Global number field search results

Further refine search

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 608)

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