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 846)

Label	Polynomial	Discriminant	Galois group	Class group
12.10.104424406621339.1	x^12 - 6x^11 + 10x^10 + 3x^9 - 29x^8 + 35x^7 + 7x^6 - 49x^5 + 19x^4 + 18x^3 - 9x^2 - 2x + 1	\( -\,7^{8}\cdot 211\cdot 293^{2} \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.10.115472708921875.1	x^12 - 10x^10 - 2x^9 + 33x^8 + 12x^7 - 43x^6 - 23x^5 + 19x^4 + 17x^3 - 4x - 1	\( -\,5^{6}\cdot 7390253371 \)	$S_6\wr C_2$ (as 12T299)	Trivial
12.10.115555016421875.1	x^12 - x^11 - 9x^10 + 10x^9 + 26x^8 - 33x^7 - 22x^6 + 41x^5 - 13x^4 - 12x^3 + 19x^2 - 5x - 1	\( -\,5^{6}\cdot 491\cdot 3881^{2} \)	12T260	Trivial
12.10.118319190921875.1	x^12 - 9x^10 - 3x^9 + 27x^8 + 21x^7 - 36x^6 - 42x^5 + 18x^4 + 29x^3 + x^2 - 5x - 1	\( -\,5^{6}\cdot 59\cdot 11329^{2} \)	12T260	Trivial
12.10.119171067348991.1	x^12 - 11x^10 - 4x^9 + 37x^8 + 20x^7 - 54x^6 - 27x^5 + 35x^4 + 13x^3 - 10x^2 - 2x + 1	\( -\,7^{8}\cdot 181^{2}\cdot 631 \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.10.137691709155347.1	x^12 - 2x^11 - 8x^10 + 19x^9 + 21x^8 - 58x^7 - 27x^6 + 69x^5 + 26x^4 - 30x^3 - 13x^2 + 2x + 1	\( -\,107\cdot 1134389^{2} \)	12T293	Trivial
12.10.168600935531327.1	x^12 - 4x^11 - x^10 + 23x^9 - 26x^8 - 23x^7 + 56x^6 - 6x^5 - 39x^4 + 11x^3 + 10x^2 - 2x - 1	\( -\,13^{10}\cdot 1223 \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.10.172770619021119.1	x^12 - x^11 - 10x^10 + 7x^9 + 33x^8 - 12x^7 - 50x^6 + x^5 + 38x^4 + 7x^3 - 12x^2 - 2x + 1	\( -\,3^{6}\cdot 7^{10}\cdot 839 \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.10.173022521421875.1	x^12 - 2x^11 - 6x^10 + 13x^9 + 10x^8 - 30x^7 + 2x^6 + 30x^5 - 16x^4 - 13x^3 + 9x^2 + 2x - 1	\( -\,5^{6}\cdot 6679\cdot 1657949 \)	$S_6\wr C_2$ (as 12T299)	Trivial
12.10.174247057020339.1	x^12 - 9x^10 - 3x^9 + 24x^8 + 18x^7 - 15x^6 - 30x^5 - 6x^4 + 17x^3 + 6x^2 - 3x - 1	\( -\,3^{16}\cdot 199\cdot 20341 \)	12T292	Trivial
12.10.212024878470419.1	x^12 - x^11 - 10x^10 + 9x^9 + 32x^8 - 32x^7 - 40x^6 + 47x^5 + 18x^4 - 27x^3 + 5x - 1	\( -\,7^{8}\cdot 36779219 \)	12T292	Trivial
12.10.248331672071147.1	x^12 - 10x^10 - 2x^9 + 31x^8 + 6x^7 - 35x^6 - x^5 + 10x^4 - 5x^3 + 3x^2 + 2x - 1	\( -\,7\cdot 101\cdot 592661^{2} \)	12T293	Trivial
12.10.385228876000000.1	x^12 - 3x^11 - 6x^10 + 20x^9 + 7x^8 - 42x^7 + 21x^6 + 26x^5 - 53x^4 + 10x^3 + 30x^2 - 11x + 1	\( -\,2^{8}\cdot 5^{6}\cdot 19^{4}\cdot 739 \)	12T208	Trivial
12.10.396348306546875.1	x^12 - 3x^11 - 7x^10 + 23x^9 + 16x^8 - 60x^7 - 14x^6 + 65x^5 + 7x^4 - 31x^3 - 4x^2 + 5x + 1	\( -\,5^{6}\cdot 29^{3}\cdot 1040071 \)	12T274	Trivial
12.10.438643405484375.1	x^12 - 2x^11 - 8x^10 + 17x^9 + 17x^8 - 47x^7 - 5x^6 + 58x^5 - 13x^4 - 31x^3 + 8x^2 + 5x - 1	\( -\,5^{6}\cdot 7^{2}\cdot 13^{2}\cdot 29^{3}\cdot 139 \)	12T274	Trivial
12.10.492092096000000.1	x^12 - 4x^11 - x^10 + 20x^9 - 20x^8 - 16x^7 + 41x^6 - 8x^5 - 30x^4 + 10x^3 + 9x^2 - 2x - 1	\( -\,2^{12}\cdot 5^{6}\cdot 19^{4}\cdot 59 \)	12T208	Trivial
12.10.564668382613504.1	x^12 - 4x^10 - 2x^8 + 22x^6 - 24x^4 + 9x^2 - 1	\( -\,2^{12}\cdot 13^{10} \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.10.652184962479099.1	x^12 - 2x^11 - 6x^10 + 22x^9 - 12x^8 - 46x^7 + 60x^6 + 37x^5 - 67x^4 - 15x^3 + 27x^2 + 3x - 3	\( -\,3^{3}\cdot 7^{2}\cdot 113\cdot 257^{4} \)	12T250	Trivial
12.10.704117429874688.1	x^12 - 4x^11 - 3x^10 + 28x^9 - 20x^8 - 32x^7 + 35x^6 - 8x^5 - 6x^4 + 26x^3 - 7x^2 - 10x + 1	\( -\,2^{12}\cdot 37^{6}\cdot 67 \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.10.809662500831232.1	x^12 - 6x^11 + 5x^10 + 30x^9 - 58x^8 - 6x^7 + 67x^6 - 34x^5 + 28x^4 - 50x^3 + 27x^2 - 2x - 1	\( -\,2^{22}\cdot 37^{4}\cdot 103 \)	12T193	Trivial
12.10.821483713801107.1	x^12 - 12x^10 - 3x^9 + 50x^8 + 28x^7 - 96x^6 - 71x^5 + 81x^4 + 65x^3 - 22x^2 - 19x - 1	\( -\,3^{2}\cdot 7^{3}\cdot 61\cdot 257^{4} \)	12T250	Trivial
12.10.1042033516000000.1	x^12 - 3x^11 - 3x^10 + 5x^9 + 7x^8 + 28x^7 - 3x^6 - 62x^5 - 5x^4 + 37x^3 + 4x^2 - 6x - 1	\( -\,2^{8}\cdot 5^{6}\cdot 37^{4}\cdot 139 \)	12T193	Trivial
12.10.1087609273238272.1	x^12 - x^11 - 8x^10 + 6x^9 + 21x^8 - 4x^7 - 27x^6 - 14x^5 + 17x^4 + 18x^3 - 2x^2 - 5x - 1	\( -\,2^{8}\cdot 37^{4}\cdot 317\cdot 7151 \)	12T294	Trivial
12.10.1100183484179200.1	x^12 - x^11 - 12x^10 + 10x^9 + 59x^8 - 46x^7 - 141x^6 + 114x^5 + 149x^4 - 130x^3 - 42x^2 + 39x - 1	\( -\,2^{8}\cdot 5^{2}\cdot 37^{6}\cdot 67 \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.10.2132354108301979.1	x^12 - 4x^11 - 4x^10 + 29x^9 - 3x^8 - 71x^7 + 24x^6 + 67x^5 - 20x^4 - 23x^3 + 5x^2 + x - 1	\( -\,19^{3}\cdot 103^{3}\cdot 293\cdot 971 \)	12T289	Trivial
12.10.2647588864000000.1	x^12 - 6x^11 + 5x^10 + 30x^9 - 54x^8 - 30x^7 + 103x^6 - 2x^5 - 82x^4 + 6x^3 + 27x^2 + 2x - 1	\( -\,2^{22}\cdot 5^{6}\cdot 71\cdot 569 \)	12T261	Trivial
12.10.2918880929197399.1	x^12 - 4x^11 + 24x^9 - 30x^8 - 48x^7 + 87x^6 + 34x^5 - 79x^4 - 5x^3 + 22x^2 - 2x - 1	\( -\,19^{4}\cdot 103^{4}\cdot 199 \)	12T227	Trivial
12.10.3329577743355827.1	x^12 - 4x^11 - 5x^10 + 32x^9 + 2x^8 - 90x^7 + 18x^6 + 105x^5 - 25x^4 - 37x^3 + 10x^2 - 7x - 1	\( -\,19^{4}\cdot 103^{4}\cdot 227 \)	12T227	Trivial
12.10.4528333294697216.1	x^12 - 3x^11 - 6x^10 + 24x^9 + 5x^8 - 66x^7 + 25x^6 + 72x^5 - 47x^4 - 26x^3 + 22x^2 - x - 1	\( -\,2^{8}\cdot 37^{4}\cdot 9438251 \)	12T294	Trivial
12.10.6065138113068939.1	x^12 - 4x^11 - 6x^10 + 34x^9 + 10x^8 - 106x^7 - x^6 + 145x^5 - 9x^4 - 81x^3 + 6x^2 + 15x - 1	\( -\,3\cdot 19^{3}\cdot 103^{3}\cdot 269741 \)	12T289	Trivial
12.10.6189907940737024.1	x^12 - 8x^10 + 16x^8 + 10x^6 - 51x^4 + 34x^2 - 1	\( -\,2^{30}\cdot 7^{8} \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.10.7340688973975552.1	x^12 - 13x^10 + 52x^8 - 78x^6 + 26x^4 + 26x^2 - 13	\( -\,2^{12}\cdot 13^{11} \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.10.7770704775363639.1	x^12 - 2x^11 - 10x^10 + 20x^9 + 35x^8 - 71x^7 - 49x^6 + 105x^5 + 22x^4 - 57x^3 - 2x^2 + 8x - 1	\( -\,3^{2}\cdot 401\cdot 2153146238671 \)	$S_{12}$ (as 12T301)	Trivial
12.10.11517353618919691.1	x^12 - 3x^11 - 9x^10 + 28x^9 + 33x^8 - 97x^7 - 65x^6 + 149x^5 + 72x^4 - 91x^3 - 37x^2 + 11x + 3	\( -\,2539073\cdot 4536046667 \)	$S_{12}$ (as 12T301)	Trivial
12.10.19499511680335872.1	x^12 - 6x^10 + 3x^8 + 24x^6 - 36x^4 + 18x^2 - 3	\( -\,2^{24}\cdot 3^{19} \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.10.19499511680335872.2	x^12 - 6x^10 + 3x^8 + 42x^6 - 90x^4 + 54x^2 - 3	\( -\,2^{24}\cdot 3^{19} \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.10.33174037869887488.1	x^12 - 14x^10 + 63x^8 - 112x^6 + 63x^4 + 14x^2 - 7	\( -\,2^{24}\cdot 7^{11} \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial (GRH)
12.10.33174037869887488.2	x^12 - 28x^8 + 84x^6 - 91x^4 + 42x^2 - 7	\( -\,2^{24}\cdot 7^{11} \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial (GRH)
12.10.36138776487264256.1	x^12 - 8x^10 - 8x^8 + 176x^6 - 384x^4 + 288x^2 - 64	\( -\,2^{18}\cdot 13^{10} \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.10.43329355585159168.1	x^12 - 8x^10 + 12x^8 + 22x^6 - 63x^4 + 42x^2 - 7	\( -\,2^{30}\cdot 7^{9} \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial (GRH)
12.10.43329355585159168.2	x^12 - 10x^10 + 31x^8 - 22x^6 - 42x^4 + 56x^2 - 7	\( -\,2^{30}\cdot 7^{9} \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial (GRH)
12.10.44644157912109375.1	x^12 - 12x^10 + 54x^8 - 118x^6 + 141x^4 - 15x^3 - 90x^2 + 45x - 5	\( -\,3^{18}\cdot 5^{9}\cdot 59 \)	12T264	Trivial
12.10.46221064723759104.1	x^12 - 6x^10 - 3x^8 + 38x^6 - 42x^4 + 12x^2 - 1	\( -\,2^{30}\cdot 3^{16} \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.10.49519263525896192.1	x^12 - 12x^10 + 50x^8 - 80x^6 + 24x^4 + 32x^2 - 8	\( -\,2^{33}\cdot 7^{8} \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial (GRH)
12.10.51998697814228992.1	x^12 - 12x^10 + 48x^8 - 68x^6 + 12x^4 + 24x^2 - 8	\( -\,2^{27}\cdot 3^{18} \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial (GRH)
12.10.51998697814228992.2	x^12 - 6x^10 - 6x^8 + 68x^6 - 96x^4 + 48x^2 - 8	\( -\,2^{27}\cdot 3^{18} \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.10.66270093164000000.1	x^12 - 3x^11 - 8x^10 + 38x^9 + 3x^8 - 134x^7 + 17x^6 + 178x^5 + 5x^4 - 80x^3 - 22x^2 + 3x + 1	\( -\,2^{8}\cdot 5^{6}\cdot 11\cdot 197^{4} \)	12T240	Trivial
12.10.92935153036000000.1	x^12 - 3x^11 - 5x^10 + 15x^9 - 7x^8 + 56x^7 - 21x^6 - 266x^5 + 145x^4 + 273x^3 - 114x^2 - 46x + 1	\( -\,2^{8}\cdot 5^{6}\cdot 11^{4}\cdot 17^{4}\cdot 19 \)	12T240	Trivial
12.10.102594674359524096.1	x^12 - 6x^11 + 20x^10 - 45x^9 + 29x^8 + 88x^7 - 129x^6 - 44x^5 + 111x^4 + 11x^3 - 31x^2 - 5x + 1	\( -\,2^{8}\cdot 3^{7}\cdot 17\cdot 47^{6} \)	12T224	Trivial
12.10.117046181009836107.1	x^12 - 6x^11 + 54x^9 - 66x^8 - 138x^7 + 298x^6 + 69x^5 - 459x^4 + 129x^3 + 225x^2 - 108x + 9	\( -\,3^{16}\cdot 71^{4}\cdot 107 \)	12T188	Trivial