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 51939)

Label	Polynomial	Discriminant	Galois group	Class group
12.2.167630295667.1	x^12 - 3x^11 + 4x^10 - x^9 - 6x^8 + 15x^7 - 19x^6 + 15x^5 - 6x^4 - x^3 + 4x^2 - 3x + 1	\( -\,29^{2}\cdot 43\cdot 2153^{2} \)	12T293	Trivial
12.2.168661105243.1	x^12 - 5x^11 + 12x^10 - 16x^9 + 12x^8 - 4x^7 + x^6 - 3x^5 + 4x^4 - 3x^3 + x^2 - 1	\( -\,67\cdot 131^{2}\cdot 383^{2} \)	12T293	Trivial
12.2.173809422763.1	x^12 - 2x^11 + 3x^10 - 2x^9 - 2x^8 + 4x^7 - 2x^5 + 4x^3 - 3x^2 - x + 1	\( -\,31^{4}\cdot 53^{2}\cdot 67 \)	12T250	Trivial
12.2.175113024319.1	x^12 - 4x^11 + 8x^10 - 9x^9 + 4x^8 + 5x^7 - 16x^6 + 23x^5 - 24x^4 + 19x^3 - 12x^2 + 5x - 1	\( -\,23^{4}\cdot 79\cdot 89^{2} \)	12T250	Trivial
12.2.175122415616.1	x^12 - 4x^11 + 10x^10 - 16x^9 + 17x^8 - 6x^7 - 12x^6 + 30x^5 - 37x^4 + 30x^3 - 17x^2 + 6x - 1	\( -\,2^{18}\cdot 71\cdot 97^{2} \)	12T260	Trivial
12.2.177788874752.1	x^12 - 4x^9 + 3x^8 - 4x^7 + 11x^6 - 8x^5 + 8x^4 - 14x^3 + 13x^2 - 6x + 1	\( -\,2^{12}\cdot 31^{4}\cdot 47 \)	12T227	Trivial
12.2.204800642687.1	x^12 - 3x^11 + 5x^10 - 3x^9 - 4x^8 + 12x^7 - 15x^6 + 12x^5 - 4x^4 - 3x^3 + 5x^2 - 3x + 1	\( -\,23\cdot 197^{2}\cdot 479^{2} \)	12T293	Trivial
12.2.205567038859.1	x^12 - x^11 + 2x^10 + x^8 + 4x^7 - 5x^6 + 4x^5 - 8x^4 + 4x^3 - 4x^2 + 2x - 1	\( -\,7^{8}\cdot 13^{2}\cdot 211 \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.2.206487484375.1	x^12 - x^11 + 2x^10 + x^9 - 3x^8 + 8x^7 - 13x^6 + 16x^5 - 17x^4 + 13x^3 - 8x^2 + 3x - 1	\( -\,5^{6}\cdot 79\cdot 409^{2} \)	12T260	Trivial
12.2.208976546875.1	x^12 - 2x^11 + 4x^10 - 5x^9 + 4x^8 + x^7 - 9x^6 + 18x^5 - 22x^4 + 19x^3 - 12x^2 + 5x - 1	\( -\,5^{6}\cdot 19\cdot 839^{2} \)	12T260	Trivial
12.2.225117671875.1	x^12 - x^10 - x^9 - x^8 + 3x^7 + 3x^6 - 2x^4 - 2x^3 - 1	\( -\,5^{6}\cdot 179\cdot 80489 \)	$S_6\wr C_2$ (as 12T299)	Trivial
12.2.233544944483.1	x^12 - 3x^11 + 2x^10 + 5x^9 - 9x^8 + 3x^7 + 6x^6 - 7x^5 + 3x^4 + x^3 - x^2 + x - 1	\( -\,23^{4}\cdot 101\cdot 8263 \)	12T294	Trivial
12.2.238362687139.1	x^12 - 2x^11 + 4x^10 - 4x^9 + x^8 + 3x^7 - 8x^6 + 7x^5 - 3x^4 - 2x^3 + 4x^2 - 3x + 1	\( -\,23^{4}\cdot 317\cdot 2687 \)	12T294	Trivial
12.2.239557046875.1	x^12 - x^10 - x^9 + 2x^7 - 2x^6 + x^4 + x^3 - x + 1	\( -\,5^{6}\cdot 19\cdot 806929 \)	$S_6\wr C_2$ (as 12T299)	Trivial
12.2.247087671875.1	x^12 - x^11 - 3x^9 + x^7 + 3x^6 + x^5 - 3x^3 - x + 1	\( -\,5^{6}\cdot 11^{3}\cdot 109^{2} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.2.255609008128.1	x^12 - 2x^11 + 3x^10 - 4x^9 + 7x^8 - 8x^7 - 2x^6 + 18x^5 - 28x^4 + 22x^3 - 11x^2 + 4x - 1	\( -\,2^{12}\cdot 23^{4}\cdot 223 \)	12T227	Trivial
12.2.257978421875.1	x^12 - 2x^11 + 2x^9 - 5x^7 + 10x^6 - 16x^5 + 20x^4 - 19x^3 + 12x^2 - 5x + 1	\( -\,5^{6}\cdot 23^{4}\cdot 59 \)	12T193	Trivial
12.2.266846228071.1	x^12 - x^11 + 2x^10 - 3x^9 + 3x^8 - 4x^7 + 3x^6 - 4x^5 + 3x^4 - 3x^3 + 2x^2 - x + 1	\( -\,31\cdot 92779^{2} \)	12T293	Trivial
12.2.273636802651.1	x^12 - x^11 + 5x^10 - 4x^9 + 12x^8 - 6x^7 + 15x^6 - 6x^5 + 9x^4 - 5x^3 + x^2 - 3x - 1	\( -\,283^{3}\cdot 12073 \)	12T289	Trivial
12.2.279198105664.1	x^12 - 5x^10 + 9x^8 - 7x^6 + x^4 + 3x^2 - 1	\( -\,2^{6}\cdot 257^{4} \)	12T227	Trivial
12.2.288323843827.1	x^12 - 3x^11 + 8x^9 - 6x^8 - 7x^7 + 10x^6 + x^5 - 7x^4 + x^3 + 4x^2 - 1	\( -\,283^{3}\cdot 12721 \)	12T289	Trivial
12.2.293890894259.1	x^12 - x^9 - x^4 + x + 1	\( -\,103\cdot 2853309653 \)	$S_{12}$ (as 12T301)	Trivial
12.2.299095170283.1	x^12 - 2x^11 + 4x^10 - x^9 - 2x^8 + 6x^7 - 4x^6 - 2x^5 + 2x^4 - 2x^3 - 2x^2 + 1	\( -\,7^{8}\cdot 13^{2}\cdot 307 \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.2.307980921875.1	x^12 - 2x^11 + 3x^10 - 7x^9 + 12x^8 - 12x^7 + 13x^6 - 12x^5 + 5x^4 + 2x^3 - 3x^2 + 2x - 1	\( -\,5^{6}\cdot 11^{3}\cdot 59\cdot 251 \)	12T274	Trivial
12.2.314972378176.1	x^12 - x^10 - 3x^8 + x^6 + 3x^4 - x^2 - 1	\( -\,2^{6}\cdot 31^{4}\cdot 73^{2} \)	12T186	Trivial
12.2.327779546875.1	x^12 - 2x^11 + 2x^10 - 3x^9 + x^8 + x^7 + x^4 - x^3 + x^2 + x - 1	\( -\,5^{6}\cdot 11^{3}\cdot 15761 \)	12T274	Trivial
12.2.336393921875.1	x^12 - x^11 - x^10 - x^9 + 3x^8 - x^7 - x^6 - x^5 + 3x^4 - x^3 - x^2 - x + 1	\( -\,5^{6}\cdot 11\cdot 1399^{2} \)	12T260	Trivial
12.2.341962230519.1	x^12 - 4x^11 + 10x^10 - 20x^9 + 31x^8 - 43x^7 + 52x^6 - 56x^5 + 52x^4 - 39x^3 + 21x^2 - 7x + 1	\( -\,3^{3}\cdot 7^{8}\cdot 13^{3} \)	$C_4^2.(C_3\times D_4)$ (as 12T141)	Trivial
12.2.349257427087.1	x^12 - 4x^11 + 8x^10 - 10x^9 + 9x^8 - 12x^7 + 18x^6 - 18x^5 + 14x^4 - 9x^3 + 5x^2 - 2x - 1	\( -\,127\cdot 229^{4} \)	12T227	Trivial
12.2.362031460339.1	x^12 - x^7 + x^6 + 2x^5 - 2x^4 + x^3 - x^2 - x + 1	\( -\,362031460339 \)	$S_{12}$ (as 12T301)	Trivial
12.2.373065296875.1	x^12 - 2x^11 - 2x^10 + 8x^9 - 12x^7 + 3x^6 + 11x^5 - 5x^4 - 6x^3 + 3x^2 + x - 1	\( -\,5^{6}\cdot 19^{3}\cdot 59^{2} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.2.396228830787.1	x^12 - 2x^11 - x^10 + 4x^9 - 3x^7 - x^6 + 3x^4 + x^3 - 3x^2 - x + 1	\( -\,3^{3}\cdot 23^{4}\cdot 229^{2} \)	12T186	Trivial
12.2.398786546875.1	x^12 - 3x^11 + 4x^10 - 3x^9 + 4x^8 - 7x^7 + 7x^6 - x^5 - 4x^4 + 4x^3 - x^2 + x - 1	\( -\,5^{6}\cdot 19^{3}\cdot 61^{2} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.2.419159399791.1	x^12 - 2x^11 + 3x^9 - 2x^8 - x^7 + x^6 - x^5 + x^4 + 2x^3 - 2x^2 + 1	\( -\,11^{4}\cdot 31^{5} \)	$C_2 \times S_4$ (as 12T22)	Trivial
12.2.438976000000.1	x^12 - x^11 + 2x^10 - 3x^8 + 6x^7 - 9x^6 + 6x^5 - 3x^4 + 2x^2 - x + 1	\( -\,2^{12}\cdot 5^{6}\cdot 19^{3} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.2.447330484375.1	x^12 - 2x^11 + x^10 - 3x^9 + 8x^8 - 3x^7 - 2x^6 - 4x^5 + 2x^4 + 9x^3 - 9x^2 + 4x - 1	\( -\,5^{6}\cdot 31^{5} \)	$(C_6\times C_2):C_2$ (as 12T13)	Trivial
12.2.451992187175.1	x^12 - x^11 + 4x^10 + x^9 - x^8 + 12x^7 - 9x^6 + 12x^5 - x^4 + x^3 + 4x^2 - x + 1	\( -\,5^{2}\cdot 23^{5}\cdot 53^{2} \)	12T223	Trivial
12.2.458342033107.1	x^12 - 3x^11 + 2x^10 + 3x^9 - 6x^8 + 3x^7 + 4x^6 - 10x^5 + 8x^4 - x^3 - 2x^2 + x - 1	\( -\,7^{8}\cdot 43^{3} \)	$(C_2^2.\SL(2,3)):C_2$ (as 12T104)	Trivial
12.2.458342033107.2	x^12 - 4x^11 + 6x^10 - 4x^9 + x^8 - 3x^7 + 5x^6 - 3x^5 + x^4 - 4x^3 + 6x^2 - 4x + 1	\( -\,7^{8}\cdot 43^{3} \)	$(C_2^2.\SL(2,3)):C_2$ (as 12T104)	Trivial
12.2.530569362483.1	x^12 - x^11 + x^10 - 3x^9 + 6x^8 - 7x^7 + 4x^6 - 6x^5 + 10x^4 - 11x^3 + 5x^2 + x - 1	\( -\,3^{4}\cdot 17^{2}\cdot 283^{3} \)	12T258	Trivial
12.2.533806460928.1	x^12 - 5x^11 + 13x^10 - 23x^9 + 31x^8 - 32x^7 + 27x^6 - 17x^5 + 8x^4 - 2x^3 + x - 1	\( -\,2^{12}\cdot 3^{3}\cdot 13^{6} \)	$S_3\times D_4$ (as 12T28)	Trivial
12.2.562523516779.1	x^12 - 2x^11 - x^10 + 7x^9 - 5x^8 - 6x^7 + 11x^6 - 3x^5 - 5x^4 + 6x^3 - 2x^2 - x + 1	\( -\,7^{8}\cdot 97579 \)	12T292	Trivial
12.2.566636000000.1	x^12 - 4x^10 - x^9 + 7x^8 + 4x^7 - 5x^6 - 8x^5 + x^4 + 7x^3 - x^2 - 3x + 1	\( -\,2^{8}\cdot 5^{6}\cdot 7^{4}\cdot 59 \)	12T193	Trivial
12.2.644204000000.1	x^12 - 3x^11 + 3x^10 - x^9 - 3x^8 + 4x^7 - x^6 + 8x^5 - 7x^4 - 3x^3 - 2x^2 + 4x - 1	\( -\,2^{8}\cdot 5^{6}\cdot 11^{5} \)	$(C_6\times C_2):C_2$ (as 12T13)	Trivial
12.2.644204000000.2	x^12 - 3x^11 + 2x^10 + 4x^9 - 7x^8 + 2x^7 + 3x^6 + 2x^5 - 7x^4 + 4x^3 + 2x^2 - 3x + 1	\( -\,2^{8}\cdot 5^{6}\cdot 11^{5} \)	$D_6:D_6$ (as 12T81)	Trivial
12.2.659081523200.1	x^12 - 2x^11 + 5x^10 - 2x^9 + 6x^8 - 2x^7 + 11x^6 + 2x^5 - x^4 + 2x^3 + 4x - 1	\( -\,2^{12}\cdot 5^{2}\cdot 23^{5} \)	$C_2\times C_2^2:S_4$ (as 12T100)	Trivial
12.2.713607421387.1	x^12 - 4x^10 - 2x^9 + 6x^8 + 10x^7 - x^6 - 13x^5 - 9x^4 + 4x^3 + 9x^2 + 5x + 1	\( -\,7^{8}\cdot 123787 \)	12T292	Trivial
12.2.738751981811.1	x^12 - 3x^11 + 4x^10 - x^9 - 6x^8 + 9x^7 - 2x^6 - 8x^5 + 8x^4 - x^3 - 4x^2 + 3x - 1	\( -\,79^{2}\cdot 491^{3} \)	12T281	Trivial
12.2.742534191307.1	x^12 - 5x^11 + 10x^10 - 6x^9 - 10x^8 + 21x^7 - 10x^6 - 8x^5 + 10x^4 + 2x^3 - 8x^2 + 5x - 1	\( -\,181^{2}\cdot 283^{3} \)	12T281	Trivial
12.2.780912359375.1	x^12 - 2x^11 + 2x^10 - 5x^9 + 6x^8 - 3x^7 + 5x^6 - 4x^5 - x^4 + 2x^2 - x - 1	\( -\,5^{6}\cdot 71\cdot 839^{2} \)	12T260	Trivial