Global number field search results

Further refine search

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
6.0.12125035439375.1	x^6 + 210x^4 + 11025x^2 + 268700	\( -\,5^{4}\cdot 2687^{3} \)	$S_3$ (as 6T2)	$[27, 459]$
6.0.13089194025263.1	x^6 + 154x^4 + 5929x^2 + 94268	\( -\,23567^{3} \)	$S_3$ (as 6T2)	$[17, 629]$
6.0.13506194937375.2	x^6 - 3x^5 + 33x^4 - 5x^3 + 2094x^2 - 7272x + 51456	\( -\,3^{8}\cdot 5^{3}\cdot 7^{4}\cdot 19^{3} \)	$C_6$ (as 6T1)	$[39, 312]$
6.0.20182663951319.2	x^6 - x^5 + 685x^4 - 1375x^3 + 124850x^2 - 124160x + 5586976	\( -\,31^{5}\cdot 89^{3} \)	$C_6$ (as 6T1)	$[2, 6, 1134]$
6.0.21831946858463.1	x^6 - x^5 + 195x^4 - 139x^3 + 15588x^2 - 3116x + 483536	\( -\,7^{3}\cdot 31^{4}\cdot 41^{3} \)	$C_6$ (as 6T1)	$[10346]$
6.0.21886175968511.2	x^6 - x^5 + 563x^4 + 1141x^3 + 62116x^2 + 61540x + 1661392	\( -\,43^{5}\cdot 53^{3} \)	$C_6$ (as 6T1)	$[10136]$
6.0.23708977432375.1	x^6 - x^5 + 201x^4 - 143x^3 + 16462x^2 - 3352x + 521536	\( -\,5^{3}\cdot 31^{4}\cdot 59^{3} \)	$C_6$ (as 6T1)	$[11768]$
6.0.24977753031287.1	x^6 - x^5 + 1633x^4 - 1089x^3 + 893807x^2 - 297025x + 163965437	\( -\,7^{4}\cdot 37^{3}\cdot 59^{3} \)	$C_6$ (as 6T1)	$[7, 1638]$ (GRH)
6.0.26129053130623.3	x^6 - x^5 + 747x^4 - 1499x^3 + 148100x^2 - 147348x + 7219808	\( -\,31^{5}\cdot 97^{3} \)	$C_6$ (as 6T1)	$[2, 2, 3380]$
6.0.26301884074767.3	x^6 + 441x^4 - 910x^3 + 50652x^2 - 84168x + 1876672	\( -\,3^{9}\cdot 7^{5}\cdot 43^{3} \)	$C_6$ (as 6T1)	$[2, 9672]$
6.0.26949731383519.2	x^6 - x^5 + 1675x^4 - 1117x^3 + 940245x^2 - 312481x + 176872079	\( -\,7^{4}\cdot 2239^{3} \)	$C_6$ (as 6T1)	$[28, 420]$ (GRH)
6.0.27825682278247.1	x^6 - x^5 + 1693x^4 - 1129x^3 + 960507x^2 - 319225x + 182604617	\( -\,7^{4}\cdot 31^{3}\cdot 73^{3} \)	$C_6$ (as 6T1)	$[10582]$ (GRH)
6.0.28121828974911.2	x^6 - x^5 + 1699x^4 - 1133x^3 + 967309x^2 - 321489x + 184542631	\( -\,3^{3}\cdot 7^{4}\cdot 757^{3} \)	$C_6$ (as 6T1)	$[2, 6, 924]$ (GRH)
6.0.28420069497239.2	x^6 - x^5 + 426x^4 + 726x^3 + 50437x^2 + 201323x + 1440144	\( -\,7^{4}\cdot 43^{3}\cdot 53^{3} \)	$D_{6}$ (as 6T3)	$[8, 1680]$ (GRH)
6.0.28720411221103.2	x^6 - x^5 + 1711x^4 - 1141x^3 + 980985x^2 - 326041x + 188459699	\( -\,7^{4}\cdot 2287^{3} \)	$C_6$ (as 6T1)	$[11049]$ (GRH)
6.0.28909195092288.2	x^6 - 2x^5 + 1716x^4 - 2286x^3 + 986135x^2 - 657808x + 189777601	\( -\,2^{6}\cdot 3^{3}\cdot 7^{4}\cdot 191^{3} \)	$C_6$ (as 6T1)	$[2, 5064]$ (GRH)
6.0.29022861522375.4	x^6 - 3x^5 + 153x^4 - 245x^3 + 12774x^2 - 24552x + 467776	\( -\,3^{9}\cdot 5^{3}\cdot 7^{4}\cdot 17^{3} \)	$C_6$ (as 6T1)	$[6, 2394]$
6.0.30253896018983.1	x^6 - x^5 + 1741x^4 - 1161x^3 + 1015595x^2 - 337561x + 198494009	\( -\,7^{4}\cdot 13^{3}\cdot 179^{3} \)	$C_6$ (as 6T1)	$[2, 6, 1008]$ (GRH)
6.0.30283098402375.3	x^6 - 3x^5 + 303x^4 - 545x^3 + 39624x^2 - 59652x + 2086176	\( -\,3^{8}\cdot 5^{3}\cdot 7^{5}\cdot 13^{3} \)	$C_6$ (as 6T1)	$[6, 4710]$
6.0.30294370655591.1	x^6 - x^5 + 2129x^4 - 2129x^3 + 1295953x^2 - 1295953x + 197957201	\( -\,7^{5}\cdot 1217^{3} \)	$C_6$ (as 6T1)	$[2, 2, 3410]$ (GRH)
6.0.30861636507863.2	x^6 + 170x^4 - 128x^3 + 7225x^2 - 10880x + 129564	\( -\,7^{3}\cdot 4481^{3} \)	$D_{6}$ (as 6T3)	$[6, 1716]$
6.0.30882256504407.2	x^6 - x^5 + 1753x^4 - 1169x^3 + 1029607x^2 - 342225x + 202605397	\( -\,3^{3}\cdot 7^{4}\cdot 11^{3}\cdot 71^{3} \)	$C_6$ (as 6T1)	$[2, 4, 4, 336]$ (GRH)
6.0.30921815325184.1	x^6 - 2x^5 + 1755x^4 - 2338x^3 + 1031362x^2 - 687968x + 202950553	\( -\,2^{9}\cdot 7^{4}\cdot 293^{3} \)	$C_6$ (as 6T1)	$[2, 24, 216]$ (GRH)
6.0.32122219436447.1	x^6 - x^5 + 2171x^4 - 2171x^3 + 1347571x^2 - 1347571x + 209884571	\( -\,7^{5}\cdot 17^{3}\cdot 73^{3} \)	$C_6$ (as 6T1)	$[2, 5418]$ (GRH)
6.0.32268097512063.1	x^6 - 3x^5 + 57x^4 - 53x^3 + 3462x^2 - 9960x + 93248	\( -\,3^{8}\cdot 7^{4}\cdot 127^{3} \)	$C_6$ (as 6T1)	$[2, 6690]$
6.0.32291634881943.2	x^6 - x^5 + 225x^4 - 159x^3 + 20198x^2 - 4376x + 693376	\( -\,3^{3}\cdot 31^{4}\cdot 109^{3} \)	$C_6$ (as 6T1)	$[2, 2, 3276]$
6.0.32491090444687.2	x^6 - x^5 + 1783x^4 - 1189x^3 + 1065057x^2 - 354025x + 213131387	\( -\,7^{4}\cdot 2383^{3} \)	$C_6$ (as 6T1)	$[11049]$ (GRH)
6.0.33083784209567.2	x^6 - x^5 + 155x^4 - 211x^3 + 16444x^2 + 21020x + 746656	\( -\,7^{5}\cdot 13^{4}\cdot 41^{3} \)	$C_6$ (as 6T1)	$[3, 6342]$
6.0.33141820926375.3	x^6 - x^5 + 809x^4 - 1623x^3 + 173334x^2 - 172520x + 9143296	\( -\,3^{3}\cdot 5^{3}\cdot 7^{3}\cdot 31^{5} \)	$C_6$ (as 6T1)	$[2, 2, 3130]$
6.0.33301141325312.1	x^6 + 2198x^4 + 1380344x^2 + 216714008	\( -\,2^{9}\cdot 7^{5}\cdot 157^{3} \)	$C_6$ (as 6T1)	$[6, 1998]$ (GRH)
6.0.33810130196479.2	x^6 - x^5 - x^4 - 107x^3 + 2144x^2 + 8956x + 50896	\( -\,7^{4}\cdot 13^{4}\cdot 79^{3} \)	$C_6$ (as 6T1)	$[3, 3, 1185]$
6.0.33862075931504.2	x^6 - 3x^5 + 1303x^4 - 2427x^3 + 354090x^2 - 519134x + 24613258	\( -\,2^{4}\cdot 37^{3}\cdot 347^{3} \)	$D_{6}$ (as 6T3)	$[26, 390]$ (GRH)
6.0.34312283687375.1	x^6 - 2x^5 + 24x^4 - 686x^3 + 8919x^2 - 23872x + 118016	\( -\,5^{3}\cdot 67^{3}\cdot 97^{3} \)	$S_3$ (as 6T2)	$[2, 2, 16, 176]$
6.0.34324284187683.2	x^6 - x^5 + 1816x^4 - 1211x^3 + 1104745x^2 - 367236x + 225124159	\( -\,3^{3}\cdot 7^{4}\cdot 809^{3} \)	$C_6$ (as 6T1)	$[3, 4074]$ (GRH)
6.0.34664828562875.2	x^6 - x^5 + 1822x^4 - 1215x^3 + 1112039x^2 - 369664x + 227351879	\( -\,5^{3}\cdot 7^{4}\cdot 487^{3} \)	$C_6$ (as 6T1)	$[11154]$ (GRH)
6.0.34720118315375.2	x^6 - x^5 + 231x^4 - 163x^3 + 21192x^2 - 4652x + 741536	\( -\,5^{3}\cdot 31^{4}\cdot 67^{3} \)	$C_6$ (as 6T1)	$[10422]$
6.0.35223173014311.1	x^6 - 3x^5 + 1311x^4 - 2615x^3 + 576843x^2 - 578169x + 85182681	\( -\,3^{8}\cdot 17^{3}\cdot 103^{3} \)	$C_6$ (as 6T1)	$[2, 6, 1008]$ (GRH)
6.0.35569457993216.2	x^6 - 2x^5 + 1839x^4 - 2450x^3 + 1132218x^2 - 755224x + 233364209	\( -\,2^{9}\cdot 7^{4}\cdot 307^{3} \)	$C_6$ (as 6T1)	$[2, 12, 612]$ (GRH)
6.0.37290981137375.2	x^6 - x^5 + 1867x^4 - 1245x^3 + 1167509x^2 - 388129x + 244529999	\( -\,5^{3}\cdot 7^{4}\cdot 499^{3} \)	$C_6$ (as 6T1)	$[12264]$ (GRH)
6.0.38377498425959.2	x^6 - x^5 + 1885x^4 - 1257x^3 + 1190075x^2 - 395641x + 251636489	\( -\,7^{4}\cdot 11^{3}\cdot 229^{3} \)	$C_6$ (as 6T1)	$[15168]$ (GRH)
6.0.38743482298927.1	x^6 - x^5 + 2311x^4 - 2311x^3 + 1526911x^2 - 1526911x + 253085911	\( -\,7^{5}\cdot 1321^{3} \)	$C_6$ (as 6T1)	$[10854]$ (GRH)
6.0.38974743355968.2	x^6 - 2x^5 + 1896x^4 - 2526x^3 + 1203335x^2 - 802648x + 255643381	\( -\,2^{6}\cdot 3^{3}\cdot 7^{4}\cdot 211^{3} \)	$C_6$ (as 6T1)	$[2, 2, 2, 1470]$ (GRH)
6.0.39749351140287.1	x^6 - 3x^5 + 1365x^4 - 2723x^3 + 625173x^2 - 626553x + 96070539	\( -\,3^{8}\cdot 1823^{3} \)	$C_6$ (as 6T1)	$[12285]$ (GRH)
6.0.39858737252551.2	x^6 - x^5 + 1909x^4 - 1273x^3 + 1220499x^2 - 405769x + 261324161	\( -\,7^{4}\cdot 2551^{3} \)	$C_6$ (as 6T1)	$[3, 3813]$ (GRH)
6.0.40018763789199.2	x^6 - x^5 + 831x^4 - 549x^3 + 234935x^2 - 82343x + 22583965	\( -\,3^{3}\cdot 13^{4}\cdot 373^{3} \)	$C_6$ (as 6T1)	$[3, 4128]$ (GRH)
6.0.41308916090447.1	x^6 - x^5 + 871x^4 - 1747x^3 + 200552x^2 - 199676x + 11381248	\( -\,31^{5}\cdot 113^{3} \)	$C_6$ (as 6T1)	$[17212]$ (GRH)
6.0.41836770602991.2	x^6 - x^5 + 1568x^4 - 1569x^3 + 377526x^2 + 1570x + 23220625	\( -\,3^{3}\cdot 7^{3}\cdot 13^{5}\cdot 23^{3} \)	$C_6$ (as 6T1)	$[2, 2, 2786]$ (GRH)
6.0.42346221455027.2	x^6 - x^5 + 1948x^4 - 1299x^3 + 1270757x^2 - 422500x + 277591607	\( -\,7^{4}\cdot 19^{3}\cdot 137^{3} \)	$C_6$ (as 6T1)	$[11940]$ (GRH)
6.0.42729727290359.1	x^6 - x^5 + 249x^4 - 175x^3 + 24318x^2 - 5528x + 899264	\( -\,31^{4}\cdot 359^{3} \)	$C_6$ (as 6T1)	$[13129]$
6.0.42897187405359.2	x^6 - 3x^5 + 345x^4 - 629x^3 + 49830x^2 - 72168x + 2851136	\( -\,3^{8}\cdot 7^{5}\cdot 73^{3} \)	$C_6$ (as 6T1)	$[19194]$

In order to download results, .