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 99)

Label	Polynomial	Discriminant	Galois group	Class group
12.4.2438900000000.1	x^12 - x^11 - 2x^10 - 2x^9 + 5x^8 + 6x^7 - 7x^6 - 6x^5 + 5x^4 + 2x^3 - 2x^2 + x + 1	\( 2^{8}\cdot 5^{8}\cdot 29^{3} \)	$S_3^2:C_4$ (as 12T80)	Trivial
12.4.4691011328125.1	x^12 - 3x^11 + x^10 + 8x^9 - 21x^8 + 39x^7 - 58x^6 + 62x^5 - 44x^4 + 16x^3 - 3x + 1	\( 5^{8}\cdot 229^{3} \)	$S_3^2:C_4$ (as 12T80)	Trivial
12.2.14849488671875.1	x^12 - 4x^11 + 7x^10 - 10x^9 + 13x^8 - 15x^7 + 16x^6 - 10x^5 + 2x^4 + 2x^2 - 2x - 1	\( -\,5^{8}\cdot 11^{3}\cdot 13^{4} \)	$S_3^2:C_4$ (as 12T80)	Trivial
12.2.17476123046875.1	x^12 - 3x^11 + x^10 + 15x^9 - 45x^8 + 77x^7 - 91x^6 + 77x^5 - 45x^4 + 15x^3 + x^2 - 3x + 1	\( -\,5^{11}\cdot 71^{3} \)	$S_3^2:C_4$ (as 12T80)	Trivial
12.0.40975526953125.1	x^12 - 3x^11 + 5x^10 - 9x^9 + 15x^8 - 15x^7 + 13x^6 - 15x^5 + 15x^4 - 9x^3 + 5x^2 - 3x + 1	\( 3^{4}\cdot 5^{8}\cdot 109^{3} \)	$S_3^2:C_4$ (as 12T80)	Trivial
12.0.57145404956672.1	x^12 - 3x^11 + 12x^10 - 26x^9 + 53x^8 - 83x^7 + 112x^6 - 124x^5 + 118x^4 - 88x^3 + 60x^2 - 24x + 8	\( 2^{13}\cdot 17^{8} \)	$S_3^2:C_4$ (as 12T80)	Trivial
12.6.144504250032987.1	x^12 - 6x^11 + 10x^10 + 4x^9 - 18x^8 - 16x^7 + 39x^6 + 21x^5 - 37x^4 - 7x^3 + 12x^2 + x - 1	\( -\,3^{11}\cdot 13^{8} \)	$S_3^2:C_4$ (as 12T80)	Trivial
12.6.276307801171875.1	x^12 - 6x^10 - 5x^9 - 9x^8 + 58x^6 + 90x^5 + 114x^4 + 135x^3 + 99x^2 + 45x + 9	\( -\,3^{12}\cdot 5^{8}\cdot 11^{3} \)	$S_3^2:C_4$ (as 12T80)	Trivial
12.4.836109873446912.2	x^12 - 2x^10 + 5x^8 + 28x^6 - 13x^4 - 74x^2 + 23	\( 2^{36}\cdot 23^{3} \)	$S_3^2:C_4$ (as 12T80)	Trivial
12.0.836109873446912.3	x^12 + 2x^10 + 5x^8 - 28x^6 - 13x^4 + 74x^2 + 23	\( 2^{36}\cdot 23^{3} \)	$S_3^2:C_4$ (as 12T80)	$[2]$
12.0.914326479306752.1	x^12 + 12x^10 + 49x^8 + 88x^6 + 64x^4 + 14x^2 + 8	\( 2^{17}\cdot 17^{8} \)	$S_3^2:C_4$ (as 12T80)	Trivial
12.4.3657305917227008.2	x^12 - 8x^10 + 33x^8 - 78x^6 + 108x^4 - 68x^2 + 8	\( 2^{19}\cdot 17^{8} \)	$S_3^2:C_4$ (as 12T80)	Trivial
12.2.5739519416467456.2	x^12 + 10x^10 + 19x^8 + 32x^6 - 16x^4 - 40x^2 - 4	\( -\,2^{36}\cdot 17^{4} \)	$S_3^2:C_4$ (as 12T80)	Trivial
12.6.5739519416467456.2	x^12 - 10x^10 + 19x^8 - 32x^6 - 16x^4 + 40x^2 - 4	\( -\,2^{36}\cdot 17^{4} \)	$S_3^2:C_4$ (as 12T80)	Trivial (GRH)
12.4.14629223668908032.5	x^12 - 12x^10 + 49x^8 - 88x^6 + 64x^4 - 14x^2 + 8	\( 2^{21}\cdot 17^{8} \)	$S_3^2:C_4$ (as 12T80)	Trivial
12.0.17547210909508096.1	x^12 - x^11 + 4x^10 - 20x^9 + 25x^8 - 43x^7 + 122x^6 - 101x^5 + 168x^4 - 78x^3 + 81x^2 - 19x + 13	\( 2^{9}\cdot 17^{11} \)	$S_3^2:C_4$ (as 12T80)	$[2]$
12.6.36520347436056576.2	x^12 - 12x^10 + 54x^8 - 100x^6 + 33x^4 + 72x^2 - 16	\( -\,2^{36}\cdot 3^{12} \)	$S_3^2:C_4$ (as 12T80)	Trivial (GRH)
12.2.36520347436056576.4	x^12 + 12x^10 + 54x^8 + 100x^6 + 33x^4 - 72x^2 - 16	\( -\,2^{36}\cdot 3^{12} \)	$S_3^2:C_4$ (as 12T80)	Trivial
12.0.65025690039453125.1	x^12 - 3x^11 + 20x^10 - 40x^9 + 135x^8 - 168x^7 + 324x^6 - 175x^5 + 200x^4 - 65x^3 + 95x^2 + 100x + 25	\( 5^{8}\cdot 5501^{3} \)	$S_3^2:C_4$ (as 12T80)	$[5]$
12.6.73040694872113152.2	x^12 - 12x^10 + 54x^8 - 108x^6 + 81x^4 - 8	\( -\,2^{37}\cdot 3^{12} \)	$S_3^2:C_4$ (as 12T80)	Trivial
12.2.73040694872113152.23	x^12 + 12x^10 + 54x^8 + 108x^6 + 81x^4 - 8	\( -\,2^{37}\cdot 3^{12} \)	$S_3^2:C_4$ (as 12T80)	$[2]$
12.0.110149448801189888.5	x^12 - 8x^10 - 4x^9 + 35x^8 + 80x^7 + 20x^6 - 96x^5 - 68x^4 + 64x^3 + 128x^2 - 128x + 32	\( 2^{28}\cdot 17^{7} \)	$S_3^2:C_4$ (as 12T80)	Trivial
12.0.110149448801189888.7	x^12 - 2x^11 + 9x^10 - 8x^9 + 30x^8 - 28x^7 + 118x^6 - 64x^5 + 208x^4 - 400x^3 + 440x^2 + 64x + 128	\( 2^{28}\cdot 17^{7} \)	$S_3^2:C_4$ (as 12T80)	$[3]$
12.0.113186888059191296.1	x^12 - 4x^10 - 24x^8 + 60x^6 + 189x^4 + 56x^2 + 14	\( 2^{37}\cdot 7^{7} \)	$S_3^2:C_4$ (as 12T80)	$[2]$
12.4.113186888059191296.1	x^12 - 4x^10 - 20x^8 + 60x^6 + 133x^4 - 128x^2 + 14	\( 2^{37}\cdot 7^{7} \)	$S_3^2:C_4$ (as 12T80)	Trivial
12.0.113186888059191296.2	x^12 + 4x^10 - 20x^8 - 60x^6 + 133x^4 + 128x^2 + 14	\( 2^{37}\cdot 7^{7} \)	$S_3^2:C_4$ (as 12T80)	$[2]$
12.4.113186888059191296.3	x^12 + 4x^10 - 24x^8 - 60x^6 + 189x^4 - 56x^2 + 14	\( 2^{37}\cdot 7^{7} \)	$S_3^2:C_4$ (as 12T80)	Trivial
12.0.114172357111328125.1	x^12 - 2x^11 + 13x^10 - 33x^9 + 71x^8 - 184x^7 + 319x^6 - 378x^5 + 1268x^4 - 99x^3 + 2343x^2 + 41x + 1691	\( 5^{9}\cdot 3881^{3} \)	$S_3^2:C_4$ (as 12T80)	$[20]$
12.6.126927759749414912.1	x^12 - 12x^10 + 28x^8 - 36x^6 + 5x^4 + 8x^2 - 2	\( -\,2^{37}\cdot 31^{4} \)	$S_3^2:C_4$ (as 12T80)	Trivial
12.2.126927759749414912.6	x^12 + 12x^10 + 28x^8 + 36x^6 + 5x^4 - 8x^2 - 2	\( -\,2^{37}\cdot 31^{4} \)	$S_3^2:C_4$ (as 12T80)	$[2]$
12.6.280755374552129536.1	x^12 - 5x^11 - 2x^10 + 50x^9 - 83x^8 - 75x^7 + 380x^6 - 330x^5 - 100x^4 + 356x^3 - 240x^2 + 80x - 16	\( -\,2^{13}\cdot 17^{11} \)	$S_3^2:C_4$ (as 12T80)	$[2]$ (GRH)
12.6.328683126924509184.1	x^12 - 30x^8 - 12x^6 + 297x^4 - 252x^2 - 36	\( -\,2^{36}\cdot 3^{14} \)	$S_3^2:C_4$ (as 12T80)	Trivial
12.2.328683126924509184.14	x^12 - 30x^8 + 12x^6 + 297x^4 + 252x^2 - 36	\( -\,2^{36}\cdot 3^{14} \)	$S_3^2:C_4$ (as 12T80)	$[2]$
12.4.442302123053416448.10	x^12 - 4x^11 + 16x^9 - 168x^8 + 112x^7 - 116x^6 - 344x^5 - 19x^4 - 524x^3 + 1652x^2 + 1176x + 686	\( 2^{36}\cdot 23^{5} \)	$S_3^2:C_4$ (as 12T80)	Trivial (GRH)
12.0.442302123053416448.14	x^12 - 4x^11 + 12x^10 - 24x^9 + 64x^8 - 304x^7 + 300x^6 - 488x^5 + 3837x^4 - 4620x^3 + 2176x^2 - 9248x + 9826	\( 2^{36}\cdot 23^{5} \)	$S_3^2:C_4$ (as 12T80)	$[2, 2]$
12.12.571326958400000000.1	x^12 - 3x^11 - 16x^10 + 44x^9 + 99x^8 - 214x^7 - 329x^6 + 415x^5 + 567x^4 - 243x^3 - 351x^2 + 29	\( 2^{12}\cdot 5^{8}\cdot 11^{4}\cdot 29^{3} \)	$S_3^2:C_4$ (as 12T80)	Trivial (GRH)
12.6.657366253849018368.11	x^12 - 12x^10 + 12x^8 + 132x^6 - 315x^4 + 144x^2 - 18	\( -\,2^{37}\cdot 3^{14} \)	$S_3^2:C_4$ (as 12T80)	Trivial
12.2.657366253849018368.22	x^12 + 12x^10 + 12x^8 - 132x^6 - 315x^4 - 144x^2 - 18	\( -\,2^{37}\cdot 3^{14} \)	$S_3^2:C_4$ (as 12T80)	Trivial
12.0.1123021498208518144.2	x^12 - 3x^11 + 2x^10 + 21x^9 - 32x^8 - 45x^7 + 351x^6 - 584x^5 + 648x^4 - 412x^3 + 988x^2 - 1272x + 1208	\( 2^{15}\cdot 17^{11} \)	$S_3^2:C_4$ (as 12T80)	$[2]$
12.12.1296131454900000000.1	x^12 - 24x^10 + 216x^8 - 888x^6 + 1584x^4 - 40x^3 - 864x^2 + 240x - 16	\( 2^{8}\cdot 3^{12}\cdot 5^{8}\cdot 29^{3} \)	$S_3^2:C_4$ (as 12T80)	Trivial (GRH)
12.4.1762391180819038208.3	x^12 + 2x^10 - 4x^9 + 20x^8 - 64x^7 + 36x^6 - 24x^5 - 187x^4 + 32x^3 - 94x^2 - 180x - 46	\( 2^{32}\cdot 17^{7} \)	$S_3^2:C_4$ (as 12T80)	Trivial
12.4.1762391180819038208.5	x^12 - 4x^11 + 6x^10 - 12x^9 + 42x^8 + 8x^7 + 128x^6 + 112x^5 + 193x^4 - 636x^3 - 354x^2 + 212x + 98	\( 2^{32}\cdot 17^{7} \)	$S_3^2:C_4$ (as 12T80)	Trivial
12.6.2958148142320582656.1	x^12 - 12x^10 - 16x^9 - 18x^8 + 48x^7 - 12x^6 - 720x^5 - 1455x^4 - 464x^3 + 864x^2 + 384x - 128	\( -\,2^{36}\cdot 3^{16} \)	$S_3^2:C_4$ (as 12T80)	Trivial (GRH)
12.2.2958148142320582656.74	x^12 + 12x^10 - 32x^9 + 90x^8 - 240x^7 + 580x^6 - 1440x^5 + 1233x^4 - 1072x^3 + 576x^2 - 384x + 128	\( -\,2^{36}\cdot 3^{16} \)	$S_3^2:C_4$ (as 12T80)	$[2]$ (GRH)
12.4.3524782361638076416.4	x^12 + 4x^10 - 22x^8 - 200x^6 - 664x^4 - 864x^2 + 136	\( 2^{33}\cdot 17^{7} \)	$S_3^2:C_4$ (as 12T80)	Trivial
12.0.3524782361638076416.7	x^12 + 28x^8 + 24x^6 + 68x^4 + 272x^2 + 136	\( 2^{33}\cdot 17^{7} \)	$S_3^2:C_4$ (as 12T80)	$[4]$
12.4.3524782361638076416.12	x^12 + 28x^8 - 24x^6 + 68x^4 - 272x^2 + 136	\( 2^{33}\cdot 17^{7} \)	$S_3^2:C_4$ (as 12T80)	Trivial
12.0.3524782361638076416.18	x^12 - 4x^10 - 22x^8 + 200x^6 - 664x^4 + 864x^2 + 136	\( 2^{33}\cdot 17^{7} \)	$S_3^2:C_4$ (as 12T80)	$[12]$
12.2.4492085992834072576.2	x^12 + 17x^8 + 238x^6 - 68x^4 - 2040x^2 - 2176	\( -\,2^{17}\cdot 17^{11} \)	$S_3^2:C_4$ (as 12T80)	$[2]$
12.4.4492085992834072576.10	x^12 - 17x^10 + 85x^8 - 306x^6 + 748x^4 - 1003x^2 + 544	\( 2^{17}\cdot 17^{11} \)	$S_3^2:C_4$ (as 12T80)	$[2]$