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 all 48 matches)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.7320500000000.1	x^12 - x^11 - 2x^10 + 6x^9 + 4x^8 - 3x^7 + 7x^6 + 6x^5 - 5x^4 + 9x^3 + 15x^2 + 3x + 1	\( 2^{8}\cdot 5^{9}\cdot 11^{4} \)	$C_2.S_3^2$ (as 12T39)	Trivial
12.0.20617189453125.1	x^12 - 3x^11 + 2x^10 + x^9 - 5x^8 + 13x^7 + 2x^6 - 32x^5 + 20x^4 + x^3 + 2x^2 + 2x + 1	\( 3^{4}\cdot 5^{9}\cdot 19^{4} \)	$C_2.S_3^2$ (as 12T39)	Trivial
12.0.25949267578125.2	x^12 - 5x^9 + 10x^6 - 10x^3 + 5	\( 3^{12}\cdot 5^{11} \)	$C_2.S_3^2$ (as 12T39)	Trivial
12.0.30012500000000.1	x^12 - 5x^11 + 15x^10 - 35x^9 + 65x^8 - 100x^7 + 125x^6 - 130x^5 + 115x^4 - 65x^3 + 10x^2 + 5	\( 2^{8}\cdot 5^{11}\cdot 7^{4} \)	$C_2.S_3^2$ (as 12T39)	Trivial
12.4.117128000000000.1	x^12 - 2x^11 + 6x^9 - 13x^8 - 6x^7 + 17x^6 - 4x^5 - 23x^4 - 2x^3 + 13x^2 + 8x + 1	\( 2^{12}\cdot 5^{9}\cdot 11^{4} \)	$C_2.S_3^2$ (as 12T39)	Trivial
12.4.185554705078125.1	x^12 - 2x^11 + 3x^10 - 11x^9 + 3x^8 - 24x^7 + 17x^6 + 24x^5 + 3x^4 + 11x^3 + 3x^2 + 2x + 1	\( 3^{6}\cdot 5^{9}\cdot 19^{4} \)	$C_2.S_3^2$ (as 12T39)	Trivial
12.4.233543408203125.1	x^12 - 3x^11 + 6x^10 - 15x^9 + 15x^8 - 18x^7 + 24x^6 - 18x^5 + 45x^4 - 45x^3 - 9x^2 + 27x - 9	\( 3^{14}\cdot 5^{11} \)	$C_2.S_3^2$ (as 12T39)	Trivial
12.4.1470612500000000.1	x^12 - x^11 - 6x^10 + 15x^8 + 14x^7 - 9x^6 - 34x^5 - 15x^4 + 50x^3 - 36x^2 + 21x + 11	\( 2^{8}\cdot 5^{11}\cdot 7^{6} \)	$C_2.S_3^2$ (as 12T39)	Trivial
12.4.4477795463856128.10	x^12 - 8x^10 + 28x^8 - 68x^6 + 84x^4 - 8x^2 + 2	\( 2^{35}\cdot 19^{4} \)	$C_2.S_3^2$ (as 12T39)	Trivial
12.0.4477795463856128.17	x^12 + 8x^10 + 28x^8 + 68x^6 + 84x^4 + 8x^2 + 2	\( 2^{35}\cdot 19^{4} \)	$C_2.S_3^2$ (as 12T39)	Trivial
12.0.9615263544639488.2	x^12 + 8x^10 + 24x^8 + 32x^6 + 17x^4 + 8x^2 + 8	\( 2^{35}\cdot 23^{4} \)	$C_2.S_3^2$ (as 12T39)	Trivial
12.4.9615263544639488.4	x^12 - 8x^10 + 24x^8 - 32x^6 + 17x^4 - 8x^2 + 8	\( 2^{35}\cdot 23^{4} \)	$C_2.S_3^2$ (as 12T39)	Trivial
12.0.18260173718028288.13	x^12 + 4x^6 + 2	\( 2^{35}\cdot 3^{12} \)	$C_2.S_3^2$ (as 12T39)	Trivial
12.4.18260173718028288.15	x^12 - 4x^6 + 2	\( 2^{35}\cdot 3^{12} \)	$C_2.S_3^2$ (as 12T39)	Trivial
12.0.96938888000000000.1	x^12 - x^11 + 4x^10 - 6x^9 + 52x^8 + 135x^7 + 295x^6 + 312x^5 + 793x^4 + 453x^3 + 105x^2 - 3x + 1	\( 2^{12}\cdot 5^{9}\cdot 59^{4} \)	$C_2.S_3^2$ (as 12T39)	$[6]$
12.0.164341563462254592.3	x^12 + 12x^10 + 66x^8 + 132x^6 + 36x^4 - 72x^2 + 18	\( 2^{35}\cdot 3^{14} \)	$C_2.S_3^2$ (as 12T39)	$[2]$
12.4.164341563462254592.17	x^12 - 12x^10 + 66x^8 - 132x^6 + 36x^4 + 72x^2 + 18	\( 2^{35}\cdot 3^{14} \)	$C_2.S_3^2$ (as 12T39)	Trivial
12.0.268657648751953125.1	x^12 - 2x^11 + 15x^10 - 14x^9 + 72x^8 - 56x^7 + 137x^6 + 456x^5 + 982x^4 + 303x^3 + 738x^2 + 378x + 81	\( 3^{4}\cdot 5^{9}\cdot 7^{4}\cdot 29^{4} \)	$C_2.S_3^2$ (as 12T39)	$[12]$
12.4.1479074071160291328.2	x^12 + 12x^10 + 18x^8 - 112x^6 + 81x^4 - 36x^2 + 2	\( 2^{35}\cdot 3^{16} \)	$C_2.S_3^2$ (as 12T39)	$[2]$
12.0.1479074071160291328.20	x^12 - 12x^10 + 18x^8 + 112x^6 + 81x^4 + 36x^2 + 2	\( 2^{35}\cdot 3^{16} \)	$C_2.S_3^2$ (as 12T39)	$[2]$
12.4.1616484162452062208.13	x^12 + 16x^10 + 92x^8 - 156x^6 - 1780x^4 - 2584x^2 + 722	\( 2^{35}\cdot 19^{6} \)	$C_2.S_3^2$ (as 12T39)	Trivial (GRH)
12.0.1616484162452062208.104	x^12 - 16x^10 + 92x^8 + 156x^6 - 1780x^4 + 2584x^2 + 722	\( 2^{35}\cdot 19^{6} \)	$C_2.S_3^2$ (as 12T39)	$[10]$
12.12.2417918838767578125.1	x^12 - 3x^11 - 28x^10 + 98x^9 + 233x^8 - 1071x^7 - 374x^6 + 4658x^5 - 2354x^4 - 7196x^3 + 6782x^2 + 1684x - 2399	\( 3^{6}\cdot 5^{9}\cdot 7^{4}\cdot 29^{4} \)	$C_2.S_3^2$ (as 12T39)	Trivial (GRH)
12.12.13164224788845703125.1	x^12 - x^11 - 33x^10 + 31x^9 + 407x^8 - 342x^7 - 2337x^6 + 1623x^5 + 6392x^4 - 3122x^3 - 7965x^2 + 1986x + 3691	\( 3^{4}\cdot 5^{9}\cdot 7^{6}\cdot 29^{4} \)	$C_2.S_3^2$ (as 12T39)	Trivial (GRH)
12.4.13311666640442621952.14	x^12 - 12x^10 + 18x^8 + 48x^6 - 63x^4 - 108x^2 + 18	\( 2^{35}\cdot 3^{18} \)	$C_2.S_3^2$ (as 12T39)	$[2]$
12.0.13311666640442621952.25	x^12 + 12x^10 + 18x^8 - 48x^6 - 63x^4 + 108x^2 + 18	\( 2^{35}\cdot 3^{18} \)	$C_2.S_3^2$ (as 12T39)	$[2, 2]$
12.4.29951249940995899392.49	x^12 - 72x^6 + 648	\( 2^{33}\cdot 3^{20} \)	$C_2.S_3^2$ (as 12T39)	Trivial
12.0.29951249940995899392.52	x^12 + 72x^6 + 648	\( 2^{33}\cdot 3^{20} \)	$C_2.S_3^2$ (as 12T39)	Trivial (GRH)
12.0.119804999763983597568.68	x^12 + 36x^6 + 162	\( 2^{35}\cdot 3^{20} \)	$C_2.S_3^2$ (as 12T39)	Trivial (GRH)
12.4.119804999763983597568.80	x^12 - 36x^6 + 162	\( 2^{35}\cdot 3^{20} \)	$C_2.S_3^2$ (as 12T39)	Trivial (GRH)
12.0.119804999763983597568.84	x^12 + 144x^6 + 2592	\( 2^{35}\cdot 3^{20} \)	$C_2.S_3^2$ (as 12T39)	Trivial (GRH)
12.4.119804999763983597568.85	x^12 - 144x^6 + 2592	\( 2^{35}\cdot 3^{20} \)	$C_2.S_3^2$ (as 12T39)	Trivial (GRH)
12.0.269561249468963094528.8	x^12 + 24x^6 + 72	\( 2^{33}\cdot 3^{22} \)	$C_2.S_3^2$ (as 12T39)	$[2]$ (GRH)
12.4.269561249468963094528.15	x^12 - 24x^6 + 72	\( 2^{33}\cdot 3^{22} \)	$C_2.S_3^2$ (as 12T39)	Trivial (GRH)
12.0.1078244997875852378112.4	x^12 + 12x^6 + 18	\( 2^{35}\cdot 3^{22} \)	$C_2.S_3^2$ (as 12T39)	$[2]$ (GRH)
12.4.1078244997875852378112.15	x^12 - 12x^6 + 18	\( 2^{35}\cdot 3^{22} \)	$C_2.S_3^2$ (as 12T39)	Trivial (GRH)
12.0.1078244997875852378112.65	x^12 + 48x^6 + 288	\( 2^{35}\cdot 3^{22} \)	$C_2.S_3^2$ (as 12T39)	$[2]$ (GRH)
12.4.1078244997875852378112.77	x^12 - 48x^6 + 288	\( 2^{35}\cdot 3^{22} \)	$C_2.S_3^2$ (as 12T39)	Trivial (GRH)
12.4.2690744965595458961408.19	x^12 - 920x^8 + 1656x^6 + 186737x^4 - 1265368x^2 + 2238728	\( 2^{35}\cdot 23^{8} \)	$C_2.S_3^2$ (as 12T39)	$[2]$ (GRH)
12.0.2690744965595458961408.26	x^12 - 920x^8 - 1656x^6 + 186737x^4 + 1265368x^2 + 2238728	\( 2^{35}\cdot 23^{8} \)	$C_2.S_3^2$ (as 12T39)	$[2, 2, 10]$ (GRH)
12.4.61578162252603107311616.8	x^12 - 52x^10 + 754x^8 - 2288x^6 + 5681x^4 - 260x^2 + 7514	\( 2^{35}\cdot 13^{11} \)	$C_2.S_3^2$ (as 12T39)	$[2, 6]$ (GRH)
12.4.61578162252603107311616.12	x^12 + 104x^8 - 416x^6 + 3601x^4 - 14352x^2 + 10400	\( 2^{35}\cdot 13^{11} \)	$C_2.S_3^2$ (as 12T39)	$[2, 6]$ (GRH)
12.0.61578162252603107311616.31	x^12 + 52x^10 + 754x^8 + 2288x^6 + 5681x^4 + 260x^2 + 7514	\( 2^{35}\cdot 13^{11} \)	$C_2.S_3^2$ (as 12T39)	$[2, 60]$ (GRH)
12.0.61578162252603107311616.37	x^12 + 104x^8 + 416x^6 + 3601x^4 + 14352x^2 + 10400	\( 2^{35}\cdot 13^{11} \)	$C_2.S_3^2$ (as 12T39)	$[2, 60]$ (GRH)
12.0.419206323505881263292547072.9	x^12 + 812x^8 + 1624x^6 + 169969x^4 + 906192x^2 + 75168	\( 2^{35}\cdot 29^{11} \)	$C_2.S_3^2$ (as 12T39)	$[20]$ (GRH)
12.0.419206323505881263292547072.11	x^12 - 580x^8 + 696x^6 + 124033x^4 + 781376x^2 + 133632	\( 2^{35}\cdot 29^{11} \)	$C_2.S_3^2$ (as 12T39)	$[68]$ (GRH)
12.4.419206323505881263292547072.11	x^12 + 812x^8 - 1624x^6 + 169969x^4 - 906192x^2 + 75168	\( 2^{35}\cdot 29^{11} \)	$C_2.S_3^2$ (as 12T39)	$[2]$ (GRH)
12.4.419206323505881263292547072.16	x^12 - 580x^8 - 696x^6 + 124033x^4 - 781376x^2 + 133632	\( 2^{35}\cdot 29^{11} \)	$C_2.S_3^2$ (as 12T39)	$[2]$ (GRH)