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 795)

Label	Polynomial	Discriminant	Galois group	Class group
6.0.434124812919959.1	x^6 - 2x^5 + 130x^4 + 1156x^3 + 21805x^2 + 120742x + 431736	\( -\,7^{3}\cdot 29^{3}\cdot 373^{3} \)	$S_3$ (as 6T2)	$[172, 1204]$
6.0.1196113162160951.1	x^6 - 2x^5 + 84x^4 - 1318x^3 + 29495x^2 - 104328x + 407844	\( -\,101^{3}\cdot 1051^{3} \)	$S_3$ (as 6T2)	$[31, 3286]$
6.0.1230408947652416.4	x^6 - 2x^5 - 9x^4 - 550x^3 + 27374x^2 - 211512x + 507024	\( -\,2^{6}\cdot 7^{3}\cdot 43^{3}\cdot 89^{3} \)	$S_3$ (as 6T2)	$[2, 2, 2, 42, 378]$ (GRH)
6.0.3735924498042463.1	x^6 - 231x^4 - 6x^3 + 52132x^2 - 464808x + 1396512	\( -\,155167^{3} \)	$S_3$ (as 6T2)	$[44, 2948]$ (GRH)
6.0.4292283249804096.1	x^6 - 20x^4 - 1590x^3 + 40729x^2 - 390390x + 1647750	\( -\,2^{6}\cdot 3^{3}\cdot 29^{3}\cdot 467^{3} \)	$S_3$ (as 6T2)	$[2, 82, 656]$ (GRH)
6.0.5929249598574875.1	x^6 + 352x^4 + 30976x^2 + 1628955	\( -\,5^{3}\cdot 53^{3}\cdot 683^{3} \)	$S_3$ (as 6T2)	$[2, 2, 48, 720]$ (GRH)
6.0.6504017544722944.1	x^6 + 186x^4 + 8649x^2 + 186664	\( -\,2^{9}\cdot 23333^{3} \)	$S_3$ (as 6T2)	$[2, 46, 1150]$ (GRH)
6.0.6591269545312375.1	x^6 + 202x^4 + 10201x^2 + 749980	\( -\,5^{3}\cdot 7^{3}\cdot 11^{3}\cdot 487^{3} \)	$S_3$ (as 6T2)	$[2, 82, 902]$ (GRH)
6.0.6697296155387375.1	x^6 + 282x^4 + 19881x^2 + 753980	\( -\,5^{3}\cdot 37699^{3} \)	$S_3$ (as 6T2)	$[2, 34, 3400]$ (GRH)
6.0.6756306913606823.1	x^6 + 107x^4 - 1120x^3 + 50124x^2 - 59920x + 313600	\( -\,79^{3}\cdot 2393^{3} \)	$S_3$ (as 6T2)	$[4, 28, 952]$ (GRH)
6.0.7167176823334464.1	x^6 - 2x^5 - 113x^4 - 1002x^3 + 52566x^2 - 514800x + 2046600	\( -\,2^{6}\cdot 3^{3}\cdot 16067^{3} \)	$S_3$ (as 6T2)	$[106, 1802]$ (GRH)
6.0.7381046301066927.1	x^6 + 199x^4 - 1536x^3 + 58576x^2 - 152832x + 589824	\( -\,3^{3}\cdot 64901^{3} \)	$S_3$ (as 6T2)	$[2, 2, 6, 18, 270]$ (GRH)
6.0.8234453780075375.1	x^6 - 42x^4 + 441x^2 + 3230960	\( -\,5^{3}\cdot 40387^{3} \)	$S_3$ (as 6T2)	$[2, 2, 2, 18, 1674]$ (GRH)
6.0.8556758507142656.1	x^6 - 2x^5 - 155x^4 + 1180x^3 + 56194x^2 - 284408x + 466680	\( -\,2^{9}\cdot 37^{3}\cdot 691^{3} \)	$S_3$ (as 6T2)	$[2, 2, 74, 2294]$ (GRH)
6.0.9691389429113664.1	x^6 - 2x^5 + 107x^4 + 2290x^3 + 53714x^2 + 340192x + 1648408	\( -\,2^{6}\cdot 3^{3}\cdot 109^{3}\cdot 163^{3} \)	$S_3$ (as 6T2)	$[2, 2, 2, 40, 440]$ (GRH)
6.0.9990203924970304.1	x^6 - 2x^5 - 129x^4 - 2850x^3 + 204234x^2 - 2170648x + 9313144	\( -\,2^{6}\cdot 7^{4}\cdot 4021^{3} \)	$S_3$ (as 6T2)	$[2, 26, 2418]$ (GRH)
6.0.10354387647305079.1	x^6 - 2x^5 + 106x^4 - 3144x^3 + 60285x^2 - 486486x + 2799288	\( -\,3^{3}\cdot 7^{3}\cdot 97^{3}\cdot 107^{3} \)	$S_3$ (as 6T2)	$[2, 2, 2, 56, 1064]$ (GRH)
6.0.10741052552777119.1	x^6 - 105x^4 - 92x^3 + 57916x^2 - 436448x + 884672	\( -\,23^{3}\cdot 53^{3}\cdot 181^{3} \)	$S_3$ (as 6T2)	$[2, 2, 34, 986]$ (GRH)
6.0.10796058994178375.1	x^6 + 178x^4 + 7921x^2 + 884060	\( -\,5^{3}\cdot 44203^{3} \)	$S_3$ (as 6T2)	$[49, 4606]$ (GRH)
6.0.11326956495912000.1	x^6 + 292x^4 + 21316x^2 + 898320	\( -\,2^{6}\cdot 3^{3}\cdot 5^{3}\cdot 19^{3}\cdot 197^{3} \)	$S_3$ (as 6T2)	$[2, 2, 126, 378]$ (GRH)
6.0.13457495511656000.1	x^6 - 218x^4 + 11881x^2 + 2140740	\( -\,2^{6}\cdot 5^{3}\cdot 7^{3}\cdot 1699^{3} \)	$S_3$ (as 6T2)	$[2, 94, 1222]$ (GRH)
6.0.13530938286500271.1	x^6 - 3x^5 - 765x^4 - 4317x^3 + 167112x^2 + 2342628x + 8977968	\( -\,3^{9}\cdot 7^{4}\cdot 13^{3}\cdot 19^{4} \)	$C_6$ (as 6T1)	$[4, 12, 4332]$ (GRH)
6.0.13556180395584000.2	x^6 + 58x^4 + 841x^2 + 238440	\( -\,2^{9}\cdot 3^{3}\cdot 5^{3}\cdot 1987^{3} \)	$S_3$ (as 6T2)	$[2, 2, 4, 48, 144]$ (GRH)
6.0.14053352827968000.1	x^6 - 2x^5 - 127x^4 + 2776x^3 + 61778x^2 + 71848x + 1994296	\( -\,2^{9}\cdot 3^{3}\cdot 5^{3}\cdot 2011^{3} \)	$S_3$ (as 6T2)	$[2, 110, 660]$ (GRH)
6.0.14473801966789927.1	x^6 + 219x^4 - 2880x^3 + 72916x^2 - 315360x + 2073600	\( -\,243703^{3} \)	$S_3$ (as 6T2)	$[43, 3053]$ (GRH)
6.0.19257452166464000.3	x^6 + 86x^4 - 3552x^3 + 68859x^2 - 554796x + 3757266	\( -\,2^{9}\cdot 5^{3}\cdot 6701^{3} \)	$S_3$ (as 6T2)	$[2, 2, 54, 1134]$ (GRH)
6.0.19371479668946432.1	x^6 - 2x^5 + 77x^4 - 1804x^3 + 70314x^2 - 65664x + 746496	\( -\,2^{9}\cdot 59^{3}\cdot 569^{3} \)	$S_3$ (as 6T2)	$[6, 6, 48, 144]$ (GRH)
6.0.20196089557410375.4	x^6 - 3x^5 - 1791x^4 - 16881x^3 + 843462x^2 + 17882964x + 98667864	\( -\,3^{9}\cdot 5^{3}\cdot 7^{4}\cdot 43^{4} \)	$C_6$ (as 6T1)	$[2, 2, 2, 6, 2382]$ (GRH)
6.0.21206090047385088.4	x^6 + 130x^4 + 4225x^2 + 2491128	\( -\,2^{9}\cdot 3^{3}\cdot 19^{3}\cdot 607^{3} \)	$S_3$ (as 6T2)	$[18, 90, 90]$ (GRH)
6.0.23614494625920375.1	x^6 - 3x^5 - 1863x^4 - 10041x^3 + 899622x^2 + 12195684x + 44428536	\( -\,3^{9}\cdot 5^{3}\cdot 313^{4} \)	$C_6$ (as 6T1)	$[2, 2, 2, 16, 912]$ (GRH)
6.0.24269941493035184.2	x^6 - 2x^5 + 189x^4 - 1648x^3 + 125195x^2 + 1011750x + 3405375	\( -\,2^{4}\cdot 89^{3}\cdot 1291^{3} \)	$S_3$ (as 6T2)	$[63, 2520]$ (GRH)
6.0.24516380321944064.2	x^6 - 2x^5 + 165x^4 + 3212x^3 + 75974x^2 + 567336x + 3139848	\( -\,2^{9}\cdot 36313^{3} \)	$S_3$ (as 6T2)	$[2, 38, 1900]$ (GRH)
6.0.24895041720063488.1	x^6 - 2x^5 + 269x^4 - 5164x^3 + 95850x^2 - 656064x + 5992704	\( -\,2^{9}\cdot 17^{3}\cdot 19^{3}\cdot 113^{3} \)	$S_3$ (as 6T2)	$[2, 98, 1078]$ (GRH)
6.0.28851959379246912.1	x^6 - 2x^5 - 113x^4 + 942x^3 + 79098x^2 + 872928x + 2931768	\( -\,2^{6}\cdot 3^{3}\cdot 61^{3}\cdot 419^{3} \)	$S_3$ (as 6T2)	$[2, 122, 976]$ (GRH)
6.0.31508983563080192.1	x^6 + 346x^4 + 29929x^2 + 2842632	\( -\,2^{9}\cdot 13^{3}\cdot 3037^{3} \)	$S_3$ (as 6T2)	$[2, 2, 68, 884]$ (GRH)
6.0.32285191027713536.1	x^6 - 572x^4 + 81796x^2 + 56697696	\( -\,2^{9}\cdot 11^{4}\cdot 1627^{3} \)	$S_3$ (as 6T2)	$[2, 72, 936]$ (GRH)
6.0.32932935158150656.1	x^6 + 246x^4 - 1968x^3 + 95263x^2 - 722868x + 1689462	\( -\,2^{9}\cdot 103^{3}\cdot 389^{3} \)	$S_3$ (as 6T2)	$[82, 1558]$ (GRH)
6.0.33595399126917711.1	x^6 - 2x^5 + 1678x^3 + 78991x^2 - 807516x + 2719776	\( -\,3^{3}\cdot 59^{3}\cdot 1823^{3} \)	$S_3$ (as 6T2)	$[78, 3744]$ (GRH)
6.0.34970915843140096.1	x^6 + 412x^4 + 42436x^2 + 1308064	\( -\,2^{9}\cdot 41^{3}\cdot 997^{3} \)	$S_3$ (as 6T2)	$[82, 1230]$ (GRH)
6.0.35190747414720000.3	x^6 - 140x^4 + 4900x^2 + 3832800	\( -\,2^{9}\cdot 3^{3}\cdot 5^{4}\cdot 1597^{3} \)	$S_3$ (as 6T2)	$[3, 114, 570]$ (GRH)
6.0.35421663620873375.1	x^6 - 2x^5 + 46x^4 + 2244x^3 + 80321x^2 + 215710x + 1391984	\( -\,5^{3}\cdot 19^{3}\cdot 3457^{3} \)	$S_3$ (as 6T2)	$[2, 2, 20, 1380]$ (GRH)
6.0.35426840980886991.2	x^6 + 358x^4 + 32041x^2 + 5254896	\( -\,3^{3}\cdot 83^{3}\cdot 1319^{3} \)	$S_3$ (as 6T2)	$[2, 2, 2, 2, 14, 700]$ (GRH)
6.0.35908258065878528.1	x^6 - 2x^5 - 119x^4 - 464x^3 + 86662x^2 - 1284608x + 5363856	\( -\,2^{9}\cdot 11^{3}\cdot 23^{3}\cdot 163^{3} \)	$S_3$ (as 6T2)	$[2, 134, 938]$ (GRH)
6.0.36772473732908400.1	x^6 - 3x^5 + 837x^4 - 1645x^3 + 253404x^2 - 273882x + 27516128	\( -\,2^{4}\cdot 3^{10}\cdot 5^{2}\cdot 19^{3}\cdot 61^{3} \)	$D_{6}$ (as 6T3)	$[8, 14128]$ (GRH)
6.0.37102284377888256.1	x^6 + 174x^4 + 7569x^2 + 285056	\( -\,2^{9}\cdot 3^{8}\cdot 17^{3}\cdot 131^{3} \)	$S_3$ (as 6T2)	$[50, 2850]$ (GRH)
6.0.37280792061188047.1	x^6 - 2x^5 + 182x^4 - 4988x^3 + 96513x^2 - 268002x + 5860328	\( -\,173^{3}\cdot 1931^{3} \)	$S_3$ (as 6T2)	$[2, 50, 1350]$ (GRH)
6.0.37289162544169472.1	x^6 + 300x^4 + 22500x^2 + 1336352	\( -\,2^{9}\cdot 41761^{3} \)	$S_3$ (as 6T2)	$[33, 3168]$ (GRH)
6.0.38833347568292919.1	x^6 - 3x^5 - 387x^4 + 147x^3 + 58842x^2 + 143640x + 1958400	\( -\,3^{9}\cdot 37^{3}\cdot 79^{4} \)	$C_6$ (as 6T1)	$[2, 2, 4, 20, 1560]$ (GRH)
6.0.38979943105723047.1	x^6 - 2x^5 + 26x^4 - 3476x^3 + 88373x^2 - 1229858x + 7130872	\( -\,3^{3}\cdot 113021^{3} \)	$S_3$ (as 6T2)	$[65, 8190]$ (GRH)
6.0.39475916046787375.2	x^6 + 582x^4 + 84681x^2 + 5447920	\( -\,5^{3}\cdot 68099^{3} \)	$S_3$ (as 6T2)	$[8, 72, 864]$ (GRH)