Number field search results

Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)

Results (1-50 of 2432 matches)

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Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Narrow class group	Unit group torsion	Unit group rank	Regulator
6.0.434124812919959.1	$x^{6} - 2 x^{5} + 130 x^{4} + 1156 x^{3} + 21805 x^{2} + 120742 x + 431736$	$6$	[0,3]	$-\,7^{3}\cdot 29^{3}\cdot 373^{3}$	$3$	$275.170856015$	$275.1708560149494$		✓		$S_3$ (as 6T2)	$[172, 1204]$	$[172, 1204]$	$2$	$2$	$134.7953465601386$
6.0.1196113162160951.1	$x^{6} - 2 x^{5} + 84 x^{4} - 1318 x^{3} + 29495 x^{2} - 104328 x + 407844$	$6$	[0,3]	$-\,101^{3}\cdot 1051^{3}$	$2$	$325.808225802$	$325.8082258016209$		✓		$S_3$ (as 6T2)	$[31, 3286]$	$[31, 3286]$	$2$	$2$	$301.88150706410164$
6.0.1230408947652416.4	$x^{6} - 2 x^{5} - 9 x^{4} - 550 x^{3} + 27374 x^{2} - 211512 x + 507024$	$6$	[0,3]	$-\,2^{6}\cdot 7^{3}\cdot 43^{3}\cdot 89^{3}$	$4$	$327.346910784$	$327.34691078426266$		✓		$S_3$ (as 6T2)	$[2, 2, 2, 42, 378]$	$[2, 2, 2, 42, 378]$	$2$	$2$	$63.88445725995891$
6.0.3735924498042463.1	$x^{6} - 231 x^{4} - 6 x^{3} + 52132 x^{2} - 464808 x + 1396512$	$6$	[0,3]	$-\,155167^{3}$	$1$	$393.912426816$	$393.91242681591046$		✓		$S_3$ (as 6T2)	$[44, 2948]$	$[44, 2948]$	$2$	$2$	$104.62436771857402$
6.0.4292283249804096.1	$x^{6} - 20 x^{4} - 1590 x^{3} + 40729 x^{2} - 390390 x + 1647750$	$6$	[0,3]	$-\,2^{6}\cdot 3^{3}\cdot 29^{3}\cdot 467^{3}$	$4$	$403.132732484$	$403.1327324839798$		✓		$S_3$ (as 6T2)	$[2, 82, 656]$	$[2, 82, 656]$	$2$	$2$	$108.14590866828806$
6.0.5929249598574875.1	$x^{6} + 352 x^{4} + 30976 x^{2} + 1628955$	$6$	[0,3]	$-\,5^{3}\cdot 53^{3}\cdot 683^{3}$	$3$	$425.435071427$	$425.43507142688645$		✓		$S_3$ (as 6T2)	$[2, 2, 48, 720]$	$[2, 2, 48, 720]$	$2$	$2$	$57.57360158722312$
6.0.6504017544722944.1	$x^{6} + 186 x^{4} + 8649 x^{2} + 186664$	$6$	[0,3]	$-\,2^{9}\cdot 23333^{3}$	$2$	$432.046293816$	$432.04629381583635$		✓		$S_3$ (as 6T2)	$[2, 46, 1150]$	$[2, 46, 1150]$	$2$	$2$	$75.53117556085728$
6.0.6591269545312375.1	$x^{6} + 202 x^{4} + 10201 x^{2} + 749980$	$6$	[0,3]	$-\,5^{3}\cdot 7^{3}\cdot 11^{3}\cdot 487^{3}$	$4$	$433.006928351$	$433.0069283510369$		✓		$S_3$ (as 6T2)	$[2, 82, 902]$	$[2, 82, 902]$	$2$	$2$	$246.36990146833654$
6.0.6697296155387375.1	$x^{6} + 282 x^{4} + 19881 x^{2} + 753980$	$6$	[0,3]	$-\,5^{3}\cdot 37699^{3}$	$2$	$434.160108716$	$434.16010871566726$		✓		$S_3$ (as 6T2)	$[2, 34, 3400]$	$[2, 34, 3400]$	$2$	$2$	$177.6737007414822$
6.0.6756306913606823.1	$x^{6} + 107 x^{4} - 1120 x^{3} + 50124 x^{2} - 59920 x + 313600$	$6$	[0,3]	$-\,79^{3}\cdot 2393^{3}$	$2$	$434.795354161$	$434.79535416101214$		✓		$S_3$ (as 6T2)	$[4, 28, 952]$	$[4, 28, 952]$	$2$	$2$	$218.34880336343033$
6.0.7167176823334464.1	$x^{6} - 2 x^{5} - 113 x^{4} - 1002 x^{3} + 52566 x^{2} - 514800 x + 2046600$	$6$	[0,3]	$-\,2^{6}\cdot 3^{3}\cdot 16067^{3}$	$3$	$439.094522854$	$439.0945228535651$		✓		$S_3$ (as 6T2)	$[106, 1802]$	$[106, 1802]$	$2$	$2$	$115.18606330955983$
6.0.7381046301066927.1	$x^{6} + 199 x^{4} - 1536 x^{3} + 58576 x^{2} - 152832 x + 589824$	$6$	[0,3]	$-\,3^{3}\cdot 64901^{3}$	$2$	$441.251628892$	$441.25162889217756$		✓		$S_3$ (as 6T2)	$[2, 2, 6, 18, 270]$	$[2, 2, 6, 18, 270]$	$2$	$2$	$284.5458713951712$
6.0.8234453780075375.1	$x^{6} - 42 x^{4} + 441 x^{2} + 3230960$	$6$	[0,3]	$-\,5^{3}\cdot 40387^{3}$	$2$	$449.371783716$	$449.3717837158893$		✓		$S_3$ (as 6T2)	$[2, 2, 2, 18, 1674]$	$[2, 2, 2, 18, 1674]$	$2$	$2$	$154.85770406822115$
6.0.8556758507142656.1	$x^{6} - 2 x^{5} - 155 x^{4} + 1180 x^{3} + 56194 x^{2} - 284408 x + 466680$	$6$	[0,3]	$-\,2^{9}\cdot 37^{3}\cdot 691^{3}$	$3$	$452.256564353$	$452.2565643525807$		✓		$S_3$ (as 6T2)	$[2, 2, 74, 2294]$	$[2, 2, 74, 2294]$	$2$	$2$	$77.48434323062678$
6.0.9691389429113664.1	$x^{6} - 2 x^{5} + 107 x^{4} + 2290 x^{3} + 53714 x^{2} + 340192 x + 1648408$	$6$	[0,3]	$-\,2^{6}\cdot 3^{3}\cdot 109^{3}\cdot 163^{3}$	$4$	$461.740186685$	$461.74018668510973$		✓		$S_3$ (as 6T2)	$[2, 2, 2, 40, 440]$	$[2, 2, 2, 40, 440]$	$2$	$2$	$221.9117894285191$
6.0.9990203924970304.1	$x^{6} - 2 x^{5} - 129 x^{4} - 2850 x^{3} + 204234 x^{2} - 2170648 x + 9313144$	$6$	[0,3]	$-\,2^{6}\cdot 7^{4}\cdot 4021^{3}$	$3$	$464.083070157$	$464.08307015660216$		✓		$S_3$ (as 6T2)	$[2, 26, 2418]$	$[2, 26, 2418]$	$2$	$2$	$95.84647397862258$
6.0.10354387647305079.1	$x^{6} - 2 x^{5} + 106 x^{4} - 3144 x^{3} + 60285 x^{2} - 486486 x + 2799288$	$6$	[0,3]	$-\,3^{3}\cdot 7^{3}\cdot 97^{3}\cdot 107^{3}$	$4$	$466.860792957$	$466.86079295653$		✓		$S_3$ (as 6T2)	$[2, 2, 2, 56, 1064]$	$[2, 2, 2, 56, 1064]$	$2$	$2$	$141.07909034336527$
6.0.10741052552777119.1	$x^{6} - 105 x^{4} - 92 x^{3} + 57916 x^{2} - 436448 x + 884672$	$6$	[0,3]	$-\,23^{3}\cdot 53^{3}\cdot 181^{3}$	$3$	$469.722258361$	$469.72225836125756$		✓		$S_3$ (as 6T2)	$[2, 2, 34, 986]$	$[2, 2, 34, 986]$	$2$	$2$	$119.51111985989868$
6.0.10796058994178375.1	$x^{6} + 178 x^{4} + 7921 x^{2} + 884060$	$6$	[0,3]	$-\,5^{3}\cdot 44203^{3}$	$2$	$470.122324507$	$470.12232450714356$		✓		$S_3$ (as 6T2)	$[49, 4606]$	$[49, 4606]$	$2$	$2$	$97.01604594569513$
6.0.11326956495912000.1	$x^{6} + 292 x^{4} + 21316 x^{2} + 898320$	$6$	[0,3]	$-\,2^{6}\cdot 3^{3}\cdot 5^{3}\cdot 19^{3}\cdot 197^{3}$	$5$	$473.898723358$	$473.8987233576389$		✓		$S_3$ (as 6T2)	$[2, 2, 126, 378]$	$[2, 2, 126, 378]$	$2$	$2$	$52.31802018506783$
6.0.11688197085904192.2	$x^{6} - 2 x^{5} + 12708 x^{4} - 16942 x^{3} + 53864983 x^{2} - 35912816 x + 76153126321$	$6$	[0,3]	$-\,2^{6}\cdot 7^{4}\cdot 19^{3}\cdot 223^{3}$	$4$	$476.3848274235706$	$476.3848274235706$	✓	✓	?	$C_6$ (as 6T1)	$[2, 2, 38, 684]$	$[2, 2, 38, 684]$	$2$	$2$	$2.1018187284902896$
6.0.13457495511656000.1	$x^{6} - 218 x^{4} + 11881 x^{2} + 2140740$	$6$	[0,3]	$-\,2^{6}\cdot 5^{3}\cdot 7^{3}\cdot 1699^{3}$	$4$	$487.708929588$	$487.70892958813045$		✓		$S_3$ (as 6T2)	$[2, 94, 1222]$	$[2, 94, 1222]$	$2$	$2$	$224.63884810155562$
6.0.13530938286500271.1	$x^{6} - 3 x^{5} - 765 x^{4} - 4317 x^{3} + 167112 x^{2} + 2342628 x + 8977968$	$6$	[0,3]	$-\,3^{9}\cdot 7^{4}\cdot 13^{3}\cdot 19^{4}$	$4$	$488.151527038$	$488.1515270376549$	✓	✓		$C_6$ (as 6T1)	$[4, 12, 4332]$	$[4, 12, 4332]$	$2$	$2$	$127.01361460330098$
6.0.13556180395584000.2	$x^{6} + 58 x^{4} + 841 x^{2} + 238440$	$6$	[0,3]	$-\,2^{9}\cdot 3^{3}\cdot 5^{3}\cdot 1987^{3}$	$4$	$488.303184507$	$488.30318450733046$		✓		$S_3$ (as 6T2)	$[2, 2, 4, 48, 144]$	$[2, 2, 4, 48, 144]$	$2$	$2$	$86.51521701062532$
6.0.14053352827968000.1	$x^{6} - 2 x^{5} - 127 x^{4} + 2776 x^{3} + 61778 x^{2} + 71848 x + 1994296$	$6$	[0,3]	$-\,2^{9}\cdot 3^{3}\cdot 5^{3}\cdot 2011^{3}$	$4$	$491.243320565$	$491.2433205652775$		✓		$S_3$ (as 6T2)	$[2, 110, 660]$	$[2, 110, 660]$	$2$	$2$	$88.01975207185744$
6.0.14473801966789927.1	$x^{6} + 219 x^{4} - 2880 x^{3} + 72916 x^{2} - 315360 x + 2073600$	$6$	[0,3]	$-\,243703^{3}$	$1$	$493.662840408$	$493.6628404083094$		✓		$S_3$ (as 6T2)	$[43, 3053]$	$[43, 3053]$	$2$	$2$	$148.14868432700314$
6.0.16697131399920699.1	$x^{6} - 3 x^{5} + 2760 x^{4} - 5445 x^{3} + 2614539 x^{2} - 2809182 x + 849218525$	$6$	[0,3]	$-\,3^{8}\cdot 7^{5}\cdot 13^{3}\cdot 41^{3}$	$4$	$505.5610930594331$	$505.5610930594331$	✓	✓		$C_6$ (as 6T1)	$[3, 6, 11886]$	$[3, 6, 11886]$	$2$	$2$	$16.806760168964384$
6.0.16921977457945664.2	$x^{6} + 11609 x^{4} + 20733674 x^{2} + 9257585441$	$6$	[0,3]	$-\,2^{6}\cdot 13^{5}\cdot 19^{3}\cdot 47^{3}$	$4$	$506.68943865842726$	$506.68943865842726$	✓	✓		$C_6$ (as 6T1)	$[2, 2, 2, 14, 1638]$	$[2, 2, 2, 14, 1638]$	$2$	$2$	$5.46019947037753$
6.0.17172651297819136.2	$x^{6} + 17626 x^{4} + 88764536 x^{2} + 111754550824$	$6$	[0,3]	$-\,2^{9}\cdot 7^{5}\cdot 1259^{3}$	$3$	$507.93276108108995$	$507.93276108108995$	✓	✓	?	$C_6$ (as 6T1)	$[2, 6, 6, 1830]$	$[2, 6, 6, 1830]$	$2$	$2$	$2.1018187284902896$
6.0.19257452166464000.3	$x^{6} + 86 x^{4} - 3552 x^{3} + 68859 x^{2} - 554796 x + 3757266$	$6$	[0,3]	$-\,2^{9}\cdot 5^{3}\cdot 6701^{3}$	$3$	$517.725796151$	$517.7257961508196$		✓		$S_3$ (as 6T2)	$[2, 2, 54, 1134]$	$[2, 2, 54, 1134]$	$2$	$2$	$143.93004661741952$
6.0.19323478649664000.2	$x^{6} - 2 x^{5} + 15027 x^{4} - 20034 x^{3} + 75310322 x^{2} - 50210224 x + 125877031561$	$6$	[0,3]	$-\,2^{9}\cdot 3^{3}\cdot 5^{3}\cdot 7^{4}\cdot 167^{3}$	$5$	$518.0212218812186$	$518.0212218812186$	✓	✓	?	$C_6$ (as 6T1)	$[2, 2, 2, 2, 10836]$	$[2, 2, 2, 2, 10836]$	$2$	$2$	$2.1018187284902896$
6.0.19371479668946432.1	$x^{6} - 2 x^{5} + 77 x^{4} - 1804 x^{3} + 70314 x^{2} - 65664 x + 746496$	$6$	[0,3]	$-\,2^{9}\cdot 59^{3}\cdot 569^{3}$	$3$	$518.235467717$	$518.2354677171372$		✓		$S_3$ (as 6T2)	$[6, 6, 48, 144]$	$[6, 6, 48, 144]$	$2$	$2$	$113.81046897747618$
6.0.20196089557410375.4	$x^{6} - 3 x^{5} - 1791 x^{4} - 16881 x^{3} + 843462 x^{2} + 17882964 x + 98667864$	$6$	[0,3]	$-\,3^{9}\cdot 5^{3}\cdot 7^{4}\cdot 43^{4}$	$4$	$521.848630382$	$521.8486303816346$	✓	✓		$C_6$ (as 6T1)	$[2, 2, 2, 6, 2382]$	$[2, 2, 2, 6, 2382]$	$2$	$2$	$265.3617536785364$
6.0.21206090047385088.4	$x^{6} + 130 x^{4} + 4225 x^{2} + 2491128$	$6$	[0,3]	$-\,2^{9}\cdot 3^{3}\cdot 19^{3}\cdot 607^{3}$	$4$	$526.110254604$	$526.1102546044888$		✓		$S_3$ (as 6T2)	$[18, 90, 90]$	$[18, 90, 90]$	$2$	$2$	$138.68163400435773$
6.0.23614494625920375.1	$x^{6} - 3 x^{5} - 1863 x^{4} - 10041 x^{3} + 899622 x^{2} + 12195684 x + 44428536$	$6$	[0,3]	$-\,3^{9}\cdot 5^{3}\cdot 313^{4}$	$3$	$535.627799662$	$535.627799662383$	✓	✓		$C_6$ (as 6T1)	$[2, 2, 2, 16, 912]$	$[2, 2, 2, 16, 912]$	$2$	$2$	$204.75036004382392$
6.0.24269941493035184.2	$x^{6} - 2 x^{5} + 189 x^{4} - 1648 x^{3} + 125195 x^{2} + 1011750 x + 3405375$	$6$	[0,3]	$-\,2^{4}\cdot 89^{3}\cdot 1291^{3}$	$3$	$538.077445563$	$538.077445563129$		✓		$S_3$ (as 6T2)	$[63, 2520]$	$[63, 2520]$	$2$	$2$	$87.41318768101202$
6.0.24516380321944064.2	$x^{6} - 2 x^{5} + 165 x^{4} + 3212 x^{3} + 75974 x^{2} + 567336 x + 3139848$	$6$	[0,3]	$-\,2^{9}\cdot 36313^{3}$	$2$	$538.984229825$	$538.984229824955$		✓		$S_3$ (as 6T2)	$[2, 38, 1900]$	$[2, 38, 1900]$	$2$	$2$	$173.52673656496034$
6.0.24895041720063488.1	$x^{6} - 2 x^{5} + 269 x^{4} - 5164 x^{3} + 95850 x^{2} - 656064 x + 5992704$	$6$	[0,3]	$-\,2^{9}\cdot 17^{3}\cdot 19^{3}\cdot 113^{3}$	$4$	$540.362841061$	$540.3628410614483$		✓		$S_3$ (as 6T2)	$[2, 98, 1078]$	$[2, 98, 1078]$	$2$	$2$	$160.24547544000745$
6.0.27056588409536000.2	$x^{6} + 20510 x^{4} + 120188600 x^{2} + 176076299000$	$6$	[0,3]	$-\,2^{9}\cdot 5^{3}\cdot 7^{5}\cdot 293^{3}$	$4$	$547.9137162458014$	$547.9137162458014$	✓	✓	?	$C_6$ (as 6T1)	$[2, 2, 8, 72, 144]$	$[2, 2, 8, 72, 144]$	$2$	$2$	$2.1018187284902896$
6.0.28851959379246912.1	$x^{6} - 2 x^{5} - 113 x^{4} + 942 x^{3} + 79098 x^{2} + 872928 x + 2931768$	$6$	[0,3]	$-\,2^{6}\cdot 3^{3}\cdot 61^{3}\cdot 419^{3}$	$4$	$553.812242552$	$553.8122425515709$		✓		$S_3$ (as 6T2)	$[2, 122, 976]$	$[2, 122, 976]$	$2$	$2$	$73.47516354166768$
6.0.31508983563080192.1	$x^{6} + 346 x^{4} + 29929 x^{2} + 2842632$	$6$	[0,3]	$-\,2^{9}\cdot 13^{3}\cdot 3037^{3}$	$3$	$562.003558708$	$562.0035587075939$		✓		$S_3$ (as 6T2)	$[2, 2, 68, 884]$	$[2, 2, 68, 884]$	$2$	$2$	$108.31250137952946$
6.0.32285191027713536.1	$x^{6} - 572 x^{4} + 81796 x^{2} + 56697696$	$6$	[0,3]	$-\,2^{9}\cdot 11^{4}\cdot 1627^{3}$	$3$	$564.287669055$	$564.2876690548468$		✓		$S_3$ (as 6T2)	$[2, 72, 936]$	$[2, 72, 936]$	$2$	$2$	$173.93419350219264$
6.0.32932935158150656.1	$x^{6} + 246 x^{4} - 1968 x^{3} + 95263 x^{2} - 722868 x + 1689462$	$6$	[0,3]	$-\,2^{9}\cdot 103^{3}\cdot 389^{3}$	$3$	$566.158988271$	$566.1589882709626$		✓		$S_3$ (as 6T2)	$[82, 1558]$	$[82, 1558]$	$2$	$2$	$102.43013100836534$
6.0.33038976568013559.1	$x^{6} - x^{5} + 1997 x^{4} - 4039 x^{3} + 1241402 x^{2} - 1239280 x + 188320768$	$6$	[0,3]	$-\,3^{3}\cdot 11^{3}\cdot 13^{5}\cdot 19^{5}$	$4$	$566.4624125303741$	$566.4624125303741$	✓	✓		$C_6$ (as 6T1)	$[2, 2, 2, 2, 8778]$	$[2, 2, 2, 2, 8778]$	$2$	$2$	$401.504315636586$
6.0.33595399126917711.1	$x^{6} - 2 x^{5} + 1678 x^{3} + 78991 x^{2} - 807516 x + 2719776$	$6$	[0,3]	$-\,3^{3}\cdot 59^{3}\cdot 1823^{3}$	$3$	$568.041371733$	$568.0413717327286$		✓		$S_3$ (as 6T2)	$[78, 3744]$	$[78, 3744]$	$2$	$2$	$530.3952835094761$
6.0.34970915843140096.1	$x^{6} + 412 x^{4} + 42436 x^{2} + 1308064$	$6$	[0,3]	$-\,2^{9}\cdot 41^{3}\cdot 997^{3}$	$3$	$571.853127997$	$571.8531279970408$		✓		$S_3$ (as 6T2)	$[82, 1230]$	$[82, 1230]$	$2$	$2$	$53.77771353305888$
6.0.35180787147158016.2	$x^{6} + 22386 x^{4} + 143180856 x^{2} + 228946188744$	$6$	[0,3]	$-\,2^{9}\cdot 3^{3}\cdot 7^{5}\cdot 13^{3}\cdot 41^{3}$	$5$	$572.4236809377272$	$572.4236809377272$	✓	✓	?	$C_6$ (as 6T1)	$[2, 2, 2, 2, 2, 6, 6, 156]$	$[2, 2, 2, 2, 2, 6, 6, 156]$	$2$	$2$	$2.1018187284902896$
6.0.35190747414720000.3	$x^{6} - 140 x^{4} + 4900 x^{2} + 3832800$	$6$	[0,3]	$-\,2^{9}\cdot 3^{3}\cdot 5^{4}\cdot 1597^{3}$	$4$	$572.4506882$	$572.4506882004093$		✓		$S_3$ (as 6T2)	$[3, 114, 570]$	$[3, 114, 570]$	$2$	$2$	$154.53439156675068$
6.0.35421663620873375.1	$x^{6} - 2 x^{5} + 46 x^{4} + 2244 x^{3} + 80321 x^{2} + 215710 x + 1391984$	$6$	[0,3]	$-\,5^{3}\cdot 19^{3}\cdot 3457^{3}$	$3$	$573.075038717$	$573.0750387165716$		✓		$S_3$ (as 6T2)	$[2, 2, 20, 1380]$	$[2, 2, 20, 1380]$	$2$	$2$	$1276.4647725437578$
6.0.35426840980886991.2	$x^{6} + 358 x^{4} + 32041 x^{2} + 5254896$	$6$	[0,3]	$-\,3^{3}\cdot 83^{3}\cdot 1319^{3}$	$3$	$573.088998324$	$573.088998323995$		✓		$S_3$ (as 6T2)	$[2, 2, 2, 2, 14, 700]$	$[2, 2, 2, 2, 14, 700]$	$2$	$2$	$1046.9526516251765$

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