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 224)

Label	Polynomial	Discriminant	Galois group	Class group
12.4.892226390625.1	x^12 - x^11 - 3x^10 + 2x^9 + 4x^8 - 4x^7 - 4x^6 + 9x^5 + 6x^4 - 6x^3 - 6x^2 + 1	\( 3^{4}\cdot 5^{6}\cdot 89^{3} \)	$C_2\times S_3\wr C_2$ (as 12T78)	Trivial
12.4.1463445356544.1	x^12 - 2x^9 - 3x^6 + 2x^3 + 1	\( 2^{18}\cdot 3^{4}\cdot 41^{3} \)	$C_2\times S_3\wr C_2$ (as 12T78)	Trivial
12.0.2100681216000.1	x^12 - 2x^11 + 6x^10 - 8x^9 + 15x^8 - 22x^7 + 34x^6 - 44x^5 + 47x^4 - 36x^3 + 19x^2 - 6x + 1	\( 2^{12}\cdot 3^{4}\cdot 5^{3}\cdot 37^{3} \)	$C_2\times S_3\wr C_2$ (as 12T78)	Trivial
12.0.2239909023744.1	x^12 - 3x^11 + 10x^9 - 9x^8 - 12x^7 + 27x^6 - 12x^5 - 9x^4 + 10x^3 - 3x + 1	\( 2^{12}\cdot 3^{13}\cdot 7^{3} \)	$C_2\times S_3\wr C_2$ (as 12T78)	Trivial
12.2.8818711734375.1	x^12 - 3x^11 + 2x^10 + 9x^9 - 27x^8 + 42x^7 - 47x^6 + 42x^5 - 27x^4 + 9x^3 + 2x^2 - 3x + 1	\( -\,3^{4}\cdot 5^{6}\cdot 191^{3} \)	$C_2\times S_3\wr C_2$ (as 12T78)	Trivial
12.2.11052312046875.2	x^12 - 3x^9 + 3x^6 - 3x^3 + 1	\( -\,3^{12}\cdot 5^{6}\cdot 11^{3} \)	$C_2\times S_3\wr C_2$ (as 12T78)	Trivial
12.6.12782924000000.1	x^12 - x^11 - 2x^10 + 14x^9 - 15x^8 - 16x^7 + 37x^6 - 16x^5 - 15x^4 + 14x^3 - 2x^2 - x + 1	\( -\,2^{8}\cdot 5^{6}\cdot 7^{4}\cdot 11^{3} \)	$C_2\times S_3\wr C_2$ (as 12T78)	Trivial
12.0.12879134720000.1	x^12 - 2x^11 - x^10 + 8x^9 - 5x^8 - 10x^7 + 9x^6 + 8x^5 - 2x^4 - 4x^3 + 2	\( 2^{22}\cdot 5^{4}\cdot 17^{3} \)	$C_2\times S_3\wr C_2$ (as 12T78)	Trivial
12.0.14526784000000.1	x^12 - 5x^11 + 12x^10 - 16x^9 + 10x^8 + x^7 + x^6 - 10x^5 + x^4 + 5x^3 + 7x^2 + 3x + 1	\( 2^{12}\cdot 5^{6}\cdot 61^{3} \)	$C_2\times S_3\wr C_2$ (as 12T78)	Trivial
12.0.71328803586048.1	x^12 + 4x^6 - 4x^3 + 1	\( 2^{27}\cdot 3^{12} \)	$C_2\times S_3\wr C_2$ (as 12T78)	Trivial
12.6.74247443359375.1	x^12 - 3x^11 - 2x^10 + 5x^9 + 4x^8 + 9x^7 - 6x^6 - 22x^5 + 11x^4 + 13x^3 - 11x^2 + x + 1	\( -\,5^{9}\cdot 11^{3}\cdot 13^{4} \)	$C_2\times S_3\wr C_2$ (as 12T78)	Trivial
12.0.75144747810816.1	x^12 - 4x^11 + 6x^10 - 4x^9 + 7x^8 + 4x^6 - 8x^5 + 8x^2 + 2	\( 2^{35}\cdot 3^{7} \)	$C_2\times S_3\wr C_2$ (as 12T78)	Trivial
12.4.213986410758144.1	x^12 - 6x^10 + 12x^8 - 24x^6 + 21x^4 + 6x^2 + 6	\( 2^{27}\cdot 3^{13} \)	$C_2\times S_3\wr C_2$ (as 12T78)	Trivial
12.4.418054936723456.1	x^12 - 4x^11 + 6x^10 + 4x^9 - 23x^8 + 24x^7 - 24x^6 + 32x^5 - 16x^4 - 16x^3 + 16x^2 - 2	\( 2^{35}\cdot 23^{3} \)	$C_2\times S_3\wr C_2$ (as 12T78)	Trivial
12.2.570630428688384.6	x^12 - 4x^9 - 2x^6 - 4x^3 + 1	\( -\,2^{30}\cdot 3^{12} \)	$C_2\times S_3\wr C_2$ (as 12T78)	Trivial
12.0.676302730297344.1	x^12 - 4x^11 + 10x^10 - 12x^9 + 17x^8 - 16x^7 + 32x^6 - 24x^5 + 32x^4 - 8x^3 + 8x^2 + 2	\( 2^{35}\cdot 3^{9} \)	$C_2\times S_3\wr C_2$ (as 12T78)	Trivial
12.0.760840571584512.3	x^12 - 4x^11 + 2x^10 + 8x^9 + x^8 - 28x^7 + 16x^6 + 8x^5 + 4x^4 - 8x + 6	\( 2^{32}\cdot 3^{11} \)	$C_2\times S_3\wr C_2$ (as 12T78)	Trivial
12.4.884272562962432.1	x^12 - 4x^11 + 4x^10 - 12x^8 + 8x^7 + 16x^6 - 24x^5 + 13x^4 + 28x^3 - 20x^2 + 24x - 2	\( 2^{30}\cdot 7^{7} \)	$C_2\times S_3\wr C_2$ (as 12T78)	Trivial
12.0.1141260857376768.15	x^12 - 12x^10 + 54x^8 - 116x^6 + 129x^4 - 72x^2 + 32	\( 2^{31}\cdot 3^{12} \)	$C_2\times S_3\wr C_2$ (as 12T78)	Trivial
12.0.1711891286065152.1	x^12 + 2x^10 - 4x^9 - 11x^8 - 16x^7 + 6x^6 + 24x^5 + 37x^4 + 52x^3 + 44x^2 + 16x + 2	\( 2^{30}\cdot 3^{13} \)	$C_2\times S_3\wr C_2$ (as 12T78)	Trivial
12.4.1711891286065152.3	x^12 + 6x^10 + 21x^8 + 12x^6 + 15x^4 - 138x^2 + 75	\( 2^{30}\cdot 3^{13} \)	$C_2\times S_3\wr C_2$ (as 12T78)	Trivial
12.6.2282521714753536.1	x^12 - 12x^10 - 4x^9 + 54x^8 + 36x^7 - 100x^6 - 108x^5 + 33x^4 + 100x^3 + 72x^2 + 24x + 2	\( -\,2^{32}\cdot 3^{12} \)	$C_2\times S_3\wr C_2$ (as 12T78)	Trivial
12.4.3423782572130304.1	x^12 - 6x^10 - 12x^6 + 21x^4 - 6x^2 + 6	\( 2^{31}\cdot 3^{13} \)	$C_2\times S_3\wr C_2$ (as 12T78)	Trivial
12.4.3537090251849728.1	x^12 - 2x^10 - 7x^8 - 16x^7 + 8x^6 + 64x^5 + 33x^4 - 88x^3 - 98x^2 + 40x + 73	\( 2^{32}\cdot 7^{7} \)	$C_2\times S_3\wr C_2$ (as 12T78)	Trivial
12.2.4565043429507072.16	x^12 - 4x^9 + 10x^6 + 12x^3 - 1	\( -\,2^{33}\cdot 3^{12} \)	$C_2\times S_3\wr C_2$ (as 12T78)	Trivial
12.0.4565043429507072.1	x^12 - 4x^9 + 10x^6 + 4x^3 + 1	\( 2^{33}\cdot 3^{12} \)	$C_2\times S_3\wr C_2$ (as 12T78)	Trivial
12.0.4565043429507072.9	x^12 - 12x^10 + 60x^8 - 36x^6 - 3x^4 + 2	\( 2^{33}\cdot 3^{12} \)	$C_2\times S_3\wr C_2$ (as 12T78)	Trivial
12.0.6086724572676096.3	x^12 - 4x^11 + 10x^10 - 20x^9 + 33x^8 - 40x^7 + 44x^6 - 32x^5 + 36x^4 - 16x^3 + 6	\( 2^{35}\cdot 3^{11} \)	$C_2\times S_3\wr C_2$ (as 12T78)	Trivial
12.0.6086724572676096.8	x^12 - 4x^6 + 69x^4 + 36x^2 + 6	\( 2^{35}\cdot 3^{11} \)	$C_2\times S_3\wr C_2$ (as 12T78)	Trivial (GRH)
12.4.6847565144260608.3	x^12 - 6x^10 + 15x^8 - 24x^6 + 24x^4 - 24x^2 + 12	\( 2^{32}\cdot 3^{13} \)	$C_2\times S_3\wr C_2$ (as 12T78)	Trivial
12.4.6884340550074368.1	x^12 + 2x^10 - 4x^9 + 12x^8 - 24x^7 + 26x^6 - 4x^5 - 37x^4 + 32x^3 - 16x^2 - 12x + 1	\( 2^{24}\cdot 17^{7} \)	$C_2\times S_3\wr C_2$ (as 12T78)	Trivial
12.4.6884340550074368.2	x^12 - 10x^10 - 16x^9 + 23x^8 + 100x^7 + 108x^6 + 24x^5 - 32x^4 - 4x^3 + 30x^2 + 16x + 1	\( 2^{24}\cdot 17^{7} \)	$C_2\times S_3\wr C_2$ (as 12T78)	Trivial
12.0.10951200375570432.2	x^12 - 8x^9 + 30x^6 - 64x^3 + 64	\( 2^{22}\cdot 3^{12}\cdot 17^{3} \)	$C_2\times S_3\wr C_2$ (as 12T78)	Trivial
12.0.10968475320188928.9	x^12 - 12x^10 + 54x^8 - 108x^6 + 81x^4 + 48	\( 2^{20}\cdot 3^{21} \)	$C_2\times S_3\wr C_2$ (as 12T78)	Trivial
12.0.10968475320188928.10	x^12 + 12x^10 + 54x^8 + 108x^6 + 81x^4 + 48	\( 2^{20}\cdot 3^{21} \)	$C_2\times S_3\wr C_2$ (as 12T78)	Trivial
12.0.15407021574586368.1	x^12 - 4x^9 + 14x^6 - 4x^3 + 1	\( 2^{30}\cdot 3^{15} \)	$C_2\times S_3\wr C_2$ (as 12T78)	$[3]$
12.0.15407021574586368.7	x^12 - 8x^9 + 24x^6 - 16x^3 + 8	\( 2^{30}\cdot 3^{15} \)	$C_2\times S_3\wr C_2$ (as 12T78)	Trivial
12.0.17495004736000000.1	x^12 - 3x^11 + 18x^10 - 45x^9 + 133x^8 - 244x^7 + 461x^6 - 623x^5 + 782x^4 - 729x^3 + 593x^2 - 396x + 176	\( 2^{12}\cdot 5^{6}\cdot 11^{3}\cdot 59^{3} \)	$C_2\times S_3\wr C_2$ (as 12T78)	$[4]$
12.6.18260173718028288.1	x^12 - 12x^10 - 8x^9 + 54x^8 + 72x^7 - 88x^6 - 216x^5 - 39x^4 + 208x^3 + 180x^2 + 24x - 14	\( -\,2^{35}\cdot 3^{12} \)	$C_2\times S_3\wr C_2$ (as 12T78)	Trivial
12.0.18260173718028288.9	x^12 + 12x^10 + 60x^8 + 36x^6 - 3x^4 + 2	\( 2^{35}\cdot 3^{12} \)	$C_2\times S_3\wr C_2$ (as 12T78)	Trivial
12.0.18260173718028288.67	x^12 - 12x^10 - 8x^9 + 54x^8 + 72x^7 - 80x^6 - 216x^5 - 87x^4 + 136x^3 + 252x^2 + 240x + 132	\( 2^{35}\cdot 3^{12} \)	$C_2\times S_3\wr C_2$ (as 12T78)	Trivial
12.0.27537362200297472.1	x^12 - 6x^10 + 7x^8 - 28x^6 + 119x^4 + 34x^2 + 17	\( 2^{26}\cdot 17^{7} \)	$C_2\times S_3\wr C_2$ (as 12T78)	$[2]$
12.0.27537362200297472.3	x^12 + 10x^10 + 32x^8 - 12x^7 + 54x^6 - 80x^5 - 34x^4 + 36x^3 + 108x^2 + 128x + 54	\( 2^{26}\cdot 17^{7} \)	$C_2\times S_3\wr C_2$ (as 12T78)	$[2]$
12.4.37913186137014272.15	x^12 - 4x^10 + 2x^8 - 8x^6 + 25x^4 + 12x^2 + 8	\( 2^{27}\cdot 7^{10} \)	$C_2\times S_3\wr C_2$ (as 12T78)	$[3]$
12.0.43873901280755712.5	x^12 - 12x^10 + 54x^8 - 114x^6 + 117x^4 - 54x^2 + 12	\( 2^{22}\cdot 3^{21} \)	$C_2\times S_3\wr C_2$ (as 12T78)	Trivial
12.0.43873901280755712.13	x^12 + 12x^10 + 54x^8 + 114x^6 + 117x^4 + 54x^2 + 12	\( 2^{22}\cdot 3^{21} \)	$C_2\times S_3\wr C_2$ (as 12T78)	Trivial
12.0.45694663348640553.1	x^12 - 7x^9 + 25x^6 - 56x^3 + 64	\( 3^{8}\cdot 13^{6}\cdot 113^{3} \)	$C_2\times S_3\wr C_2$ (as 12T78)	$[3]$
12.2.51998697814228992.30	x^12 - 8x^9 + 36x^6 - 80x^3 - 8	\( -\,2^{27}\cdot 3^{18} \)	$C_2\times S_3\wr C_2$ (as 12T78)	Trivial
12.2.51998697814228992.45	x^12 - 12x^9 - 10x^6 - 12x^3 + 1	\( -\,2^{27}\cdot 3^{18} \)	$C_2\times S_3\wr C_2$ (as 12T78)	Trivial
12.0.51998697814228992.1	x^12 - 4x^9 + 20x^6 - 8x^3 + 1	\( 2^{27}\cdot 3^{18} \)	$C_2\times S_3\wr C_2$ (as 12T78)	$[2]$