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 288)

Label	Polynomial	Discriminant	Galois group	Class group
12.2.20433779818496.2	x^12 - 4x^11 + 10x^10 - 10x^9 - 2x^8 + 24x^7 - 44x^6 + 48x^5 - 40x^4 + 36x^3 - 28x^2 + 12x - 2	\( -\,2^{20}\cdot 11^{7} \)	$\GL(2,Z/4)$ (as 12T52)	Trivial
12.2.52428800000000.1	x^12 - 6x^8 + 17x^4 - 8	\( -\,2^{27}\cdot 5^{8} \)	$\GL(2,Z/4)$ (as 12T52)	Trivial
12.2.58188380811264.1	x^12 + 3x^10 + 11x^8 - 10x^7 - 7x^6 + 18x^5 - 26x^4 + 14x^3 - 12x^2 + 14x - 2	\( -\,2^{12}\cdot 3^{6}\cdot 11^{7} \)	$\GL(2,Z/4)$ (as 12T52)	Trivial
12.2.70655493361664.1	x^12 - x^10 - 4x^9 - 8x^7 - 9x^6 + 20x^5 + 8x^4 - 16x^3 - x^2 + 4x - 1	\( -\,2^{12}\cdot 29^{7} \)	$\GL(2,Z/4)$ (as 12T52)	Trivial
12.0.72712409055232.1	x^12 - 6x^11 + 18x^10 - 22x^9 + 4x^8 + 24x^7 - 28x^6 + 16x^5 - 8x^3 + 8x^2 - 4x + 2	\( 2^{20}\cdot 37^{5} \)	$\GL(2,Z/4)$ (as 12T52)	Trivial
12.2.107983916761088.11	x^12 - 6x^10 + 6x^8 - 16x^7 - 22x^6 - 28x^5 - 59x^4 - 40x^3 + 4x - 1	\( -\,2^{24}\cdot 23^{5} \)	$\GL(2,Z/4)$ (as 12T52)	$[2]$
12.2.107983916761088.14	x^12 - 3x^8 - 16x^7 - 10x^6 + 44x^5 + 118x^4 + 144x^3 + 100x^2 + 40x + 7	\( -\,2^{24}\cdot 23^{5} \)	$\GL(2,Z/4)$ (as 12T52)	Trivial
12.0.207059946098688.1	x^12 - 2x^11 + 11x^10 - 8x^9 + 34x^8 - 18x^7 + 23x^6 - 12x^5 - 2x^4 + 14x^3 - x^2 - 4x + 1	\( 2^{12}\cdot 3^{6}\cdot 37^{5} \)	$\GL(2,Z/4)$ (as 12T52)	$[2]$
12.2.240734712102912.1	x^12 + 12x^4 - 12	\( -\,2^{24}\cdot 3^{15} \)	$\GL(2,Z/4)$ (as 12T52)	Trivial
12.2.326940477095936.2	x^12 - 4x^8 + 4x^4 - 44	\( -\,2^{24}\cdot 11^{7} \)	$\GL(2,Z/4)$ (as 12T52)	Trivial
12.2.480317450223616.8	x^12 - 6x^10 - 4x^9 + 12x^8 - 8x^7 - 6x^6 + 15x^4 - 8x^3 - 20x^2 + 24x - 9	\( -\,2^{24}\cdot 31^{5} \)	$\GL(2,Z/4)$ (as 12T52)	Trivial
12.2.480317450223616.11	x^12 - 4x^9 + 3x^8 + 24x^7 + 14x^6 - 16x^5 - 68x^4 - 96x^3 - 52x^2 - 12x - 1	\( -\,2^{24}\cdot 31^{5} \)	$\GL(2,Z/4)$ (as 12T52)	$[2]$
12.2.892554561978368.8	x^12 - 4x^11 + 4x^10 + 2x^9 + 10x^8 - 36x^7 - 4x^6 + 10x^5 + 41x^4 - 54x^3 + 30x^2 - 8x + 1	\( -\,2^{18}\cdot 23^{7} \)	$\GL(2,Z/4)$ (as 12T52)	Trivial
12.2.892554561978368.9	x^12 + 2x^10 - 14x^9 + 5x^8 - 18x^7 + 32x^6 - 32x^5 + 34x^4 - 22x^3 + 8x^2 - 4x + 1	\( -\,2^{18}\cdot 23^{7} \)	$\GL(2,Z/4)$ (as 12T52)	Trivial
12.2.937292452593664.3	x^12 - 4x^11 + 2x^10 + 10x^9 - 20x^8 + 12x^7 - 8x^6 + 44x^5 - 82x^4 + 36x^3 - 16x^2 - 2	\( -\,2^{20}\cdot 19^{7} \)	$\GL(2,Z/4)$ (as 12T52)	Trivial
12.2.962938848411648.5	x^12 + 3x^8 + 3x^4 - 3	\( -\,2^{26}\cdot 3^{15} \)	$\GL(2,Z/4)$ (as 12T52)	Trivial
12.2.1307761908383744.4	x^12 - 5x^8 - 13x^4 - 11	\( -\,2^{26}\cdot 11^{7} \)	$\GL(2,Z/4)$ (as 12T52)	Trivial
12.2.1307761908383744.5	x^12 - x^8 + 3x^4 - 11	\( -\,2^{26}\cdot 11^{7} \)	$\GL(2,Z/4)$ (as 12T52)	Trivial
12.2.1310720000000000.4	x^12 - 2x^10 - 10x^8 - 20x^7 + 20x^6 + 20x^5 - 25x^4 + 20x^3 + 18x^2 - 20x + 14	\( -\,2^{27}\cdot 5^{10} \)	$\GL(2,Z/4)$ (as 12T52)	$[2]$
12.2.1542441841901568.2	x^12 - 6x^11 + 21x^10 - 50x^9 + 90x^8 - 126x^7 + 138x^6 - 108x^5 + 45x^4 + 10x^3 - 24x^2 + 12x - 2	\( -\,2^{14}\cdot 3^{23} \)	$\GL(2,Z/4)$ (as 12T52)	Trivial
12.2.1925877696823296.1	x^12 - 6x^10 - 4x^9 + 12x^8 + 12x^7 + 6x^6 + 12x^5 + 3x^4 - 4x^3 + 12x^2 - 8	\( -\,2^{27}\cdot 3^{15} \)	$\GL(2,Z/4)$ (as 12T52)	Trivial
12.2.1925877696823296.5	x^12 - 6x^10 - 4x^9 + 24x^7 + 18x^6 + 24x^5 - 4x^3 - 6x^2 + 1	\( -\,2^{27}\cdot 3^{15} \)	$\GL(2,Z/4)$ (as 12T52)	Trivial
12.2.2258673530454016.1	x^12 - 4x^11 + 10x^10 - 18x^9 + 20x^8 - 6x^7 - 24x^6 + 40x^5 + 2x^4 - 14x^3 + 4x^2 + 2x - 1	\( -\,2^{14}\cdot 13^{10} \)	$\GL(2,Z/4)$ (as 12T52)	$[3]$
12.2.2888816545234944.7	x^12 - 4x^9 + 6x^8 + 24x^7 + 26x^6 + 24x^5 + 51x^4 + 40x^3 - 54x^2 + 12x + 62	\( -\,2^{26}\cdot 3^{16} \)	$\GL(2,Z/4)$ (as 12T52)	Trivial
12.2.3249918613389312.1	x^12 - 6x^10 + 15x^8 - 10x^6 - 15x^4 + 24x^2 - 8	\( -\,2^{23}\cdot 3^{18} \)	$\GL(2,Z/4)$ (as 12T52)	$[3]$
12.2.3355443200000000.5	x^12 - 4x^8 - 3x^4 - 2	\( -\,2^{33}\cdot 5^{8} \)	$\GL(2,Z/4)$ (as 12T52)	Trivial
12.2.4521951575146496.1	x^12 + 2x^8 + x^4 - 116	\( -\,2^{18}\cdot 29^{7} \)	$\GL(2,Z/4)$ (as 12T52)	Trivial
12.2.5777633090469888.14	x^12 - 16x^9 + 3x^8 + 12x^7 + 46x^6 + 108x^5 + 102x^4 + 96x^3 + 96x^2 + 48x + 8	\( -\,2^{27}\cdot 3^{16} \)	$\GL(2,Z/4)$ (as 12T52)	$[3]$
12.2.6169767367606272.6	x^12 - 6x^11 + 21x^10 - 44x^9 + 72x^8 - 90x^7 + 81x^6 - 36x^5 - 9x^4 + 28x^3 - 24x^2 + 12x - 2	\( -\,2^{16}\cdot 3^{23} \)	$\GL(2,Z/4)$ (as 12T52)	Trivial
12.2.7212266713513984.3	x^12 - 6x^11 + 12x^10 + 2x^9 - 58x^8 + 114x^7 - 64x^6 - 104x^5 + 219x^4 - 102x^3 - 26x^2 + 84x - 99	\( -\,2^{18}\cdot 31^{7} \)	$\GL(2,Z/4)$ (as 12T52)	Trivial (GRH)
12.2.7212266713513984.12	x^12 - 2x^10 - 14x^9 + 5x^8 + 18x^7 + 16x^6 - 32x^5 - 26x^4 - 6x^3 + 8x^2 + 4x + 1	\( -\,2^{18}\cdot 31^{7} \)	$\GL(2,Z/4)$ (as 12T52)	Trivial
12.2.8421963387109376.1	x^12 - 4x^9 - 20x^8 - 36x^7 - 44x^6 - 64x^5 - 88x^4 - 64x^3 - 2x^2 - 72x - 113	\( -\,2^{27}\cdot 13^{7} \)	$\GL(2,Z/4)$ (as 12T52)	$[2]$
12.2.8421963387109376.6	x^12 - 8x^8 + 29x^4 - 26	\( -\,2^{27}\cdot 13^{7} \)	$\GL(2,Z/4)$ (as 12T52)	$[2]$
12.4.9840053002328125.1	x^12 - x^11 + 3x^10 - 11x^9 + 6x^8 - x^7 + 27x^6 - 218x^5 + 349x^4 - 298x^3 + 296x^2 - 136x - 16	\( 5^{6}\cdot 229^{5} \)	$\GL(2,Z/4)$ (as 12T52)	$[2]$
12.0.10318043416969216.1	x^12 - 6x^11 + 17x^10 - 22x^9 + 5x^8 + 20x^7 - 20x^6 + 18x^4 - 4x^3 + 12x^2 + 24x + 8	\( 2^{14}\cdot 229^{5} \)	$\GL(2,Z/4)$ (as 12T52)	$[2]$
12.2.11555266180939776.6	x^12 - 6x^10 - 9x^8 - 28x^6 - 36x^4 - 4	\( -\,2^{28}\cdot 3^{16} \)	$\GL(2,Z/4)$ (as 12T52)	$[2]$
12.2.12999674453557248.8	x^12 - 8x^9 - 21x^8 - 36x^7 - 46x^6 - 60x^5 - 54x^4 - 40x^3 - 24x^2 - 8	\( -\,2^{25}\cdot 3^{18} \)	$\GL(2,Z/4)$ (as 12T52)	$[3]$
12.2.12999674453557248.16	x^12 - 12x^9 + 18x^8 - 24x^7 + 28x^6 - 72x^5 + 126x^4 - 120x^3 + 54x^2 - 12x + 1	\( -\,2^{25}\cdot 3^{18} \)	$\GL(2,Z/4)$ (as 12T52)	$[3]$
12.2.13421772800000000.14	x^12 - 8x^10 + 14x^8 - 8x^6 - 7x^4 + 8x^2 - 2	\( -\,2^{35}\cdot 5^{8} \)	$\GL(2,Z/4)$ (as 12T52)	Trivial
12.0.14560594398949509.2	x^12 - 6x^11 + 8x^10 + 15x^9 - 24x^8 - 60x^7 + 80x^6 + 99x^5 + 4x^4 - 306x^3 - 108x^2 + 297x + 171	\( 3^{7}\cdot 367^{5} \)	$\GL(2,Z/4)$ (as 12T52)	Trivial
12.2.14996679241498624.3	x^12 + 12x^8 + 36x^4 - 76	\( -\,2^{24}\cdot 19^{7} \)	$\GL(2,Z/4)$ (as 12T52)	Trivial
12.2.18087806300585984.10	x^12 - 11x^8 + 23x^4 - 29	\( -\,2^{20}\cdot 29^{7} \)	$\GL(2,Z/4)$ (as 12T52)	$[2]$
12.2.25999348907114496.4	x^12 - 6x^10 - 9x^8 + 84x^6 + 108x^4 - 36	\( -\,2^{26}\cdot 3^{18} \)	$\GL(2,Z/4)$ (as 12T52)	Trivial
12.0.29084963622092800.1	x^12 - 4x^11 - 6x^10 + 32x^9 + 23x^8 - 104x^7 - 38x^6 + 84x^5 + 17x^4 + 76x^3 + 108x^2 + 37	\( 2^{24}\cdot 5^{2}\cdot 37^{5} \)	$\GL(2,Z/4)$ (as 12T52)	$[2]$
12.2.39559797728608256.9	x^12 - 4x^11 + 6x^10 - 32x^9 + 118x^8 - 260x^7 + 476x^6 - 984x^5 + 1240x^4 - 1328x^3 + 1504x^2 - 968x + 212	\( -\,2^{24}\cdot 11^{9} \)	$\GL(2,Z/4)$ (as 12T52)	Trivial
12.2.51998697814228992.18	x^12 + 45x^4 - 18	\( -\,2^{27}\cdot 3^{18} \)	$\GL(2,Z/4)$ (as 12T52)	$[3]$
12.2.51998697814228992.26	x^12 + 6x^10 + 15x^8 + 10x^6 - 15x^4 - 24x^2 - 8	\( -\,2^{27}\cdot 3^{18} \)	$\GL(2,Z/4)$ (as 12T52)	$[3]$
12.4.53007346201264128.2	x^12 - 4x^11 + 4x^10 - 2x^9 + x^8 + 28x^7 - 108x^6 + 124x^5 - 25x^4 + 44x^3 - 128x^2 + 50x + 13	\( 2^{20}\cdot 3^{6}\cdot 37^{5} \)	$\GL(2,Z/4)$ (as 12T52)	Trivial
12.8.53007346201264128.3	x^12 - 6x^11 + 4x^10 + 26x^9 - 29x^8 - 4x^7 - 48x^6 + 20x^5 + 131x^4 - 46x^3 - 68x^2 + 10x + 1	\( 2^{20}\cdot 3^{6}\cdot 37^{5} \)	$\GL(2,Z/4)$ (as 12T52)	Trivial
12.2.54742762016210944.15	x^12 - 2x^10 - 4x^9 + 8x^8 - 12x^7 + 26x^6 + 44x^5 + 111x^4 + 308x^3 + 140x^2 - 256x - 8	\( -\,2^{26}\cdot 13^{8} \)	$\GL(2,Z/4)$ (as 12T52)	$[3]$