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 90)

Label	Polynomial	Discriminant	Galois group	Class group
12.2.4511594708992.1	x^12 - 2x^11 + 3x^10 - 2x^9 + 3x^8 - 4x^7 - 2x^6 - 4x^5 + 3x^4 - 2x^3 + 3x^2 - 2x + 1	\( -\,2^{28}\cdot 7^{5} \)	$C_3:S_3.D_4$ (as 12T82)	Trivial
12.4.8012167578125.1	x^12 - 2x^11 - 3x^10 + 3x^9 + 10x^8 + x^7 - 16x^6 - 7x^5 + 10x^4 + 3x^3 - x^2 + 3x - 1	\( 5^{8}\cdot 29^{5} \)	$C_3:S_3.D_4$ (as 12T82)	Trivial
12.2.11183262109375.1	x^12 - 3x^11 + 8x^10 - 15x^9 + 18x^8 - 15x^7 - x^6 + 15x^5 - 23x^4 + 20x^3 - 12x^2 + 4x - 1	\( -\,5^{8}\cdot 31^{5} \)	$C_3:S_3.D_4$ (as 12T82)	Trivial
12.0.40060837890625.1	x^12 - 4x^11 + 8x^10 - 12x^9 + 7x^8 + x^7 - x^6 + 7x^5 + 8x^4 - x^3 + 4x^2 + x + 1	\( 5^{9}\cdot 29^{5} \)	$C_3:S_3.D_4$ (as 12T82)	$[2]$
12.2.72185515343872.1	x^12 - 4x^11 + 4x^10 + 4x^9 - 17x^8 + 16x^7 - 12x^6 + 16x^5 - 12x^4 + 8x^3 - 4x^2 - 2	\( -\,2^{32}\cdot 7^{5} \)	$C_3:S_3.D_4$ (as 12T82)	Trivial
12.2.144371030687744.1	x^12 - 4x^9 - 6x^8 + 22x^6 - 20x^4 + 20x^3 + 4x^2 + 1	\( -\,2^{33}\cdot 7^{5} \)	$C_3:S_3.D_4$ (as 12T82)	Trivial
12.2.164995463643136.1	x^12 + 2x^8 - 4x^6 + 9x^4 - 20x^2 - 4	\( -\,2^{36}\cdot 7^{4} \)	$C_3:S_3.D_4$ (as 12T82)	Trivial
12.2.164995463643136.4	x^12 + 2x^8 + 4x^6 + 9x^4 + 20x^2 - 4	\( -\,2^{36}\cdot 7^{4} \)	$C_3:S_3.D_4$ (as 12T82)	Trivial
12.2.221068140740608.1	x^12 - 4x^11 + 4x^10 + 8x^9 - 23x^8 + 16x^7 + 12x^6 - 20x^5 - 15x^4 + 32x^3 + 2x^2 - 8x - 4	\( -\,2^{28}\cdot 7^{7} \)	$C_3:S_3.D_4$ (as 12T82)	Trivial
12.0.329920430078125.1	x^12 + 6x^10 - 4x^9 + 18x^8 + 4x^7 + 31x^6 + 30x^5 + 7x^4 + 22x^3 + 19x^2 + 10x + 5	\( 5^{8}\cdot 61^{5} \)	$C_3:S_3.D_4$ (as 12T82)	Trivial
12.2.329990927286272.3	x^12 - 4x^10 + 20x^8 - 4x^6 + 5x^4 - 2	\( -\,2^{37}\cdot 7^{4} \)	$C_3:S_3.D_4$ (as 12T82)	Trivial
12.2.329990927286272.4	x^12 + 4x^10 + 20x^8 + 4x^6 + 5x^4 - 2	\( -\,2^{37}\cdot 7^{4} \)	$C_3:S_3.D_4$ (as 12T82)	Trivial
12.2.577484122750976.1	x^12 - 4x^10 - 16x^9 + 8x^8 + 24x^7 + 36x^6 - 56x^5 - 6x^4 + 16x^3 - 8x^2 + 4	\( -\,2^{35}\cdot 7^{5} \)	$C_3:S_3.D_4$ (as 12T82)	$[2]$
12.4.1154968245501952.1	x^12 - 2x^8 - 12x^6 - 7x^4 + 28x^2 + 28	\( 2^{36}\cdot 7^{5} \)	$C_3:S_3.D_4$ (as 12T82)	Trivial
12.0.1154968245501952.2	x^12 - 2x^8 + 12x^6 - 7x^4 - 28x^2 + 28	\( 2^{36}\cdot 7^{5} \)	$C_3:S_3.D_4$ (as 12T82)	$[2]$
12.4.2309936491003904.1	x^12 - 4x^10 - 36x^6 + 77x^4 - 56x^2 + 14	\( 2^{37}\cdot 7^{5} \)	$C_3:S_3.D_4$ (as 12T82)	Trivial
12.0.2309936491003904.2	x^12 + 4x^10 + 36x^6 + 77x^4 + 56x^2 + 14	\( 2^{37}\cdot 7^{5} \)	$C_3:S_3.D_4$ (as 12T82)	$[2]$
12.2.3537090251849728.3	x^12 - 4x^11 + 6x^10 - 12x^9 + 26x^8 - 16x^7 - 36x^6 + 72x^5 - 31x^4 + 4x^3 + 2x^2 + 4x - 2	\( -\,2^{32}\cdot 7^{7} \)	$C_3:S_3.D_4$ (as 12T82)	Trivial
12.2.7074180503699456.1	x^12 - 4x^9 - 2x^8 - 8x^7 - 22x^6 + 40x^5 + 10x^4 + 20x^3 - 76x^2 + 48x - 9	\( -\,2^{33}\cdot 7^{7} \)	$C_3:S_3.D_4$ (as 12T82)	Trivial
12.2.10832338896289792.1	x^12 - 4x^11 + 10x^10 - 12x^9 + 12x^8 - 28x^7 + 8x^6 + 56x^5 + 26x^4 + 72x^3 - 58x^2 + 8x + 1	\( -\,2^{28}\cdot 7^{9} \)	$C_3:S_3.D_4$ (as 12T82)	$[3]$
12.2.10832338896289792.2	x^12 - 4x^11 + 12x^10 - 32x^9 + 80x^8 - 108x^7 + 182x^6 - 236x^5 + 118x^4 - 312x^3 - 8x^2 - 92x + 127	\( -\,2^{28}\cdot 7^{9} \)	$C_3:S_3.D_4$ (as 12T82)	$[3]$
12.2.28296722014797824.1	x^12 + 4x^10 - 48x^8 - 112x^7 - 116x^6 + 24x^5 + 346x^4 + 400x^3 - 224x^2 - 720x - 324	\( -\,2^{35}\cdot 7^{7} \)	$C_3:S_3.D_4$ (as 12T82)	$[2]$
12.6.33433243941796875.2	x^12 - 21x^10 - 21x^9 + 162x^8 + 327x^7 - 428x^6 - 1881x^5 - 1122x^4 + 3135x^3 + 6237x^2 + 4389x + 1111	\( -\,3^{12}\cdot 5^{8}\cdot 11^{5} \)	$C_3:S_3.D_4$ (as 12T82)	Trivial
12.2.36520347436056576.5	x^12 - 12x^10 + 54x^8 - 116x^6 + 129x^4 - 72x^2 - 16	\( -\,2^{36}\cdot 3^{12} \)	$C_3:S_3.D_4$ (as 12T82)	Trivial
12.2.36520347436056576.6	x^12 - 12x^10 + 18x^8 + 116x^6 + 129x^4 - 72x^2 - 16	\( -\,2^{36}\cdot 3^{12} \)	$C_3:S_3.D_4$ (as 12T82)	Trivial
12.2.36520347436056576.7	x^12 + 12x^10 + 18x^8 - 116x^6 + 129x^4 + 72x^2 - 16	\( -\,2^{36}\cdot 3^{12} \)	$C_3:S_3.D_4$ (as 12T82)	Trivial
12.2.36520347436056576.8	x^12 + 12x^10 + 54x^8 + 116x^6 + 129x^4 + 72x^2 - 16	\( -\,2^{36}\cdot 3^{12} \)	$C_3:S_3.D_4$ (as 12T82)	Trivial
12.0.56593444029595648.1	x^12 - 4x^11 + 20x^10 - 32x^9 + 66x^8 - 8x^7 + 64x^6 - 16x^5 + 34x^4 - 40x^3 + 96x^2 + 32x + 4	\( 2^{36}\cdot 7^{7} \)	$C_3:S_3.D_4$ (as 12T82)	$[6]$
12.4.56593444029595648.1	x^12 - 4x^11 + 4x^10 - 16x^9 + 84x^8 - 152x^7 + 192x^6 - 384x^5 + 283x^4 + 764x^3 - 1548x^2 + 936x - 158	\( 2^{36}\cdot 7^{7} \)	$C_3:S_3.D_4$ (as 12T82)	Trivial
12.2.73040694872113152.1	x^12 + 12x^10 + 18x^8 - 44x^6 - 111x^4 - 128	\( -\,2^{37}\cdot 3^{12} \)	$C_3:S_3.D_4$ (as 12T82)	Trivial
12.2.73040694872113152.2	x^12 - 12x^10 + 18x^8 + 44x^6 - 111x^4 - 128	\( -\,2^{37}\cdot 3^{12} \)	$C_3:S_3.D_4$ (as 12T82)	Trivial
12.2.73040694872113152.9	x^12 - 12x^10 + 54x^8 - 108x^6 + 81x^4 - 32	\( -\,2^{37}\cdot 3^{12} \)	$C_3:S_3.D_4$ (as 12T82)	Trivial
12.2.73040694872113152.10	x^12 + 12x^10 + 54x^8 + 108x^6 + 81x^4 - 32	\( -\,2^{37}\cdot 3^{12} \)	$C_3:S_3.D_4$ (as 12T82)	Trivial
12.6.105343598274047523.1	x^12 - 21x^10 - 9x^9 + 144x^8 + 45x^7 - 522x^6 - 27x^5 + 972x^4 - 297x^3 - 567x^2 + 405x - 81	\( -\,3^{17}\cdot 13^{8} \)	$C_3:S_3.D_4$ (as 12T82)	Trivial
12.0.113186888059191296.7	x^12 - 4x^10 + 52x^8 + 148x^6 + 469x^4 + 1176x^2 + 686	\( 2^{37}\cdot 7^{7} \)	$C_3:S_3.D_4$ (as 12T82)	$[2]$
12.4.113186888059191296.8	x^12 + 4x^10 + 52x^8 - 148x^6 + 469x^4 - 1176x^2 + 686	\( 2^{37}\cdot 7^{7} \)	$C_3:S_3.D_4$ (as 12T82)	Trivial
12.2.173317422340636672.3	x^12 - 10x^10 + 45x^8 + 48x^6 + 56x^4 - 56x^2 - 28	\( -\,2^{32}\cdot 7^{9} \)	$C_3:S_3.D_4$ (as 12T82)	$[3]$
12.2.173317422340636672.4	x^12 + 18x^10 + 115x^8 + 188x^6 - 133x^4 + 42x^2 - 7	\( -\,2^{32}\cdot 7^{9} \)	$C_3:S_3.D_4$ (as 12T82)	$[3]$
12.2.328683126924509184.9	x^12 + 30x^8 - 12x^6 + 153x^4 - 36x^2 - 36	\( -\,2^{36}\cdot 3^{14} \)	$C_3:S_3.D_4$ (as 12T82)	Trivial
12.2.328683126924509184.13	x^12 + 30x^8 + 12x^6 + 153x^4 + 36x^2 - 36	\( -\,2^{36}\cdot 3^{14} \)	$C_3:S_3.D_4$ (as 12T82)	$[3]$
12.2.328683126924509184.15	x^12 - 6x^10 + 21x^8 - 60x^6 + 99x^4 - 270x^2 - 9	\( -\,2^{36}\cdot 3^{14} \)	$C_3:S_3.D_4$ (as 12T82)	Trivial
12.2.328683126924509184.23	x^12 + 6x^10 + 21x^8 + 60x^6 + 99x^4 + 270x^2 - 9	\( -\,2^{36}\cdot 3^{14} \)	$C_3:S_3.D_4$ (as 12T82)	Trivial
12.2.346634844681273344.2	x^12 - 4x^10 + 10x^8 - 48x^6 + 448x^4 - 896x^2 - 224	\( -\,2^{33}\cdot 7^{9} \)	$C_3:S_3.D_4$ (as 12T82)	$[3]$
12.2.346634844681273344.9	x^12 + 12x^10 + 62x^8 + 148x^6 + 161x^4 - 56x^2 - 56	\( -\,2^{33}\cdot 7^{9} \)	$C_3:S_3.D_4$ (as 12T82)	$[3]$
12.2.396154108207169536.3	x^12 + 18x^10 + 109x^8 + 340x^6 + 83x^4 - 1398x^2 - 1681	\( -\,2^{36}\cdot 7^{8} \)	$C_3:S_3.D_4$ (as 12T82)	$[3]$
12.2.396154108207169536.4	x^12 - 18x^10 + 109x^8 - 340x^6 + 83x^4 + 1398x^2 - 1681	\( -\,2^{36}\cdot 7^{8} \)	$C_3:S_3.D_4$ (as 12T82)	$[3]$
12.2.396154108207169536.5	x^12 - 4x^11 + 4x^10 - 24x^9 + 46x^8 + 24x^7 + 184x^6 + 32x^5 - 218x^4 - 728x^3 - 1072x^2 - 880x - 388	\( -\,2^{36}\cdot 7^{8} \)	$C_3:S_3.D_4$ (as 12T82)	$[2]$
12.2.396154108207169536.10	x^12 - 4x^11 + 4x^10 + 32x^9 - 52x^8 + 24x^7 + 128x^6 - 248x^5 + 27x^4 + 252x^3 - 484x^2 + 352x - 94	\( -\,2^{36}\cdot 7^{8} \)	$C_3:S_3.D_4$ (as 12T82)	$[2]$
12.2.657366253849018368.23	x^12 + 12x^10 + 48x^8 + 36x^6 - 99x^4 - 144x^2 - 18	\( -\,2^{37}\cdot 3^{14} \)	$C_3:S_3.D_4$ (as 12T82)	Trivial
12.2.657366253849018368.34	x^12 - 12x^10 + 48x^8 - 36x^6 - 99x^4 + 144x^2 - 18	\( -\,2^{37}\cdot 3^{14} \)	$C_3:S_3.D_4$ (as 12T82)	Trivial