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 6204)

Label	Polynomial	Discriminant	Galois group	Class group
12.6.3495224609375.1	x^12 - x^11 - 4x^10 + 5x^9 - 5x^8 + 14x^7 - 19x^6 + 14x^5 - 5x^4 + 5x^3 - 4x^2 - x + 1	\( -\,5^{10}\cdot 71^{3} \)	$S_3\wr C_2$ (as 12T35)	Trivial
12.6.3647529984375.1	x^12 - x^11 - 5x^10 + 3x^9 + 10x^8 - 4x^7 - 7x^6 + 6x^5 - 9x^3 - x^2 + 5x + 1	\( -\,3^{4}\cdot 5^{6}\cdot 79\cdot 191^{2} \)	12T260	Trivial
12.6.3722179279923.1	x^12 - 3x^11 - x^10 + 11x^9 - 10x^8 - 14x^7 + 24x^6 + 10x^5 - 12x^4 - 2x^3 - 3x^2 - x + 1	\( -\,3^{3}\cdot 13^{10} \)	$D_4 \times C_3$ (as 12T14)	Trivial
12.6.3924967206547.1	x^12 - 2x^11 - 2x^10 + 10x^9 - 12x^8 + x^7 + 12x^6 - 20x^5 + 6x^4 + 12x^3 - 6x^2 - 2x + 1	\( -\,43\cdot 302123^{2} \)	12T293	Trivial
12.6.3959860197871.1	x^12 - x^11 - 5x^10 + 7x^9 + 7x^8 - 20x^7 + 3x^6 + 25x^5 - 15x^4 - 10x^3 + 11x^2 - x - 1	\( -\,67^{2}\cdot 151\cdot 2417^{2} \)	12T293	Trivial
12.6.4008072671875.1	x^12 - 4x^10 - 4x^9 + x^8 + 8x^7 + 8x^6 + x^5 - 5x^4 - 6x^3 - 2x^2 + 1	\( -\,5^{6}\cdot 61\cdot 4205191 \)	$S_6\wr C_2$ (as 12T299)	Trivial
12.6.4008854234375.1	x^12 - x^11 - 3x^10 + 2x^9 + 2x^8 - 5x^7 + 8x^6 + 8x^5 - 9x^4 - 8x^3 + 3x + 1	\( -\,5^{6}\cdot 19^{2}\cdot 61^{2}\cdot 191 \)	12T260	Trivial
12.6.4457810171875.1	x^12 - 3x^11 + 2x^10 + 3x^9 - 8x^8 + 3x^7 + 7x^6 + x^5 - 4x^4 - 5x^3 + x + 1	\( -\,5^{6}\cdot 31\cdot 101\cdot 91121 \)	$S_6\wr C_2$ (as 12T299)	Trivial
12.6.4466170043531.1	x^12 - 2x^11 - 4x^10 + 10x^9 + 3x^8 - 22x^7 + 7x^6 + 22x^5 - 17x^4 - 8x^3 + 11x^2 - x - 1	\( -\,7^{8}\cdot 43^{2}\cdot 419 \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.6.4471579046875.1	x^12 - x^11 - 3x^10 - 3x^9 + x^8 + 9x^7 + 11x^6 + 9x^5 + x^4 - 3x^3 - 3x^2 - x + 1	\( -\,5^{6}\cdot 19\cdot 3881^{2} \)	12T260	Trivial
12.6.4608482796875.1	x^12 - 4x^10 - 3x^9 + 3x^8 + 13x^7 + 4x^6 - 15x^5 - 11x^4 + 5x^3 + 8x^2 + x - 1	\( -\,5^{6}\cdot 419\cdot 839^{2} \)	12T260	Trivial
12.6.4617771109375.1	x^12 - 3x^11 + x^10 + 5x^9 - 3x^8 - 10x^7 + 11x^6 + 3x^5 - 9x^4 + 8x^3 - x^2 - 3x + 1	\( -\,5^{6}\cdot 151\cdot 1399^{2} \)	12T260	Trivial
12.6.4770738948267.1	x^12 - 3x^10 - 4x^9 + 12x^7 + x^6 - 3x^5 + 3x^4 - 7x^3 - 3x^2 + 3x + 1	\( -\,3^{16}\cdot 19^{2}\cdot 307 \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.6.5029275805211.1	x^12 - x^11 - 4x^10 + 7x^9 + 2x^8 - 14x^7 + 7x^6 + 8x^5 - 10x^4 - x^3 + 5x^2 - 1	\( -\,7^{8}\cdot 872411 \)	12T292	Trivial
12.6.5099237430147.1	x^12 - x^11 - 7x^10 + 8x^9 + 16x^8 - 16x^7 - 18x^6 + 13x^5 + 10x^4 - 8x^3 - 3x^2 + 3x + 1	\( -\,3^{3}\cdot 7^{8}\cdot 181^{2} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.6.5124671732159.1	x^12 - x^11 - x^10 - x^9 - 6x^8 + 11x^7 + 10x^6 - 10x^5 - 5x^4 - x^3 + 3x^2 + 2x - 1	\( -\,7^{8}\cdot 888959 \)	12T292	Trivial
12.6.5134519671875.1	x^12 - 3x^11 + 8x^9 - 4x^8 - 8x^7 - 3x^6 + 14x^5 + 5x^4 - 14x^3 + 3x^2 + 3x - 1	\( -\,5^{6}\cdot 11^{3}\cdot 246889 \)	12T274	Trivial
12.6.5192327768191.1	x^12 - 5x^10 + 9x^8 - 2x^7 - 9x^6 + 6x^5 + 8x^4 - 4x^3 - 5x^2 + x + 1	\( -\,5192327768191 \)	$S_{12}$ (as 12T301)	Trivial
12.6.5528913603539.1	x^12 - 3x^11 + 2x^10 + 7x^9 - 13x^8 + 3x^7 + 13x^6 - 14x^5 + 7x^3 - 4x^2 - x + 1	\( -\,197\cdot 2251\cdot 12468037 \)	$S_{12}$ (as 12T301)	Trivial
12.6.5559960326067.1	x^12 - 5x^11 + 6x^10 + 9x^9 - 26x^8 + 15x^7 - x^6 + 12x^5 - 6x^4 - 16x^3 + 5x^2 + 6x + 1	\( -\,3^{9}\cdot 7^{10} \)	$D_4 \times C_3$ (as 12T14)	Trivial
12.6.6337710296875.1	x^12 - x^11 - 4x^10 + 5x^9 + 5x^8 - 9x^7 - 5x^6 + 6x^5 + 6x^4 - 3x^3 - 4x^2 + x + 1	\( -\,5^{6}\cdot 29^{3}\cdot 16631 \)	12T274	Trivial
12.6.6395326109375.1	x^12 - 4x^11 + 17x^9 - 14x^8 - 23x^7 + 32x^6 + 4x^5 - 21x^4 + 11x^3 - 5x + 1	\( -\,5^{6}\cdot 7^{8}\cdot 71 \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.6.6815156734375.1	x^12 - 2x^11 - 2x^10 + 11x^9 - 6x^8 - 21x^7 + 19x^6 + 12x^5 - 19x^4 + 2x^3 + 8x^2 - x - 1	\( -\,5^{6}\cdot 11^{4}\cdot 31^{3} \)	$S_3\wr C_2$ (as 12T35)	Trivial
12.6.6889511421875.1	x^12 - x^11 - 5x^10 + 5x^9 + 6x^8 - 6x^7 + 2x^6 - 3x^5 - 3x^4 + 7x^3 - 3x^2 - 2x + 1	\( -\,5^{6}\cdot 29^{3}\cdot 101\cdot 179 \)	12T274	Trivial
12.6.7295734234375.1	x^12 - 4x^11 + 5x^10 - 2x^9 - 5x^8 + 14x^7 - 17x^6 + 14x^5 - 5x^4 - 2x^3 + 5x^2 - 4x + 1	\( -\,5^{6}\cdot 31\cdot 3881^{2} \)	12T260	Trivial
12.6.7811642290603.1	x^12 - 3x^11 - x^10 + 7x^9 + 4x^8 - 11x^7 - 3x^6 + 3x^5 - 3x^4 + 8x^3 + 3x^2 - 3x - 1	\( -\,491^{3}\cdot 65993 \)	12T289	Trivial
12.6.8099130339328.1	x^12 - 2x^11 - 4x^10 - 4x^9 - 2x^8 + 8x^7 + 7x^6 + 8x^5 - 2x^4 - 4x^3 - 4x^2 - 2x + 1	\( -\,2^{12}\cdot 7^{11} \)	$D_4 \times C_3$ (as 12T14)	Trivial
12.6.8121007759123.1	x^12 - 2x^11 - 2x^10 + 4x^9 - 2x^8 + 7x^7 - 14x^5 + 6x^4 + 3x^3 - 4x^2 + x + 1	\( -\,7^{8}\cdot 43\cdot 181^{2} \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.6.9120427796875.1	x^12 - x^11 - x^10 - x^9 + 2x^8 - 2x^7 - 3x^6 + 19x^5 - 21x^4 + 6x^3 + 6x^2 - 5x + 1	\( -\,5^{6}\cdot 19\cdot 79\cdot 388879 \)	$S_6\wr C_2$ (as 12T299)	Trivial
12.6.9842374000287.1	x^12 - 4x^11 + 3x^10 + 15x^9 - 40x^8 + 30x^7 + 18x^6 - 39x^5 + 12x^4 + 9x^3 - 7x^2 + 1	\( -\,3^{6}\cdot 103\cdot 107^{4} \)	12T250	Trivial
12.6.9904396000000.1	x^12 - 3x^11 - x^10 + 7x^9 - x^8 - 2x^7 + 7x^6 - 16x^5 - 9x^4 + 19x^3 + 4x^2 - 4x - 1	\( -\,2^{8}\cdot 5^{6}\cdot 19^{5} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.6.10218945315584.1	x^12 - 3x^11 - x^10 + 9x^9 - x^8 - 16x^7 + 3x^6 + 24x^5 - 9x^4 - 19x^3 + 8x^2 + 6x - 1	\( -\,2^{8}\cdot 19^{2}\cdot 37^{4}\cdot 59 \)	12T250	Trivial
12.6.10513415548928.1	x^12 - 2x^11 - x^10 + 4x^9 - 11x^8 + 20x^7 - 12x^6 + 8x^4 - 4x^3 - x^2 - 2x + 1	\( -\,2^{12}\cdot 67^{2}\cdot 83^{3} \)	12T231	Trivial
12.6.10578455953408.1	x^12 - 2x^11 - x^10 - 2x^9 + 3x^8 + 14x^7 - 20x^6 + 34x^4 + 12x^3 - x^2 + 2x + 1	\( -\,2^{18}\cdot 7^{9} \)	$D_4 \times C_3$ (as 12T14)	Trivial
12.6.10721964631207.1	x^12 - 2x^11 - x^10 + 8x^9 - 7x^8 - 3x^7 + 7x^6 - 9x^5 + 7x^4 - 6x^2 + 5x - 1	\( -\,61^{2}\cdot 1423^{3} \)	12T231	Trivial
12.6.10888658888551.1	x^12 - 2x^11 - 2x^10 + 15x^9 - 21x^8 + x^7 + 36x^6 - 50x^5 + 29x^4 - 11x^2 + 6x - 1	\( -\,31\cdot 592661^{2} \)	12T293	Trivial
12.6.10890820856071.1	x^12 - 4x^11 + 2x^10 + 13x^9 - 27x^8 + 15x^7 + 22x^6 - 42x^5 + 27x^4 - 11x^2 + 6x - 1	\( -\,13^{10}\cdot 79 \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.6.11808520366783.1	x^12 - 6x^11 + 15x^10 - 20x^9 + 11x^8 + 10x^7 - 30x^6 + 37x^5 - 15x^4 - 13x^3 + 17x^2 - 7x + 1	\( -\,7^{8}\cdot 127^{3} \)	$(C_2^2.\SL(2,3)):C_2$ (as 12T104)	Trivial
12.6.11808520366783.2	x^12 - x^11 - 5x^10 + 6x^9 + 16x^8 - 6x^7 - 26x^6 - 3x^5 + 18x^4 + 6x^3 - 6x^2 - 2x + 1	\( -\,7^{8}\cdot 127^{3} \)	$(C_2^2.\SL(2,3)):C_2$ (as 12T104)	Trivial
12.6.12110614233088.1	x^12 - 4x^11 + 4x^10 + 4x^9 - 15x^8 + 14x^7 + 12x^6 - 22x^5 - 7x^4 + 10x^3 + 5x^2 - 2x - 1	\( -\,2^{18}\cdot 7^{3}\cdot 367^{2} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.6.12520427171875.1	x^12 - x^11 - 3x^10 + x^9 + 2x^8 + 10x^7 - 7x^6 - 12x^5 + 11x^4 - x^3 - 5x^2 + 2x + 1	\( -\,5^{6}\cdot 7^{8}\cdot 139 \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.6.12685282671875.1	x^12 - 3x^11 - x^10 + 11x^9 - 6x^8 - 12x^7 - x^6 + x^5 + 12x^4 + 18x^3 + 14x^2 + 6x + 1	\( -\,5^{6}\cdot 11^{5}\cdot 71^{2} \)	$D_6\wr C_2$ (as 12T125)	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
12.6.13409105834831.1	x^12 - 4x^11 + 5x^10 - 10x^8 + 18x^7 - 11x^6 - 16x^5 + 22x^4 - 8x^2 + x + 1	\( -\,7^{8}\cdot 71\cdot 181^{2} \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.6.13907109998592.1	x^12 - 3x^10 - 4x^9 + 14x^7 + 2x^6 - 18x^5 + 5x^4 + 10x^3 - 5x^2 - 2x + 1	\( -\,2^{12}\cdot 3^{6}\cdot 167^{3} \)	12T235	Trivial
12.6.14501103264256.1	x^12 - x^11 - 7x^10 + 6x^9 + 13x^8 - 16x^7 - x^6 + 19x^5 - 17x^4 - 5x^3 + 13x^2 - 3x - 1	\( -\,2^{9}\cdot 7^{8}\cdot 17^{3} \)	$C_3\times S_4$ (as 12T45)	Trivial
12.6.14941367239327.1	x^12 - x^11 - 6x^10 + 4x^9 + 16x^8 - 6x^7 - 25x^6 + x^5 + 26x^4 + 9x^3 - 14x^2 - 7x + 1	\( -\,283^{3}\cdot 659221 \)	12T289	Trivial
12.6.15691065834027.1	x^12 - 6x^10 - 4x^9 + 15x^8 + 18x^7 - 21x^6 - 21x^5 + 10x^4 + 7x^3 - x^2 + 2x + 1	\( -\,3\cdot 349^{2}\cdot 6553^{2} \)	12T293	Trivial
12.6.17476123046875.1	x^12 - 2x^11 - 4x^10 + 10x^9 - 17x^7 + 19x^6 + 8x^5 - 25x^4 + 10x^3 + 6x^2 - 12x + 1	\( -\,5^{11}\cdot 71^{3} \)	12T238	Trivial
12.6.17553188089827.1	x^12 - 2x^11 - 5x^10 + 13x^9 + 6x^8 - 30x^7 + 5x^6 + 26x^5 - 16x^4 - 6x^3 + 9x^2 - x - 1	\( -\,3^{3}\cdot 13^{6}\cdot 367^{2} \)	12T167	Trivial