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
6.0.65499561791.1	x^6 - 2x^5 - 2x^4 - 60x^3 + 1073x^2 + 2110x + 2000	\( -\,29^{3}\cdot 139^{3} \)	$S_3$ (as 6T2)	$[7, 7, 28]$
6.0.125535755376.1	x^6 - x^5 + 10x^4 + 60x^3 + 75x^2 + 909x + 3042	\( -\,2^{4}\cdot 3^{2}\cdot 31\cdot 5303^{2} \)	$S_4\times C_2$ (as 6T11)	$[1120]$
6.0.140655018863.1	x^6 - x^5 + 127x^4 - 259x^3 + 4880x^2 - 4748x + 42688	\( -\,17^{3}\cdot 31^{5} \)	$C_6$ (as 6T1)	$[1026]$
6.0.191666276487.2	x^6 - 3x^5 - 21x^4 - 9x^3 + 588x^2 + 1572x + 3968	\( -\,3^{8}\cdot 7^{4}\cdot 23^{3} \)	$C_6$ (as 6T1)	$[3, 657]$
6.0.197356395591.1	x^6 + 15x^4 - 116x^3 + 756x^2 - 2736x + 4608	\( -\,3^{8}\cdot 311^{3} \)	$S_3$ (as 6T2)	$[6, 342]$
6.0.231440493375.7	x^6 - x^5 - 49x^4 - 75x^3 + 1008x^2 + 4156x + 6544	\( -\,3^{3}\cdot 5^{3}\cdot 7^{4}\cdot 13^{4} \)	$C_6$ (as 6T1)	$[5, 210]$
6.0.231946969919.1	x^6 - x^5 + 71x^4 - 57x^3 + 2759x^2 + 55x + 45382	\( -\,7^{5}\cdot 17^{3}\cdot 53^{2} \)	$D_{6}$ (as 6T3)	$[2, 660]$
6.0.269997268464.3	x^6 - x^5 + 167x^4 - 111x^3 + 10044x^2 - 3368x + 215758	\( -\,2^{4}\cdot 3^{3}\cdot 7^{3}\cdot 11^{3}\cdot 37^{2} \)	$D_{6}$ (as 6T3)	$[2, 522]$
6.0.296019302976.3	x^6 + 261x^4 - 2x^3 + 23772x^2 + 540x + 753297	\( -\,2^{6}\cdot 3^{8}\cdot 89^{3} \)	$C_6$ (as 6T1)	$[2, 2, 252]$
6.0.305559728327.2	x^6 - x^5 + 373x^4 - 249x^3 + 47507x^2 - 15625x + 2064257	\( -\,7^{4}\cdot 503^{3} \)	$C_6$ (as 6T1)	$[4, 252]$
6.0.310236069591.1	x^6 - 2x^5 + 35x^4 + 30x^3 + 700x^2 + 1448x + 7328	\( -\,3^{2}\cdot 7^{4}\cdot 19\cdot 53^{2}\cdot 269 \)	$S_4\times C_2$ (as 6T11)	$[6, 210]$
6.0.312771967375.2	x^6 - x^5 + 463x^4 - 463x^3 + 61447x^2 - 61447x + 2073919	\( -\,5^{3}\cdot 7^{5}\cdot 53^{3} \)	$C_6$ (as 6T1)	$[2, 518]$
6.0.321575167088.1	x^6 - 2x^5 - 3x^4 + 152x^3 + 599x^2 - 1782x + 6219	\( -\,2^{4}\cdot 7^{2}\cdot 743^{3} \)	$D_{6}$ (as 6T3)	$[3, 336]$
6.0.329868818496.3	x^6 - 2x^5 + 384x^4 - 510x^3 + 50183x^2 - 33544x + 2230669	\( -\,2^{6}\cdot 3^{3}\cdot 7^{4}\cdot 43^{3} \)	$C_6$ (as 6T1)	$[2, 2, 2, 126]$
6.0.330538324631.1	x^6 - x^5 + 33x^4 - 31x^3 + 1062x^2 + 232x + 13952	\( -\,31^{4}\cdot 71^{3} \)	$C_6$ (as 6T1)	$[1141]$
6.0.354110810319.1	x^6 + 24x^4 - 14x^3 + 423x^2 - 546x + 3088	\( -\,3^{9}\cdot 7^{4}\cdot 59\cdot 127 \)	$A_4\times C_2$ (as 6T6)	$[2, 876]$
6.0.372914405087.2	x^6 - x^5 + 491x^4 - 491x^3 + 69091x^2 - 69091x + 2470091	\( -\,7^{5}\cdot 281^{3} \)	$C_6$ (as 6T1)	$[2, 6, 108]$
6.0.384407319807.2	x^6 - x^5 + 403x^4 - 269x^3 + 55357x^2 - 18225x + 2589847	\( -\,3^{3}\cdot 7^{4}\cdot 181^{3} \)	$C_6$ (as 6T1)	$[2, 2, 252]$
6.0.384986251328.3	x^6 + 497x^4 + 70574x^2 + 2505377	\( -\,2^{6}\cdot 7^{5}\cdot 71^{3} \)	$C_6$ (as 6T1)	$[2, 4, 4, 36]$
6.0.404353609875.6	x^6 - 3x^5 + 294x^4 - 581x^3 + 29697x^2 - 30006x + 1029999	\( -\,3^{8}\cdot 5^{3}\cdot 79^{3} \)	$C_6$ (as 6T1)	$[1176]$
6.0.435944600944.2	x^6 - x^5 + 197x^4 - 131x^3 + 13814x^2 - 4628x + 342718	\( -\,2^{4}\cdot 37^{2}\cdot 271^{3} \)	$D_{6}$ (as 6T3)	$[11, 99]$
6.0.440311012911.5	x^6 + 105x^4 - 238x^3 + 3276x^2 - 4872x + 42112	\( -\,3^{9}\cdot 7^{5}\cdot 11^{3} \)	$C_6$ (as 6T1)	$[6, 342]$
6.0.441230583744.1	x^6 - x^5 + 71x^4 - 39x^3 + 2358x^2 - 1514x + 32440	\( -\,2^{6}\cdot 3^{3}\cdot 37^{3}\cdot 71^{2} \)	$D_{6}$ (as 6T3)	$[8, 128]$
6.0.442336997223.6	x^6 - 3x^5 + 303x^4 - 599x^3 + 31515x^2 - 31833x + 1124553	\( -\,3^{8}\cdot 11^{3}\cdot 37^{3} \)	$C_6$ (as 6T1)	$[2, 2, 336]$
6.0.454849890599.1	x^6 - x^5 + 346x^4 - 347x^3 + 18258x^2 + 348x + 265355	\( -\,13^{5}\cdot 107^{3} \)	$C_6$ (as 6T1)	$[5, 220]$
6.0.455331870319.2	x^6 - x^5 + 39x^4 - 35x^3 + 1288x^2 + 212x + 17824	\( -\,31^{4}\cdot 79^{3} \)	$C_6$ (as 6T1)	$[3, 465]$
6.0.463403630576.4	x^6 - 3x^5 + 313x^4 - 579x^3 + 20328x^2 - 29678x + 356938	\( -\,2^{4}\cdot 37^{3}\cdot 83^{3} \)	$D_{6}$ (as 6T3)	$[1140]$
6.0.469296461151.6	x^6 - 3x^5 - 15x^4 - 21x^3 + 678x^2 + 1824x + 6112	\( -\,3^{8}\cdot 7^{4}\cdot 31^{3} \)	$C_6$ (as 6T1)	$[6, 342]$
6.0.476858708375.2	x^6 - x^5 + 533x^4 - 533x^3 + 81397x^2 - 81397x + 3154229	\( -\,5^{3}\cdot 7^{5}\cdot 61^{3} \)	$C_6$ (as 6T1)	$[10, 110]$
6.0.478223266304.2	x^6 - 2x^5 + 435x^4 - 578x^3 + 64242x^2 - 42928x + 3219593	\( -\,2^{9}\cdot 7^{4}\cdot 73^{3} \)	$C_6$ (as 6T1)	$[5, 240]$
6.0.480232637191.1	x^6 - 2x^5 - 30x^4 + 24x^3 + 2205x^2 - 11638x + 17632	\( -\,41^{3}\cdot 191^{3} \)	$S_3$ (as 6T2)	$[7, 154]$
6.0.510465535488.3	x^6 + 444x^4 + 49284x^2 + 1215672	\( -\,2^{9}\cdot 3^{9}\cdot 37^{3} \)	$C_6$ (as 6T1)	$[2, 2, 2, 126]$
6.0.516027239399.2	x^6 - x^5 + 445x^4 - 297x^3 + 67355x^2 - 22201x + 3465449	\( -\,7^{4}\cdot 599^{3} \)	$C_6$ (as 6T1)	$[1075]$
6.0.525293283951.2	x^6 - 3x^5 + 321x^4 - 635x^3 + 35313x^2 - 35649x + 1330671	\( -\,3^{8}\cdot 431^{3} \)	$C_6$ (as 6T1)	$[4, 252]$
6.0.525515088384.3	x^6 - 2x^5 + 191x^4 - 258x^3 + 13218x^2 - 7780x + 327625	\( -\,2^{9}\cdot 3^{3}\cdot 11^{3}\cdot 13^{4} \)	$C_6$ (as 6T1)	$[2, 516]$
6.0.536980151743.3	x^6 - x^5 + 451x^4 - 301x^3 + 69165x^2 - 22801x + 3604679	\( -\,7^{4}\cdot 607^{3} \)	$C_6$ (as 6T1)	$[1443]$
6.0.541760081751.3	x^6 - 3x^5 + 51x^4 - 41x^3 + 3084x^2 - 9252x + 81264	\( -\,3^{8}\cdot 7^{5}\cdot 17^{3} \)	$C_6$ (as 6T1)	$[3, 3, 390]$
6.0.543691854704.1	x^6 + 263x^4 - 348x^3 + 18102x^2 - 13372x + 354176	\( -\,2^{4}\cdot 41^{3}\cdot 79^{3} \)	$D_{6}$ (as 6T3)	$[10, 140]$
6.0.553914311104.3	x^6 - x^5 - 9x^4 + x^3 + 448x^2 + 56x + 4480	\( -\,2^{6}\cdot 7^{4}\cdot 11^{2}\cdot 31^{3} \)	$D_{6}$ (as 6T3)	$[3, 3, 144]$
6.0.558492708375.3	x^6 - x^5 + 457x^4 - 305x^3 + 70999x^2 - 23409x + 3747589	\( -\,3^{3}\cdot 5^{3}\cdot 7^{4}\cdot 41^{3} \)	$C_6$ (as 6T1)	$[2, 2, 2, 210]$
6.0.558892224000.14	x^6 + 324x^4 - 2x^3 + 36309x^2 + 666x + 1404591	\( -\,2^{9}\cdot 3^{8}\cdot 5^{3}\cdot 11^{3} \)	$C_6$ (as 6T1)	$[14, 126]$
6.0.562327702000.2	x^6 - x^5 + 215x^4 - 143x^3 + 16364x^2 - 5480x + 438670	\( -\,2^{4}\cdot 5^{3}\cdot 37^{2}\cdot 59^{3} \)	$D_{6}$ (as 6T3)	$[2, 8, 72]$
6.0.568435616671.2	x^6 - x^5 + 195x^4 - 125x^3 + 13819x^2 - 5599x + 352585	\( -\,13^{4}\cdot 271^{3} \)	$C_6$ (as 6T1)	$[1067]$
6.0.568803016375.3	x^6 - x^5 + 13x^4 + 17x^3 + 762x^2 - 1672x + 11264	\( -\,5^{3}\cdot 11^{3}\cdot 43^{4} \)	$C_6$ (as 6T1)	$[2, 6, 84]$
6.0.570402232227.3	x^6 - 3x^5 + 330x^4 - 653x^3 + 37293x^2 - 37638x + 1442559	\( -\,3^{8}\cdot 443^{3} \)	$C_6$ (as 6T1)	$[1005]$
6.0.575100098496.10	x^6 + 111x^4 - 342x^3 + 3600x^2 - 7200x + 96000	\( -\,2^{6}\cdot 3^{9}\cdot 7^{3}\cdot 11^{3} \)	$D_{6}$ (as 6T3)	$[2, 6, 90]$
6.0.594663237952.6	x^6 - 2x^5 + 468x^4 - 622x^3 + 74263x^2 - 49616x + 3994081	\( -\,2^{6}\cdot 7^{4}\cdot 157^{3} \)	$C_6$ (as 6T1)	$[3, 3, 126]$
6.0.599215958000.1	x^6 - x^5 + 2x^4 + 84x^3 + 227x^2 - 803x + 1546	\( -\,2^{4}\cdot 5^{3}\cdot 11^{2}\cdot 19^{5} \)	$D_{6}$ (as 6T3)	$[4, 264]$
6.0.600482915136.7	x^6 - 2x^5 + 200x^4 - 270x^3 + 14439x^2 - 8548x + 372325	\( -\,2^{6}\cdot 3^{3}\cdot 13^{4}\cdot 23^{3} \)	$C_6$ (as 6T1)	$[2, 516]$
6.0.600681840240.1	x^6 - x^5 + 12x^4 - 14x^3 + 192x^2 - 256x + 4096	\( -\,2^{4}\cdot 3\cdot 5\cdot 89\cdot 5303^{2} \)	$S_4\times C_2$ (as 6T11)	$[2, 700]$

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