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 18880)

Label	Polynomial	Discriminant	Galois group	Class group
12.4.719569994873.1	x^12 - 2x^11 - 4x^10 + 8x^9 + 8x^8 - 13x^7 - 10x^6 + 8x^5 + 8x^4 - 5x^2 - x + 1	\( 23^{4}\cdot 137^{3} \)	$C_4\times C_4^2:C_3:C_2$ (as 12T150)	Trivial
12.4.734297685397.1	x^12 - x^11 - 2x^10 + x^9 + 2x^8 - x^7 - x^6 + x^5 + 2x^4 - x^3 - 2x^2 + x + 1	\( 157\cdot 68389^{2} \)	12T293	Trivial
12.4.750369026957.1	x^12 - 4x^11 + 3x^10 + 9x^9 - 17x^8 + 20x^6 - 10x^5 - 9x^4 + 6x^3 + 3x^2 - 2x - 1	\( 11^{2}\cdot 29^{2}\cdot 53\cdot 373^{2} \)	12T293	Trivial
12.4.764131428301.1	x^12 - 2x^10 - x^9 + 4x^8 + 2x^7 - 3x^5 - 5x^4 + 3x^3 + 4x^2 - x - 1	\( 764131428301 \)	$S_{12}$ (as 12T301)	Trivial
12.4.777011613097.1	x^12 - 6x^11 + 19x^10 - 40x^9 + 62x^8 - 74x^7 + 67x^6 - 44x^5 + 16x^4 + 2x^3 - 8x^2 + 5x - 1	\( 97\cdot 89501^{2} \)	12T293	Trivial
12.4.794230140625.1	x^12 - x^9 - 4x^8 + x^7 + 2x^6 + 2x^5 + x^4 - x^3 - 2x^2 - x + 1	\( 5^{6}\cdot 50830729 \)	$S_6\wr C_2$ (as 12T299)	Trivial
12.4.796918902097.1	x^12 - 3x^11 + x^10 + 3x^9 - 2x^8 + 2x^7 + x^6 - 4x^5 - 2x^4 - x^3 + x^2 + 3x + 1	\( 73\cdot 163^{2}\cdot 641^{2} \)	12T293	Trivial
12.4.802389895609.1	x^12 - 2x^11 - 2x^10 + 4x^9 + x^8 - x^7 - 2x^6 - x^5 + 2x^4 + x^3 - x^2 - 2x + 1	\( 107^{2}\cdot 70083841 \)	$S_{12}$ (as 12T301)	Trivial
12.4.819345401329.1	x^12 - x^11 - 2x^10 - x^8 + x^7 + 3x^6 + x^5 - x^4 - 2x^2 - x + 1	\( 7^{8}\cdot 13^{2}\cdot 29^{2} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	Trivial
12.4.823612912893.1	x^12 - 3x^11 + 3x^10 + 2x^9 - 9x^8 + 12x^7 - 11x^6 + 6x^5 + 3x^4 - 12x^3 + 12x^2 - 6x + 1	\( 3^{16}\cdot 19^{2}\cdot 53 \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.4.854660453125.1	x^12 - 2x^11 + 6x^9 - 6x^8 - 6x^7 + 14x^6 - 5x^5 - 9x^4 + 10x^3 - x^2 - 4x + 1	\( 5^{6}\cdot 54698269 \)	$S_6\wr C_2$ (as 12T299)	Trivial
12.4.860539390625.1	x^12 - x^11 - 2x^10 + 2x^9 - x^8 - 3x^7 + 4x^6 + x^5 - 2x^4 + 2x^3 + x^2 - 1	\( 5^{6}\cdot 19^{2}\cdot 41\cdot 61^{2} \)	12T260	Trivial
12.4.877704785881.1	x^12 - 4x^11 + 4x^10 + 4x^9 - 11x^8 + 7x^7 - 2x^6 + 13x^5 - 30x^4 + 25x^3 - 11x^2 + 6x - 1	\( 7^{2}\cdot 11^{2}\cdot 23^{6} \)	$C_2^2\times C_2^2:S_4$ (as 12T139)	Trivial
12.4.882697830400.1	x^12 - 4x^11 + 4x^10 + 4x^9 - 9x^8 + 2x^7 + 4x^6 - 2x^5 - x^4 + 2x^3 + x^2 - 2x - 1	\( 2^{18}\cdot 5^{2}\cdot 367^{2} \)	12T236	Trivial
12.4.886856703125.1	x^12 - 2x^9 - 5x^8 - 5x^7 - 7x^6 - 5x^5 - 5x^4 - 2x^3 + 1	\( 5^{6}\cdot 29\cdot 1399^{2} \)	12T260	Trivial
12.4.888218971933.1	x^12 - 6x^11 + 18x^10 - 35x^9 + 47x^8 - 44x^7 + 19x^6 + 16x^5 - 40x^4 + 39x^3 - 23x^2 + 8x - 1	\( 23^{4}\cdot 61^{2}\cdot 853 \)	12T250	Trivial
12.4.892226390625.1	x^12 - x^11 - 3x^10 + 2x^9 + 4x^8 - 4x^7 - 4x^6 + 9x^5 + 6x^4 - 6x^3 - 6x^2 + 1	\( 3^{4}\cdot 5^{6}\cdot 89^{3} \)	$C_2\times S_3\wr C_2$ (as 12T78)	Trivial
12.4.913034947181.1	x^12 - 2x^11 - 2x^10 + 4x^9 + 5x^8 - 7x^7 - 7x^6 + 7x^5 + 6x^4 - 4x^3 - 4x^2 + x + 1	\( 7^{8}\cdot 251\cdot 631 \)	12T292	Trivial
12.4.915636578125.1	x^12 + x^10 - x^9 - 3x^8 + x^7 + x^6 + 3x^5 + 3x^4 - 3x^3 - 4x^2 + x + 1	\( 5^{6}\cdot 181\cdot 569^{2} \)	12T260	Trivial
12.4.920963140625.1	x^12 - 5x^10 - x^9 + 8x^8 + 2x^7 - 4x^6 + x^5 - 3x^3 - x^2 + 2x + 1	\( 5^{6}\cdot 11^{2}\cdot 41\cdot 109^{2} \)	12T260	Trivial
12.4.933397515625.1	x^12 - x^11 - x^9 - x^8 + 2x^7 - x^6 + 2x^5 - x^4 - x^3 - x + 1	\( 5^{6}\cdot 59^{2}\cdot 131^{2} \)	12T203	Trivial
12.4.936468877312.1	x^12 - 5x^10 - 6x^9 + 11x^8 + 20x^7 - 6x^6 - 28x^5 - 6x^4 + 18x^3 + 5x^2 - 4x - 1	\( 2^{12}\cdot 19\cdot 23^{4}\cdot 43 \)	12T227	Trivial
12.4.937338265625.1	x^12 - 2x^11 + 2x^10 + x^9 - 8x^8 + 9x^7 - 8x^5 + 14x^4 - 3x^3 - 9x^2 + 3x + 1	\( 5^{6}\cdot 89\cdot 821^{2} \)	12T260	Trivial
12.4.949704822784.1	x^12 - 2x^11 + 4x^10 - 2x^9 - 4x^8 + 10x^7 - 15x^6 + 10x^5 - 4x^4 - 2x^3 + 4x^2 - 2x + 1	\( 2^{12}\cdot 15227^{2} \)	12T285	Trivial
12.4.953506996597.1	x^12 - 3x^10 - 4x^9 + 6x^8 + 7x^7 - 7x^6 - 7x^5 + 6x^4 + 4x^3 - 3x^2 + 1	\( 23^{4}\cdot 53^{2}\cdot 1213 \)	12T250	Trivial
12.4.960645015625.1	x^12 - 3x^11 + 2x^10 + 2x^9 - 4x^8 + x^7 + x^6 + x^5 - 4x^4 + 2x^3 + 2x^2 - 3x + 1	\( 5^{6}\cdot 7841^{2} \)	12T203	Trivial
12.4.968117620736.1	x^12 - 2x^11 - x^10 + 4x^9 + 4x^8 - 14x^7 + 5x^6 + 14x^5 - 15x^4 + 8x^2 - 2x - 1	\( 2^{12}\cdot 7^{8}\cdot 41 \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.4.972292630401.1	x^12 - 4x^11 + 5x^10 + 3x^9 - 20x^8 + 30x^7 - 12x^6 - 24x^5 + 43x^4 - 30x^3 + 8x^2 + 2x - 1	\( 3^{4}\cdot 331^{4} \)	$C_4^2:C_3:C_2$ (as 12T62)	Trivial
12.4.978890140625.1	x^12 - x^11 - x^10 + 2x^9 + 6x^8 - 8x^7 - 5x^6 + 8x^5 - x^4 - 4x^3 - x^2 + 2x + 1	\( 5^{6}\cdot 89\cdot 839^{2} \)	12T260	Trivial
12.4.1085603537929.1	x^12 - 6x^11 + 15x^10 - 20x^9 + 16x^8 - 10x^7 + 11x^6 - 16x^5 + 12x^4 - 2x^3 - 6x^2 + 5x - 1	\( 23^{2}\cdot 89^{2}\cdot 509^{2} \)	12T285	Trivial
12.4.1095605453125.1	x^12 - 2x^11 - x^10 + 8x^9 - 9x^8 + x^7 + 9x^6 - 9x^5 + 4x^4 + x^3 - 2x^2 + x - 1	\( 5^{6}\cdot 70118749 \)	$S_6\wr C_2$ (as 12T299)	Trivial
12.4.1153744515625.1	x^12 - 2x^10 - 2x^9 + x^8 + 4x^6 + 2x^5 - 6x^4 - 3x^3 + x^2 + 2x + 1	\( 5^{6}\cdot 13^{2}\cdot 661^{2} \)	12T236	Trivial
12.4.1158384877741.1	x^12 - 2x^11 - 2x^10 + 4x^9 + 2x^8 - 3x^7 + 3x^6 - 10x^4 + x^3 + 7x^2 + x - 1	\( 7^{8}\cdot 13^{2}\cdot 29\cdot 41 \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.4.1167128033569.1	x^12 - 3x^11 + 3x^10 + 3x^9 - 9x^8 + 8x^7 - 8x^6 - x^5 + 3x^3 + 4x^2 - x - 1	\( 29^{2}\cdot 37253^{2} \)	12T285	Trivial
12.4.1172328665957.1	x^12 - 3x^11 + 2x^10 + 3x^9 - 8x^8 + 4x^7 + 9x^6 - 7x^5 - 3x^4 + x^3 - 2x^2 + x + 1	\( 331^{3}\cdot 32327 \)	12T289	Trivial
12.4.1184054284288.1	x^12 - 2x^11 - 2x^9 - 2x^8 + 16x^7 + x^6 - 16x^5 - 2x^4 + 2x^3 + 2x + 1	\( 2^{12}\cdot 23^{4}\cdot 1033 \)	12T227	Trivial
12.4.1237419323253.1	x^12 - x^11 - 5x^10 + 5x^9 + 7x^8 - 8x^7 + x^6 + 2x^5 - 9x^4 + 4x^3 + 6x^2 - x - 1	\( 3^{2}\cdot 31^{4}\cdot 53^{3} \)	$C_4\times C_4^2:C_3:C_2$ (as 12T150)	Trivial
12.4.1255569610725.1	x^12 - x^11 + 2x^10 - 3x^9 - 4x^8 + 3x^7 - 3x^6 + 3x^5 + 2x^4 + 8x^3 - 16x^2 + 8x - 1	\( 3^{3}\cdot 5^{2}\cdot 17^{2}\cdot 23^{5} \)	12T186	Trivial
12.4.1263657015625.1	x^12 - x^11 - x^10 - 3x^9 + x^8 + 2x^7 - x^6 + 11x^5 - 11x^4 + 20x^3 - 7x^2 + 13x + 1	\( 5^{6}\cdot 17^{2}\cdot 23^{4} \)	$C_2^2\times S_4$ (as 12T48)	Trivial
12.4.1270162810225.1	x^12 - x^11 - 3x^10 + 5x^9 + 3x^8 - 6x^7 - 4x^6 - 3x^5 + 4x^4 + 7x^3 - 3x - 1	\( 5^{2}\cdot 17^{2}\cdot 13259^{2} \)	12T285	Trivial
12.4.1286838403321.1	x^12 - 2x^11 + 3x^9 - 3x^8 - x^7 + 3x^6 - x^5 - 3x^4 + 3x^3 - 2x + 1	\( 1134389^{2} \)	12T285	Trivial
12.4.1325664390625.1	x^12 - x^11 - 2x^10 + 3x^9 + x^8 - 5x^6 + 9x^4 - 4x^3 - 2x^2 + 2x - 1	\( 5^{6}\cdot 61^{2}\cdot 151^{2} \)	12T203	Trivial
12.4.1337647129637.1	x^12 - 3x^11 + 2x^10 + 5x^9 - 17x^8 + 27x^7 - 28x^6 + 14x^5 + 3x^4 - 10x^3 + 4x^2 + 2x - 1	\( 7^{8}\cdot 13^{2}\cdot 1373 \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.4.1365453235513.1	x^12 - 2x^10 - 4x^8 - x^7 + 8x^6 - 2x^4 - 2x^3 - x^2 + 3x - 1	\( 257^{4}\cdot 313 \)	12T227	Trivial
12.4.1372119390625.1	x^12 - 2x^10 - x^9 + x^7 + 4x^6 - 2x^5 - 5x^4 + 3x^3 + 3x^2 - 1	\( 5^{6}\cdot 9371^{2} \)	12T203	Trivial
12.4.1400215984201.1	x^12 - x^10 - 2x^9 - 3x^8 - 4x^7 + 2x^6 + 11x^5 + 10x^4 - x^3 - 8x^2 - 5x - 1	\( 331^{3}\cdot 38611 \)	12T289	Trivial
12.4.1417991703125.1	x^12 - 3x^11 + x^10 + 6x^9 - 10x^8 + 8x^7 + 2x^6 - 14x^5 + 11x^4 - 3x^2 + 3x - 1	\( 5^{6}\cdot 29^{3}\cdot 61^{2} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.4.1421487203125.1	x^12 - x^10 - x^9 + 2x^8 - 2x^7 - 4x^6 + 6x^5 - 2x^4 - 3x^3 + 4x^2 - 1	\( 5^{6}\cdot 11^{3}\cdot 68351 \)	12T274	Trivial
12.4.1453001214025.1	x^12 - 2x^11 - x^10 + x^9 + 5x^7 + x^6 - 5x^5 - x^3 - x^2 + 2x + 1	\( 5^{2}\cdot 491^{4} \)	$C_2\times C_4^2:C_3:C_2$ (as 12T95)	Trivial
12.4.1459264000000.1	x^12 - 4x^11 + 8x^10 - 8x^9 - 2x^8 + 18x^7 - 27x^6 + 18x^5 - 2x^4 - 8x^3 + 8x^2 - 4x + 1	\( 2^{12}\cdot 5^{6}\cdot 151^{2} \)	$S_6\times C_2$ (as 12T219)	Trivial