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 600)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.108891217701.1	x^12 - 3x^11 + 8x^10 - 17x^9 + 30x^8 - 45x^7 + 53x^6 - 51x^5 + 40x^4 - 24x^3 + 12x^2 - 4x + 1	\( 3^{9}\cdot 7^{3}\cdot 127^{2} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.0.152923610853.1	x^12 - x^11 + x^10 + x^9 - 2x^8 + 2x^7 + 2x^6 - x^5 + x^4 + x^3 + x^2 + 2x + 1	\( 3^{8}\cdot 13^{3}\cdot 103^{2} \)	$D_6\wr C_2$ (as 12T125)	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
12.2.373065296875.1	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
12.2.398786546875.1	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
12.2.438976000000.1	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
12.0.1034891890625.1	x^12 - 3x^11 + 4x^10 - 3x^9 + 3x^8 - 4x^7 + 5x^6 - 4x^5 + 3x^4 - 3x^3 + 4x^2 - 3x + 1	\( 5^{6}\cdot 31^{2}\cdot 41^{3} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.0.1280314703125.1	x^12 - x^11 + 3x^10 - 5x^9 + 7x^8 - 9x^7 + 9x^6 - 9x^5 + 7x^4 - 5x^3 + 3x^2 - x + 1	\( 5^{6}\cdot 19^{2}\cdot 61^{3} \)	$D_6\wr C_2$ (as 12T125)	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
12.0.2982672203125.1	x^12 - 2x^11 + 6x^10 - 12x^9 + 18x^8 - 26x^7 + 34x^6 - 39x^5 + 39x^4 - 28x^3 + 14x^2 - 5x + 1	\( 5^{6}\cdot 29^{2}\cdot 61^{3} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.2.3266054193152.1	x^12 - 2x^11 + x^10 + 2x^9 - 4x^8 - 6x^7 + 15x^6 - 6x^5 - 4x^4 + 2x^3 + x^2 - 2x + 1	\( -\,2^{28}\cdot 23^{3} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.4.4527589203125.1	x^12 - 4x^11 + 5x^10 - 2x^9 - 2x^8 - 2x^7 + 8x^6 + 2x^5 - 2x^4 + 2x^3 + 5x^2 + 4x + 1	\( 5^{6}\cdot 29^{3}\cdot 109^{2} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.2.4544075399168.1	x^12 - 4x^9 - 2x^8 - 8x^7 - 6x^6 - 8x^5 - 2x^4 - 4x^3 + 1	\( -\,2^{33}\cdot 23^{2} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.0.5955311894528.1	x^12 - 2x^11 + 2x^10 - 2x^9 + 4x^8 - 22x^7 + 30x^6 - 14x^5 + 12x^4 - 6x^3 + 2x^2 - 2x + 1	\( 2^{22}\cdot 17^{5} \)	$D_6\wr C_2$ (as 12T125)	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
12.6.12685282671875.1	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
12.0.17017490453125.1	x^12 - x^11 + x^10 + 5x^9 - 3x^8 + 8x^7 + 3x^6 - 5x^5 + 18x^4 - 6x^3 + 8x^2 - x + 1	\( 5^{6}\cdot 29^{2}\cdot 109^{3} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.2.18176301596672.1	x^12 - 4x^10 + 4x^6 - 3x^4 - 2	\( -\,2^{35}\cdot 23^{2} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.2.36352603193344.1	x^12 - 2x^10 - 3x^8 - 20x^6 - 13x^4 - 26x^2 - 1	\( -\,2^{36}\cdot 23^{2} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.2.36352603193344.4	x^12 + 2x^10 - 3x^8 + 20x^6 - 13x^4 + 26x^2 - 1	\( -\,2^{36}\cdot 23^{2} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.6.43785761421875.1	x^12 - 2x^11 - 4x^10 + 10x^9 - 18x^7 + 17x^6 + 11x^5 - 25x^4 + 11x^2 - x - 1	\( -\,5^{6}\cdot 11^{3}\cdot 1451^{2} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.2.52256867090432.3	x^12 - 4x^11 + 8x^10 - 4x^9 - 11x^8 + 32x^7 - 40x^6 + 32x^5 - 11x^4 - 4x^3 + 8x^2 - 4x + 1	\( -\,2^{32}\cdot 23^{3} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.8.54738442953125.1	x^12 - 6x^11 + 12x^10 - 5x^9 - 21x^8 + 48x^7 - 48x^6 + 21x^5 + 10x^4 - 22x^3 + 6x^2 + 4x - 1	\( 5^{6}\cdot 29^{3}\cdot 379^{2} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.6.55070453421875.1	x^12 - 3x^11 - x^10 + 7x^9 - 7x^8 + 11x^7 - 15x^6 + 11x^5 - 7x^4 + 7x^3 - x^2 - 3x + 1	\( -\,5^{6}\cdot 59^{3}\cdot 131^{2} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.2.55267035185152.1	x^12 - 2x^11 + 3x^10 + 2x^9 + 5x^8 - 8x^7 + 18x^6 + 4x^5 + 2x^4 - 8x^3 + 20x^2 + 8x - 4	\( -\,2^{26}\cdot 7^{7} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.2.55267035185152.2	x^12 - 2x^11 - 5x^10 + 6x^9 + 19x^8 - 12x^7 - 18x^6 - 12x^5 + 19x^4 + 6x^3 - 5x^2 - 2x + 1	\( -\,2^{26}\cdot 7^{7} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.0.100192997081088.1	x^12 - 4x^10 + 12x^8 - 12x^6 + 13x^4 + 2	\( 2^{37}\cdot 3^{6} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.0.100192997081088.2	x^12 + 4x^10 + 12x^8 + 12x^6 + 13x^4 + 2	\( 2^{37}\cdot 3^{6} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.2.106993205379072.3	x^12 - 8x^9 - 3x^8 + 12x^6 - 3x^4 - 8x^3 + 1	\( -\,2^{26}\cdot 3^{13} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.2.106993205379072.4	x^12 - 6x^10 - 4x^9 + 12x^8 + 12x^7 - 6x^6 - 12x^5 - 3x^4 - 4x^3 + 12x^2 + 4	\( -\,2^{26}\cdot 3^{13} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.2.114290809913344.1	x^12 + 2x^10 + 8x^8 + 6x^6 + 7x^4 - 12x^2 - 4	\( -\,2^{14}\cdot 17^{8} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.2.114290809913344.2	x^12 - 2x^10 + 8x^8 - 6x^6 + 7x^4 + 12x^2 - 4	\( -\,2^{14}\cdot 17^{8} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.2.126324651851776.1	x^12 - 2x^10 + 3x^8 - 8x^6 + 24x^2 - 4	\( -\,2^{30}\cdot 7^{6} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.8.129361486328125.1	x^12 - x^11 - 10x^10 + 11x^9 + 34x^8 - 39x^7 - 45x^6 + 44x^5 + 26x^4 - 25x^2 + 5	\( 5^{9}\cdot 31^{2}\cdot 41^{3} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.0.150289495621632.3	x^12 - 2x^10 + 7x^8 - 16x^6 + 24x^4 - 24x^2 + 12	\( 2^{36}\cdot 3^{7} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.0.150289495621632.4	x^12 + 2x^10 + 7x^8 + 16x^6 + 24x^4 + 24x^2 + 12	\( 2^{36}\cdot 3^{7} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.0.190569980624896.1	x^12 - 4x^11 + 4x^10 - 4x^9 + 11x^8 - 8x^6 - 16x^5 - 7x^4 + 28x^3 + 48x^2 + 24x + 4	\( 2^{27}\cdot 17^{5} \)	$D_6\wr C_2$ (as 12T125)	$[2]$
12.2.228581619826688.1	x^12 - 3x^11 + 7x^10 - 10x^9 + 7x^8 - 5x^7 - 2x^6 - 5x^5 + 7x^4 - 10x^3 + 7x^2 - 3x + 1	\( -\,2^{15}\cdot 17^{8} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.2.285315214344192.1	x^12 - 6x^10 + 4x^6 - 3x^4 - 6x^2 - 2	\( -\,2^{29}\cdot 3^{12} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.2.285315214344192.2	x^12 - 6x^10 + 9x^8 + 2x^6 - 12x^5 + 6x^4 - 2	\( -\,2^{29}\cdot 3^{12} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.0.381139961249792.2	x^12 - 4x^11 + 8x^10 - 4x^9 - 18x^8 + 44x^7 - 32x^6 - 44x^5 + 143x^4 - 168x^3 + 84x^2 - 16x + 14	\( 2^{28}\cdot 17^{5} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.2.505298607407104.1	x^12 + 2x^10 + 3x^8 + 8x^6 - 24x^2 - 4	\( -\,2^{32}\cdot 7^{6} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.2.884272562962432.2	x^12 - 2x^10 + 3x^8 - 44x^6 - 21x^4 - 42x^2 - 7	\( -\,2^{30}\cdot 7^{7} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.2.884272562962432.3	x^12 + 4x^10 - 3x^8 - 8x^7 - 16x^6 - 8x^5 - 3x^4 + 4x^2 + 1	\( -\,2^{30}\cdot 7^{7} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.2.914326479306752.3	x^12 - x^10 - 12x^8 - 50x^6 - 59x^4 - 5x^2 - 2	\( -\,2^{17}\cdot 17^{8} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.2.914326479306752.4	x^12 + 3x^10 + 5x^8 - x^6 + 12x^4 - 2x^2 - 2	\( -\,2^{17}\cdot 17^{8} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.2.1141260857376768.4	x^12 - 6x^10 + 24x^8 - 44x^6 + 69x^4 - 6x^2 - 2	\( -\,2^{31}\cdot 3^{12} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.2.1141260857376768.8	x^12 + 6x^10 + 24x^8 + 44x^6 + 69x^4 + 6x^2 - 2	\( -\,2^{31}\cdot 3^{12} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.0.1352605460594688.2	x^12 - 8x^10 + 22x^8 - 8x^7 - 40x^6 + 104x^5 + 3x^4 - 272x^3 + 272x^2 - 80x + 8	\( 2^{36}\cdot 3^{9} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.0.1352605460594688.3	x^12 + 4x^10 + 16x^8 - 40x^7 + 72x^6 - 128x^5 + 70x^4 - 32x^3 - 48x^2 + 96x + 48	\( 2^{36}\cdot 3^{9} \)	$D_6\wr C_2$ (as 12T125)	Trivial