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
6.0.2185548272.1	x^6 + 31x^4 - 12x^3 + 366x^2 - 148x + 1936	\( -\,2^{4}\cdot 43\cdot 79^{2}\cdot 509 \)	$S_4\times C_2$ (as 6T11)	$[102]$
6.0.2267030768.1	x^6 - x^5 + 32x^4 - 22x^3 + 384x^2 - 144x + 1728	\( -\,2^{4}\cdot 73\cdot 79^{2}\cdot 311 \)	$S_4\times C_2$ (as 6T11)	$[110]$
6.0.2623637527.2	x^6 - x^5 + 73x^4 - 49x^3 + 2007x^2 - 625x + 20357	\( -\,7^{4}\cdot 103^{3} \)	$C_6$ (as 6T1)	$[105]$
6.0.2648880112.1	x^6 - 3x^5 + 35x^4 - 65x^3 + 318x^2 - 286x + 484	\( -\,2^{4}\cdot 41\cdot 79^{2}\cdot 647 \)	$S_4\times C_2$ (as 6T11)	$[112]$
6.0.2826224368.1	x^6 + 35x^4 + 502x^2 - 44x + 2192	\( -\,2^{4}\cdot 11\cdot 31\cdot 79^{2}\cdot 83 \)	$S_4\times C_2$ (as 6T11)	$[2, 54]$
6.0.2878149488.1	x^6 - 2x^5 + 37x^4 - 34x^3 + 468x^2 - 120x + 2144	\( -\,2^{4}\cdot 19\cdot 37\cdot 41\cdot 79^{2} \)	$S_4\times C_2$ (as 6T11)	$[2, 52]$
6.0.2949751232.1	x^6 - 3x^5 + 41x^4 - 77x^3 + 356x^2 - 318x + 220	\( -\,2^{6}\cdot 41\cdot 71^{2}\cdot 223 \)	$S_4\times C_2$ (as 6T11)	$[104]$
6.0.3112538751.2	x^6 - x^5 + 99x^4 - 99x^3 + 2843x^2 - 2843x + 22051	\( -\,3^{3}\cdot 7^{5}\cdot 19^{3} \)	$C_6$ (as 6T1)	$[2, 56]$
6.0.3116883375.2	x^6 - x^5 - 9x^4 - 3x^3 + 152x^2 + 148x + 736	\( -\,3^{3}\cdot 5^{3}\cdot 31^{4} \)	$C_6$ (as 6T1)	$[3, 42]$
6.0.3187940831.1	x^6 - 3x^5 + 37x^4 - 69x^3 + 387x^2 - 353x + 1036	\( -\,31\cdot 37\cdot 53\cdot 229^{2} \)	$S_4\times C_2$ (as 6T11)	$[2, 52]$
6.0.3202030832.1	x^6 - x^5 + 21x^4 - 9x^3 + 110x^2 + 10x + 12	\( -\,2^{4}\cdot 7^{2}\cdot 11\cdot 13^{5} \)	$S_4\times C_2$ (as 6T11)	$[2, 78]$
6.0.3319113584.1	x^6 - 3x^5 + 33x^4 - 61x^3 + 296x^2 - 266x + 584	\( -\,2^{4}\cdot 43\cdot 79^{2}\cdot 773 \)	$S_4\times C_2$ (as 6T11)	$[108]$
6.0.3393090023.1	x^6 - 3x^5 + 39x^4 - 73x^3 + 425x^2 - 389x + 1106	\( -\,89\cdot 229^{2}\cdot 727 \)	$S_4\times C_2$ (as 6T11)	$[2, 56]$
6.0.3394205296.1	x^6 - x^5 + 27x^4 - 53x^3 + 266x^2 - 492x + 1096	\( -\,2^{4}\cdot 19\cdot 79^{2}\cdot 1789 \)	$S_4\times C_2$ (as 6T11)	$[116]$
6.0.3499230607.1	x^6 - 2x^5 + 31x^4 - 35x^3 + 324x^2 - 223x + 1432	\( -\,53\cdot 229^{2}\cdot 1259 \)	$S_4\times C_2$ (as 6T11)	$[120]$
6.0.3569979632.1	x^6 - 3x^5 + 45x^4 - 85x^3 + 626x^2 - 584x + 2690	\( -\,2^{4}\cdot 37^{2}\cdot 349\cdot 467 \)	$S_4\times C_2$ (as 6T11)	$[108]$
6.0.3630312000.2	x^6 + 105x^4 + 3150x^2 + 23625	\( -\,2^{6}\cdot 3^{3}\cdot 5^{3}\cdot 7^{5} \)	$C_6$ (as 6T1)	$[2, 2, 26]$
6.0.3669298299.1	x^6 - 3x^5 + 66x^4 - 127x^3 + 1377x^2 - 1314x + 9063	\( -\,3^{8}\cdot 559259 \)	$A_4\times C_2$ (as 6T6)	$[107]$
6.0.3974415088.5	x^6 - x^5 + 73x^4 + 75x^3 + 960x^2 + 344x + 3214	\( -\,2^{4}\cdot 7^{3}\cdot 23^{2}\cdot 37^{2} \)	$S_4\times C_2$ (as 6T11)	$[104]$
6.0.4210332239.1	x^6 - x^5 + 27x^4 - 27x^3 + 364x^2 - 252x + 1744	\( -\,31^{4}\cdot 47\cdot 97 \)	$A_4\times C_2$ (as 6T6)	$[142]$
6.0.4286177831.1	x^6 - x^5 + 48x^4 - 27x^3 + 754x^2 + 2600	\( -\,13^{4}\cdot 31\cdot 47\cdot 103 \)	$A_4\times C_2$ (as 6T6)	$[2, 54]$
6.0.4438983616.1	x^6 - 3x^5 + 17x^4 - 27x^3 + 130x^2 - 46x + 440	\( -\,2^{6}\cdot 71^{2}\cdot 13759 \)	$S_4\times C_2$ (as 6T11)	$[3, 45]$
6.0.4450055616.1	x^6 - 3x^5 + 13x^4 + 9x^3 + 14x^2 + 94x + 384	\( -\,2^{6}\cdot 3^{2}\cdot 127^{2}\cdot 479 \)	$S_4\times C_2$ (as 6T11)	$[114]$
6.0.4467667023.1	x^6 + 90x^4 - 46x^3 + 2025x^2 - 2070x + 12241	\( -\,3^{9}\cdot 61^{3} \)	$C_6$ (as 6T1)	$[104]$
6.0.4598788608.8	x^6 + 78x^4 + 1776x^2 + 10952	\( -\,2^{9}\cdot 3^{8}\cdot 37^{2} \)	$A_4\times C_2$ (as 6T6)	$[2, 52]$
6.0.4687333903.1	x^6 + 49x^4 - 47x^3 + 678x^2 - 1117x + 2132	\( -\,7\cdot 113^{2}\cdot 229^{2} \)	$S_4\times C_2$ (as 6T11)	$[114]$
6.0.4764886640.1	x^6 - 3x^5 + 47x^4 - 83x^3 + 734x^2 - 630x + 4030	\( -\,2^{4}\cdot 5\cdot 37^{2}\cdot 139\cdot 313 \)	$S_4\times C_2$ (as 6T11)	$[2, 60]$
6.0.4840461623.1	x^6 - 3x^5 + 39x^4 - 73x^3 + 452x^2 - 416x + 1544	\( -\,229^{2}\cdot 241\cdot 383 \)	$S_4\times C_2$ (as 6T11)	$[112]$
6.0.4863286768.1	x^6 - x^5 + 42x^4 - 20x^3 + 635x^2 - 99x + 3538	\( -\,2^{4}\cdot 79^{2}\cdot 113\cdot 431 \)	$S_4\times C_2$ (as 6T11)	$[124]$
6.0.4987905687.1	x^6 - 3x^5 + 27x^4 - 41x^3 + 273x^2 - 159x + 1233	\( -\,3^{2}\cdot 107^{2}\cdot 48407 \)	$S_4\times C_2$ (as 6T11)	$[105]$
6.0.5124510064.1	x^6 - x^5 + 27x^4 - 29x^3 + 260x^2 - 186x + 1304	\( -\,2^{4}\cdot 19\cdot 37\cdot 73\cdot 79^{2} \)	$S_4\times C_2$ (as 6T11)	$[2, 60]$
6.0.5190814448.1	x^6 + 41x^4 - 2x^3 + 656x^2 + 4096	\( -\,2^{4}\cdot 79^{2}\cdot 227\cdot 229 \)	$S_4\times C_2$ (as 6T11)	$[138]$
6.0.5267762279.1	x^6 - x^5 + 41x^4 - 31x^3 + 615x^2 - 225x + 3375	\( -\,13^{4}\cdot 181\cdot 1019 \)	$A_4\times C_2$ (as 6T6)	$[104]$
6.0.5281871063.1	x^6 - 2x^5 + 105x^4 - 96x^3 + 3416x^2 - 1240x + 35503	\( -\,7^{4}\cdot 97\cdot 22679 \)	$A_4\times C_2$ (as 6T6)	$[104]$
6.0.5397666491.3	x^6 - x^5 + 94x^4 - 63x^3 + 3239x^2 - 1024x + 40391	\( -\,7^{4}\cdot 131^{3} \)	$C_6$ (as 6T1)	$[105]$
6.0.5444581943.4	x^6 - 3x^5 + 31x^4 - 55x^3 + 469x^2 - 521x + 3064	\( -\,47^{3}\cdot 229^{2} \)	$D_{6}$ (as 6T3)	$[2, 60]$
6.0.5522223168.1	x^6 - 17x^4 + 31x^2 + 2673	\( -\,2^{6}\cdot 3^{3}\cdot 7^{4}\cdot 11^{3} \)	$S_3$ (as 6T2)	$[6, 18]$
6.0.5522223168.10	x^6 - 2x^5 + 96x^4 - 126x^3 + 3335x^2 - 2248x + 41581	\( -\,2^{6}\cdot 3^{3}\cdot 7^{4}\cdot 11^{3} \)	$C_6$ (as 6T1)	$[6, 18]$
6.0.5548698352.1	x^6 - 2x^5 + 45x^4 - 62x^3 + 720x^2 - 512x + 4096	\( -\,2^{4}\cdot 79^{2}\cdot 181\cdot 307 \)	$S_4\times C_2$ (as 6T11)	$[110]$
6.0.5609350656.4	x^6 + 114x^4 + 3744x^2 + 36504	\( -\,2^{9}\cdot 3^{3}\cdot 7^{4}\cdot 13^{2} \)	$A_4\times C_2$ (as 6T6)	$[2, 2, 28]$
6.0.5655743984.1	x^6 - x^5 + 44x^4 - 30x^3 + 704x^2 - 256x + 4096	\( -\,2^{4}\cdot 11\cdot 19\cdot 79^{2}\cdot 271 \)	$S_4\times C_2$ (as 6T11)	$[2, 74]$
6.0.5795359792.1	x^6 + 58x^4 + 1106x^2 + 6907	\( -\,2^{4}\cdot 229^{2}\cdot 6907 \)	$S_4\times C_2$ (as 6T11)	$[110]$
6.0.5863499975.1	x^6 - 3x^5 + 36x^4 - 67x^3 + 452x^2 - 362x + 1743	\( -\,5^{2}\cdot 53\cdot 67\cdot 257^{2} \)	$S_4\times C_2$ (as 6T11)	$[2, 52]$
6.0.5907360375.1	x^6 - 3x^5 - 27x^4 + 3x^3 + 522x^2 + 1296x + 2304	\( -\,3^{9}\cdot 5^{3}\cdot 7^{4} \)	$C_6$ (as 6T1)	$[222]$
6.0.5923358064.7	x^6 - x^5 + 21x^4 - 15x^3 + 308x^2 - 62x + 1936	\( -\,2^{4}\cdot 3^{3}\cdot 13^{3}\cdot 79^{2} \)	$D_{6}$ (as 6T3)	$[132]$
6.0.6038177216.1	x^6 - x^5 + 19x^4 - 21x^3 + 190x^2 - 100x + 1000	\( -\,2^{6}\cdot 53\cdot 67\cdot 163^{2} \)	$S_4\times C_2$ (as 6T11)	$[108]$
6.0.6043684544.1	x^6 - 2x^5 + 47x^4 - 92x^3 + 841x^2 - 1082x + 5023	\( -\,2^{6}\cdot 79^{2}\cdot 15131 \)	$S_4\times C_2$ (as 6T11)	$[102]$
6.0.6059190463.1	x^6 + 36x^4 - 5x^3 + 480x^2 - 64x + 2056	\( -\,227\cdot 229^{2}\cdot 509 \)	$S_4\times C_2$ (as 6T11)	$[104]$
6.0.6143515591.1	x^6 + 35x^4 - 7x^3 + 454x^2 - 101x + 2146	\( -\,193\cdot 229^{2}\cdot 607 \)	$S_4\times C_2$ (as 6T11)	$[136]$
6.0.6196961792.1	x^6 + 108x^4 + 3692x^2 + 40328	\( -\,2^{9}\cdot 7^{4}\cdot 71^{2} \)	$A_4\times C_2$ (as 6T6)	$[2, 52]$

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