)	$[8582]$ (GRH)
18.0.179966054889983269121047526375424.4	x^18 + 24x^16 - 6x^15 + 387x^14 + 6x^13 + 3941x^12 - 36x^11 + 28167x^10 + 5912x^9 + 163782x^8 + 50502x^7 + 623048x^6 + 233514x^5 + 2503317x^4 + 2370846x^3 + 8823831x^2 + 5384334x + 8256151	\( -\,2^{27}\cdot 3^{24}\cdot 7^{15} \)	$C_6 \times C_3$ (as 18T2)	$[2, 18, 252]$ (GRH)
18.0.185723426137096770687205679300608.1	x^18 - 6x^17 + 42x^16 - 162x^15 + 666x^14 - 1946x^13 + 5146x^12 - 10402x^11 + 17101x^10 - 23298x^9 + 62720x^8 - 128674x^7 + 171273x^6 - 132222x^5 + 221722x^4 - 340356x^3 + 777688x^2 - 587872x + 444536	\( -\,2^{18}\cdot 7^{12}\cdot 13^{15} \)	$C_6 \times C_3$ (as 18T2)	$[2, 2, 2, 18, 18]$ (GRH)
18.0.216033383169661016512360513671875.3	x^18 - 3x^17 + x^16 - x^15 + 124x^14 + 20x^13 - 15x^12 - 355x^11 + 4994x^10 + 14123x^9 + 44804x^8 + 14520x^7 + 74956x^6 - 52128x^5 + 378444x^4 + 597223x^3 + 2217367x^2 + 2753785x + 3521939	\( -\,5^{9}\cdot 7^{15}\cdot 13^{12} \)	$C_6 \times C_3$ (as 18T2)	$[6, 6, 78]$ (GRH)
18.0.216258353745310739104685841788928.3	x^18 + 36x^16 - 60x^15 + 468x^14 - 1440x^13 + 6276x^12 - 11160x^11 + 48168x^10 - 58400x^9 + 171936x^8 - 208800x^7 + 440208x^6 - 303840x^5 + 590976x^4 + 188640x^3 + 451008x^2 + 1259712	\( -\,2^{12}\cdot 3^{24}\cdot 83^{9} \)	$S_3 \times C_3$ (as 18T3)	$[2, 2, 2, 126]$ (GRH)
18.0.250219943963063581133732413702144.1	x^18 + 56x^16 + 1174x^14 + 11479x^12 + 53662x^10 + 118116x^8 + 128427x^6 + 68376x^4 + 16428x^2 + 1369	\( -\,2^{26}\cdot 37^{8}\cdot 101^{6} \)	18T461	$[2, 2, 326]$ (GRH)
18.0.265529453168247662686860141155127.2	x^18 - 3x^17 - 24x^16 + 80x^15 + 264x^14 - 996x^13 - 208x^12 + 3414x^11 - 1398x^10 - 4424x^9 + 45528x^8 - 108612x^7 + 306560x^6 - 431268x^5 + 994161x^4 - 776387x^3 + 1606332x^2 - 619836x + 1068904	\( -\,3^{24}\cdot 7^{9}\cdot 13^{12} \)	$C_6 \times C_3$ (as 18T2)	$[4, 532]$ (GRH)
18.0.317773455265378312682733715471299.2	x^18 - 9x^17 + 63x^16 - 300x^15 + 1368x^14 - 5040x^13 + 18192x^12 - 54630x^11 + 164196x^10 - 411866x^9 + 1056267x^8 - 2200338x^7 + 4844985x^6 - 8116569x^5 + 15278400x^4 - 19032684x^3 + 30278943x^2 - 21799593x + 28658393	\( -\,3^{44}\cdot 19^{9} \)	$C_{18}$ (as 18T1)	$[2, 3746]$ (GRH)
18.0.346995740849617491120493646484375.1	x^18 - 6x^17 + 9x^16 + 10x^15 + 48x^14 - 84x^13 - 486x^12 + 372x^11 + 3765x^10 + 6720x^9 + 26967x^8 - 27264x^7 + 6863x^6 - 52260x^5 + 123351x^4 + 147158x^3 + 602835x^2 + 711594x + 1307431	\( -\,3^{27}\cdot 5^{9}\cdot 13^{12} \)	$C_6 \times C_3$ (as 18T2)	$[2, 14, 98]$ (GRH)
18.0.374995864672776683690097475584000.1	x^18 + 45x^16 + 708x^14 + 5093x^12 + 18705x^10 + 36303x^8 + 37039x^6 + 19110x^4 + 4500x^2 + 375	\( -\,2^{18}\cdot 3^{27}\cdot 5^{3}\cdot 107^{6} \)	18T175	$[2, 2, 2, 182]$ (GRH)
18.0.374995864672776683690097475584000.2	x^18 + 27x^16 + 300x^14 + 1790x^12 + 6291x^10 + 13431x^8 + 17229x^6 + 12465x^4 + 4275x^2 + 375	\( -\,2^{18}\cdot 3^{27}\cdot 5^{3}\cdot 107^{6} \)	18T367	$[2, 2, 2, 308]$ (GRH)
18.0.426586204183664045323964506963968.6	x^18 + 48x^16 + 960x^14 + 10380x^12 + 65808x^10 + 247680x^8 + 531252x^6 + 576072x^4 + 226800x^2 + 1512	\( -\,2^{33}\cdot 3^{21}\cdot 7^{15} \)	$S_3 \times C_6$ (as 18T6)	$[2, 1638]$ (GRH)
18.0.497863107144137244036834347537287.1	x^18 - 7x^17 + 6x^16 + 62x^15 - 87x^14 - 453x^13 + 1582x^12 - 2109x^11 + 4032x^10 - 13245x^9 + 41381x^8 - 73223x^7 + 125132x^6 - 153409x^5 + 331388x^4 - 449504x^3 + 758771x^2 - 538288x + 477047	\( -\,7^{9}\cdot 37^{16} \)	$C_{18}$ (as 18T1)	$[9, 171]$ (GRH)
18.0.526677118301850649055916906437559.2	x^18 + 36x^16 - 15x^15 + 486x^14 - 315x^13 + 3642x^12 - 2025x^11 + 16344x^10 - 1415x^9 + 43740x^8 + 17055x^7 + 96036x^6 + 44955x^5 + 143037x^4 + 65865x^3 + 93636x^2 + 52020x + 39304	\( -\,3^{39}\cdot 37^{9} \)	$S_3 \times C_3$ (as 18T3)	$[2, 14, 56]$ (GRH)
18.0.591675863121548288056467444989952.1	x^18 + 18x^16 - 44x^15 + 234x^14 - 204x^13 + 614x^12 - 2664x^11 + 24636x^10 - 67840x^9 + 228168x^8 - 423168x^7 + 827536x^6 - 1017216x^5 + 1105152x^4 - 712448x^3 + 258048x^2 - 49152x + 8192	\( -\,2^{26}\cdot 3^{24}\cdot 23^{3}\cdot 37^{6} \)	18T228	$[2, 522]$ (GRH)
18.0.591706382841388634460616841610087.1	x^18 - 9x^17 + 32x^16 - 52x^15 + 468x^14 - 3080x^13 + 9624x^12 - 17418x^11 + 52764x^10 - 178658x^9 + 328020x^8 - 303784x^7 + 59180x^6 + 192540x^5 - 234155x^4 + 122397x^3 + 27498x^2 - 55368x + 36072	\( -\,3^{9}\cdot 7^{12}\cdot 109^{9} \)	$C_3^2 : C_2$ (as 18T4)	$[2, 18, 36]$ (GRH)
18.0.648099416547998746795472637325312.1	x^18 - 3x^17 - 18x^16 + 14x^15 + 269x^14 + 227x^13 - 1018x^12 - 2013x^11 + 4834x^10 + 14595x^9 + 19966x^8 + 34739x^7 + 153456x^6 + 301625x^5 + 410031x^4 + 401368x^3 + 783486x^2 + 990627x + 869143	\( -\,2^{12}\cdot 7^{9}\cdot 11^{6}\cdot 19^{12} \)	$S_3 \times C_6$ (as 18T6)	$[2, 2, 884]$ (GRH)
18.0.691304233720361896816117357477888.1	x^18 + 7x^16 - 46x^15 + 314x^14 - 784x^13 + 1633x^12 - 8962x^11 + 34964x^10 + 25180x^9 - 53723x^8 + 135014x^7 + 552807x^6 - 1492424x^5 + 3232214x^4 - 3603978x^3 + 3591174x^2 - 1826896x + 994969	\( -\,2^{18}\cdot 13^{15}\cdot 61^{6} \)	$S_3 \times C_6$ (as 18T6)	$[2, 2224]$ (GRH)
18.0.699527696599455687770027884019712.2	x^18 + 41x^16 + 533x^14 + 3209x^12 + 10264x^10 + 18280x^8 + 18027x^6 + 9423x^4 + 2430x^2 + 243	\( -\,2^{18}\cdot 3^{9}\cdot 53^{4}\cdot 107^{8} \)	18T881	$[1666]$ (GRH)
18.0.718606633367888171454789870996879.2	x^18 - 18x^16 - 54x^15 + 117x^14 + 648x^13 + 2301x^12 - 2511x^11 - 14661x^10 - 10260x^9 + 29970x^8 + 48843x^7 + 71814x^6 - 44469x^5 - 107280x^4 + 185679x^3 + 56880x^2 + 512000	\( -\,3^{24}\cdot 239^{9} \)	$S_3 \times C_3$ (as 18T3)	$[3, 3, 3, 45]$ (GRH)
18.0.760380330951008959273099338892571.1	x^18 - 3x^17 - 11x^16 + 24x^15 + 202x^14 - 266x^13 + 338x^12 - 612x^11 + 9498x^10 - 7614x^9 + 87170x^8 + 3818x^7 + 549956x^6 + 100280x^5 + 2351913x^4 - 160053x^3 + 6350272x^2 - 399099x + 7656713	\( -\,7^{12}\cdot 11^{9}\cdot 13^{12} \)	$C_6 \times C_3$ (as 18T2)	$[14, 182]$ (GRH)
18.0.781241669227223662759334318964736.1	x^18 + 35x^16 + 427x^14 + 2567x^12 + 8760x^10 + 18018x^8 + 22621x^6 + 16835x^4 + 6774x^2 + 1129	\( -\,2^{18}\cdot 1129^{9} \)	18T375	$[2, 1372]$ (GRH)

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