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 576)

Label	Polynomial	Discriminant	Galois group	Class group
12.2.20433779818496.1	x^12 - 4x^11 + 4x^10 + 6x^9 - 14x^8 - 4x^7 + 12x^6 + 4x^5 - 12x^3 + 4x^2 + 4x - 2	\( -\,2^{20}\cdot 11^{7} \)	$\GL(2,Z/4)$ (as 12T49)	Trivial
12.2.20433779818496.3	x^12 - 4x^11 + 6x^10 - 2x^9 + 5x^8 - 4x^7 - 8x^6 + 12x^5 - 3x^4 + 4x^3 - 10x^2 + 6x - 1	\( -\,2^{20}\cdot 11^{7} \)	$\GL(2,Z/4)$ (as 12T49)	Trivial
12.2.52428800000000.2	x^12 - x^11 - x^9 - 3x^8 - 4x^7 - 4x^5 - 3x^4 - x^3 - x + 1	\( -\,2^{27}\cdot 5^{8} \)	$\GL(2,Z/4)$ (as 12T49)	Trivial
12.2.52428800000000.3	x^12 - x^10 - 2x^9 + 6x^8 + 8x^7 + 4x^6 + 27x^4 - 15x^2 + 2x + 2	\( -\,2^{27}\cdot 5^{8} \)	$\GL(2,Z/4)$ (as 12T49)	Trivial
12.4.72712409055232.1	x^12 - 4x^11 + 4x^10 - 6x^9 + 20x^8 - 16x^7 - 24x^5 + 26x^4 + 12x^3 + 4x^2 - 16x - 2	\( 2^{20}\cdot 37^{5} \)	$\GL(2,Z/4)$ (as 12T49)	Trivial
12.4.72712409055232.2	x^12 - 2x^10 - 2x^9 - 10x^8 - 24x^7 - 20x^6 + 8x^5 + 22x^4 + 8x^3 - 8x^2 - 8x - 2	\( 2^{20}\cdot 37^{5} \)	$\GL(2,Z/4)$ (as 12T49)	Trivial
12.2.107983916761088.7	x^12 - 4x^9 + 3x^8 - 12x^5 + 8x^4 + 64x^3 - 112x^2 + 64x - 11	\( -\,2^{24}\cdot 23^{5} \)	$\GL(2,Z/4)$ (as 12T49)	Trivial
12.2.107983916761088.8	x^12 + 2x^10 - 4x^9 + 2x^8 - 8x^6 + 48x^5 - 120x^4 + 160x^3 - 120x^2 + 48x - 8	\( -\,2^{24}\cdot 23^{5} \)	$\GL(2,Z/4)$ (as 12T49)	Trivial
12.2.107983916761088.10	x^12 - 4x^10 - 12x^9 + 4x^8 + 32x^7 + 34x^6 - 16x^5 - 61x^4 - 40x^3 + 4x - 1	\( -\,2^{24}\cdot 23^{5} \)	$\GL(2,Z/4)$ (as 12T49)	Trivial
12.2.107983916761088.13	x^12 + 4x^10 - 12x^9 + 16x^8 - 32x^7 + 60x^6 - 80x^5 + 83x^4 - 80x^3 + 62x^2 - 28x + 5	\( -\,2^{24}\cdot 23^{5} \)	$\GL(2,Z/4)$ (as 12T49)	Trivial
12.2.232753523245056.1	x^12 - 6x^10 + 18x^8 - 2x^7 - 38x^6 + 48x^4 + 18x^3 - 20x^2 - 16x - 14	\( -\,2^{14}\cdot 3^{6}\cdot 11^{7} \)	$\GL(2,Z/4)$ (as 12T49)	Trivial
12.2.232753523245056.2	x^12 - 2x^11 + 4x^10 + 4x^9 - 7x^8 + 28x^7 - 34x^6 + 28x^5 - 7x^4 + 4x^3 + 4x^2 - 2x + 1	\( -\,2^{14}\cdot 3^{6}\cdot 11^{7} \)	$\GL(2,Z/4)$ (as 12T49)	Trivial
12.2.282621973446656.1	x^12 - x^11 - 2x^10 + x^9 - 3x^8 + 12x^7 + 20x^5 - 37x^4 + 13x^3 + 26x^2 + 3x - 1	\( -\,2^{14}\cdot 29^{7} \)	$\GL(2,Z/4)$ (as 12T49)	Trivial
12.2.282621973446656.2	x^12 - 5x^11 + 9x^10 + 3x^9 - 37x^8 + 51x^7 + 13x^6 - 103x^5 + 77x^4 + 59x^3 - 99x^2 + x + 46	\( -\,2^{14}\cdot 29^{7} \)	$\GL(2,Z/4)$ (as 12T49)	Trivial
12.2.385610460475392.2	x^12 - 6x^11 + 12x^10 - 2x^9 - 27x^8 + 36x^7 - 3x^6 - 36x^5 + 45x^4 - 32x^3 + 12x^2 - 6x + 1	\( -\,2^{12}\cdot 3^{23} \)	$\GL(2,Z/4)$ (as 12T49)	Trivial
12.2.385610460475392.3	x^12 - 3x^11 + 3x^10 - 7x^9 + 9x^8 - 18x^7 + 18x^6 - 18x^5 + 9x^4 - 7x^3 + 3x^2 - 3x + 1	\( -\,2^{12}\cdot 3^{23} \)	$\GL(2,Z/4)$ (as 12T49)	Trivial
12.2.480317450223616.7	x^12 + 4x^10 - 2x^8 - 24x^7 - 2x^6 - 24x^5 + 9x^4 - 16x^3 + 20x^2 + 4x - 9	\( -\,2^{24}\cdot 31^{5} \)	$\GL(2,Z/4)$ (as 12T49)	Trivial
12.2.480317450223616.9	x^12 - 2x^10 - 12x^9 + 16x^7 + 28x^6 - 12x^4 - 16x^3 - 8x^2 - 16x - 8	\( -\,2^{24}\cdot 31^{5} \)	$\GL(2,Z/4)$ (as 12T49)	Trivial
12.2.480317450223616.10	x^12 - 4x^10 + 22x^8 - 40x^7 + 8x^6 + 68x^5 - 117x^4 + 96x^3 - 46x^2 + 16x - 3	\( -\,2^{24}\cdot 31^{5} \)	$\GL(2,Z/4)$ (as 12T49)	Trivial
12.2.480317450223616.13	x^12 - 12x^9 + x^8 + 48x^6 - 8x^5 + 4x^4 - 64x^3 + 16x^2 - 16x + 3	\( -\,2^{24}\cdot 31^{5} \)	$\GL(2,Z/4)$ (as 12T49)	Trivial
12.2.722204136308736.1	x^12 - 3x^10 - 12x^8 + 40x^6 + 48x^4 - 48x^2 - 64	\( -\,2^{24}\cdot 3^{16} \)	$\GL(2,Z/4)$ (as 12T49)	Trivial
12.2.722204136308736.4	x^12 - 6x^11 + 15x^10 - 20x^9 + 15x^8 + 6x^7 - 45x^6 + 48x^5 - 36x^3 + 30x^2 - 16	\( -\,2^{24}\cdot 3^{16} \)	$\GL(2,Z/4)$ (as 12T49)	Trivial
12.4.828239784394752.1	x^12 - 4x^11 + 6x^10 - 4x^9 + 3x^8 - 20x^7 + 56x^6 - 72x^5 + 11x^4 + 44x^3 - 34x^2 - 8x + 1	\( 2^{14}\cdot 3^{6}\cdot 37^{5} \)	$\GL(2,Z/4)$ (as 12T49)	Trivial
12.4.828239784394752.2	x^12 - 4x^11 + 6x^10 + 11x^8 - 92x^7 + 206x^6 - 224x^5 + 103x^4 - 10x^3 + 6x^2 - 6x + 1	\( 2^{14}\cdot 3^{6}\cdot 37^{5} \)	$\GL(2,Z/4)$ (as 12T49)	Trivial
12.2.892554561978368.7	x^12 - 4x^11 + 2x^10 + 2x^9 + 6x^8 - 38x^7 + 82x^6 - 98x^5 + 89x^4 - 60x^3 + 26x^2 - 10x + 1	\( -\,2^{18}\cdot 23^{7} \)	$\GL(2,Z/4)$ (as 12T49)	$[2]$
12.2.892554561978368.10	x^12 - 2x^11 + 2x^10 + 12x^9 - 23x^8 + 26x^7 - 2x^6 - 2x^5 - 14x^4 + 22x^3 - 10x^2 + 1	\( -\,2^{18}\cdot 23^{7} \)	$\GL(2,Z/4)$ (as 12T49)	Trivial
12.2.892554561978368.11	x^12 - 2x^11 + 14x^9 - 6x^8 - 4x^7 + 24x^6 - 7x^4 + 12x^3 + 8x^2 + 2x + 1	\( -\,2^{18}\cdot 23^{7} \)	$\GL(2,Z/4)$ (as 12T49)	$[2]$
12.2.892554561978368.12	x^12 - 4x^11 + 4x^10 + 6x^9 - 15x^8 + 16x^7 - 20x^6 - 46x^5 + 26x^4 + 14x^3 + 16x^2 + 2x + 1	\( -\,2^{18}\cdot 23^{7} \)	$\GL(2,Z/4)$ (as 12T49)	Trivial
12.2.937292452593664.2	x^12 - 2x^10 - 10x^9 - 4x^8 - 4x^6 + 8x^5 + 6x^4 - 4x^3 - 4x^2 - 4x - 2	\( -\,2^{20}\cdot 19^{7} \)	$\GL(2,Z/4)$ (as 12T49)	Trivial
12.2.937292452593664.5	x^12 - 6x^11 + 12x^10 + 4x^9 - 50x^8 + 56x^7 + 32x^6 - 108x^5 + 56x^4 + 48x^3 - 64x^2 + 16x + 4	\( -\,2^{20}\cdot 19^{7} \)	$\GL(2,Z/4)$ (as 12T49)	Trivial
12.2.962938848411648.2	x^12 - 6x^10 - 4x^9 + 9x^8 + 24x^7 - 12x^6 - 9x^4 + 56x^3 - 54x^2 + 36x - 17	\( -\,2^{26}\cdot 3^{15} \)	$\GL(2,Z/4)$ (as 12T49)	Trivial
12.2.962938848411648.3	x^12 + 6x^10 - 8x^9 + 9x^8 - 24x^7 - 24x^6 - 72x^5 - 81x^4 - 80x^3 - 54x^2 - 24x - 5	\( -\,2^{26}\cdot 3^{15} \)	$\GL(2,Z/4)$ (as 12T49)	Trivial
12.2.1307761908383744.2	x^12 + 4x^10 - 5x^8 - 52x^6 - 93x^4 - 56x^2 - 11	\( -\,2^{26}\cdot 11^{7} \)	$\GL(2,Z/4)$ (as 12T49)	Trivial
12.2.1307761908383744.9	x^12 - 4x^10 - 5x^8 + 52x^6 - 93x^4 + 56x^2 - 11	\( -\,2^{26}\cdot 11^{7} \)	$\GL(2,Z/4)$ (as 12T49)	Trivial
12.2.1307761908383744.11	x^12 - 4x^11 + 14x^10 - 28x^9 + 7x^8 + 64x^7 - 68x^6 - 16x^5 + 69x^4 - 40x^3 - 14x^2 + 24x - 7	\( -\,2^{26}\cdot 11^{7} \)	$\GL(2,Z/4)$ (as 12T49)	Trivial
12.2.1307761908383744.13	x^12 - 4x^11 + 4x^10 - 12x^9 + 82x^8 - 232x^7 + 360x^6 - 384x^5 + 322x^4 - 204x^3 + 80x^2 - 16x + 2	\( -\,2^{26}\cdot 11^{7} \)	$\GL(2,Z/4)$ (as 12T49)	Trivial
12.2.1310720000000000.1	x^12 - 3x^11 - 2x^10 + 10x^9 - 8x^7 + 4x^6 - 4x^5 - 15x^4 + 5x^3 + 18x^2 + 6x - 16	\( -\,2^{27}\cdot 5^{10} \)	$\GL(2,Z/4)$ (as 12T49)	$[2]$
12.2.1310720000000000.3	x^12 - 4x^11 + 9x^10 - 20x^9 + 5x^8 - 4x^7 - 29x^6 + 84x^5 - 60x^4 + 40x^3 - 46x^2 + 24x - 4	\( -\,2^{27}\cdot 5^{10} \)	$\GL(2,Z/4)$ (as 12T49)	$[2]$
12.2.1925877696823296.2	x^12 - 6x^11 + 12x^10 + 4x^9 - 57x^8 + 90x^7 - 24x^6 - 72x^5 + 45x^4 + 70x^3 - 102x^2 + 48x - 8	\( -\,2^{27}\cdot 3^{15} \)	$\GL(2,Z/4)$ (as 12T49)	Trivial
12.2.1925877696823296.3	x^12 - 9x^10 + 24x^8 - 6x^6 - 39x^4 + 27x^2 - 6	\( -\,2^{27}\cdot 3^{15} \)	$\GL(2,Z/4)$ (as 12T49)	Trivial
12.2.1925877696823296.4	x^12 - 3x^11 + 5x^9 + 3x^8 + 18x^7 + 18x^5 + 3x^4 + 5x^3 - 3x + 1	\( -\,2^{27}\cdot 3^{15} \)	$\GL(2,Z/4)$ (as 12T49)	Trivial
12.2.1925877696823296.6	x^12 - 3x^11 + 3x^10 - 7x^9 + 12x^8 - 6x^7 + 6x^6 - 6x^5 - 6x^4 + 14x^3 + 6x^2 + 18x + 4	\( -\,2^{27}\cdot 3^{15} \)	$\GL(2,Z/4)$ (as 12T49)	Trivial
12.0.2579510854242304.1	x^12 - 2x^11 - 8x^10 + 12x^9 + 28x^8 - 34x^7 - 27x^6 + 54x^5 - 20x^4 - 24x^3 + 48x^2 - 32x + 8	\( 2^{12}\cdot 229^{5} \)	$\GL(2,Z/4)$ (as 12T49)	$[2]$
12.0.2579510854242304.2	x^12 - 6x^11 + 24x^10 - 57x^9 + 106x^8 - 132x^7 + 140x^6 - 92x^5 + 68x^4 - 24x^3 + 24x^2 - 4x + 8	\( 2^{12}\cdot 229^{5} \)	$\GL(2,Z/4)$ (as 12T49)	$[2]$
12.2.2888816545234944.1	x^12 - 9x^10 + 33x^8 - 46x^6 - 33x^4 + 159x^2 - 121	\( -\,2^{26}\cdot 3^{16} \)	$\GL(2,Z/4)$ (as 12T49)	$[2]$
12.2.2888816545234944.2	x^12 - 6x^11 + 15x^10 - 18x^9 - 9x^8 + 96x^7 - 176x^6 + 24x^5 + 351x^4 - 446x^3 + 75x^2 + 198x - 107	\( -\,2^{26}\cdot 3^{16} \)	$\GL(2,Z/4)$ (as 12T49)	Trivial
12.2.3851755393646592.3	x^12 - 6x^10 + 15x^8 - 48x^6 + 39x^4 - 18x^2 - 3	\( -\,2^{28}\cdot 3^{15} \)	$\GL(2,Z/4)$ (as 12T49)	Trivial
12.2.3851755393646592.8	x^12 + 6x^10 + 15x^8 + 48x^6 + 39x^4 + 18x^2 - 3	\( -\,2^{28}\cdot 3^{15} \)	$\GL(2,Z/4)$ (as 12T49)	Trivial
12.2.5231047633534976.3	x^12 - 4x^11 + 10x^10 - 28x^9 + 62x^8 - 108x^7 + 136x^6 - 108x^5 + 46x^4 + 32x^3 - 88x^2 + 64x - 26	\( -\,2^{28}\cdot 11^{7} \)	$\GL(2,Z/4)$ (as 12T49)	Trivial
12.2.5231047633534976.6	x^12 - 4x^11 + 10x^10 - 8x^9 - 6x^8 + 20x^7 - 28x^6 - 28x^5 - 4x^4 - 48x^3 - 40x^2 - 24x - 14	\( -\,2^{28}\cdot 11^{7} \)	$\GL(2,Z/4)$ (as 12T49)	Trivial