Global number field search results

Further refine search

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 410)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.1344218660864.2	x^12 - 4x^11 + 9x^10 - 12x^9 + 11x^8 - 6x^7 + x^6 + 2x^5 + x^4 - 8x^3 + 12x^2 - 8x + 2	\( 2^{16}\cdot 29^{5} \)	$C_4:S_4$ (as 12T54)	Trivial
12.0.6851714957312.1	x^12 - 6x^11 + 12x^10 - 4x^9 - 14x^8 + 8x^7 + 17x^6 - 20x^5 + 9x^4 - 2x^3 - 6x^2 + 4x + 2	\( 2^{14}\cdot 53^{5} \)	$C_4:S_4$ (as 12T54)	Trivial
12.2.9745585291264.1	x^12 - 4x^11 + 8x^10 - 12x^9 + 14x^8 - 12x^7 + 13x^6 - 14x^5 + 11x^4 - 10x^3 + 5x^2 - 1	\( -\,2^{14}\cdot 29^{6} \)	$C_4:S_4$ (as 12T54)	Trivial
12.0.13837865795584.1	x^12 - 2x^11 + 2x^10 + 4x^9 - 13x^8 + 18x^7 - 5x^6 - 16x^5 + 37x^4 - 32x^3 + 17x^2 - 4x + 1	\( 2^{14}\cdot 61^{5} \)	$C_4:S_4$ (as 12T54)	Trivial
12.0.19042491875328.1	x^12 + 3x^10 - 2x^9 + 12x^8 + 6x^7 + 24x^6 + 6x^5 + 12x^4 - 2x^3 + 3x^2 + 1	\( 2^{14}\cdot 3^{19} \)	$C_4:S_4$ (as 12T54)	Trivial
12.2.76169967501312.1	x^12 - 6x^10 + 15x^8 - 6x^6 - 27x^4 + 36x^2 - 12	\( -\,2^{16}\cdot 3^{19} \)	$C_4:S_4$ (as 12T54)	Trivial
12.0.86029994295296.7	x^12 - 2x^10 + 12x^8 - 26x^6 + 44x^4 - 50x^2 + 29	\( 2^{22}\cdot 29^{5} \)	$C_4:S_4$ (as 12T54)	Trivial
12.2.90785223184384.1	x^12 - 2x^10 - 6x^8 + 6x^4 - 2x^2 - 1	\( -\,2^{12}\cdot 53^{6} \)	$C_4:S_4$ (as 12T54)	Trivial
12.0.199336411529216.2	x^12 - 4x^11 + 12x^10 - 28x^9 + 43x^8 - 56x^7 + 76x^6 - 60x^5 - 8x^4 + 32x^3 - 8x + 2	\( 2^{29}\cdot 13^{5} \)	$C_4:S_4$ (as 12T54)	Trivial
12.0.199336411529216.3	x^12 + 2x^10 - 8x^9 + 14x^8 - 12x^7 + 32x^6 - 56x^5 + 57x^4 - 28x^3 - 10x^2 + 8x + 2	\( 2^{29}\cdot 13^{5} \)	$C_4:S_4$ (as 12T54)	Trivial
12.0.199626983903232.1	x^12 - 2x^11 + x^10 - 4x^9 + 16x^8 + 4x^7 + 11x^6 - 26x^5 - 26x^4 - 10x^3 + 25x^2 + 10x + 1	\( 2^{12}\cdot 3^{9}\cdot 19^{5} \)	$C_4:S_4$ (as 12T54)	$[2]$
12.0.209715200000000.4	x^12 - 2x^10 + 12x^8 + 4x^6 + 61x^4 + 22x^2 + 2	\( 2^{29}\cdot 5^{8} \)	$C_4:S_4$ (as 12T54)	Trivial
12.2.211027453382656.1	x^12 - 4x^9 + 15x^8 - 4x^7 - 3x^6 - 30x^5 + 49x^4 - 16x^3 - 18x^2 + 14x - 3	\( -\,2^{12}\cdot 61^{6} \)	$C_4:S_4$ (as 12T54)	Trivial
12.0.282621973446656.4	x^12 - 4x^11 + 5x^10 - 4x^9 + 21x^8 - 40x^7 + 53x^6 - 56x^5 + 69x^4 - 114x^3 + 160x^2 - 118x + 61	\( 2^{14}\cdot 29^{7} \)	$C_4:S_4$ (as 12T54)	Trivial
12.0.344119977181184.17	x^12 - 4x^10 + 15x^8 - 82x^6 + 138x^4 - 36x^2 + 116	\( 2^{24}\cdot 29^{5} \)	$C_4:S_4$ (as 12T54)	Trivial
12.0.344119977181184.18	x^12 + 23x^8 - 30x^6 - 14x^4 + 20x^2 + 116	\( 2^{24}\cdot 29^{5} \)	$C_4:S_4$ (as 12T54)	Trivial
12.2.419430400000000.2	x^12 - 2x^10 - 9x^8 + 52x^6 - 84x^4 + 48x^2 - 4	\( -\,2^{30}\cdot 5^{8} \)	$C_4:S_4$ (as 12T54)	Trivial
12.2.623717458640896.4	x^12 - 3x^10 + 2x^8 - x^6 - 2x^4 - 3x^2 - 1	\( -\,2^{20}\cdot 29^{6} \)	$C_4:S_4$ (as 12T54)	Trivial
12.0.1218719480020992.1	x^12 - 9x^10 + 30x^8 - 27x^6 + 18x^4 - 9x^2 + 3	\( 2^{20}\cdot 3^{19} \)	$C_4:S_4$ (as 12T54)	Trivial
12.0.1376479908724736.12	x^12 - 10x^10 + 43x^8 - 130x^6 + 298x^4 - 316x^2 + 116	\( 2^{26}\cdot 29^{5} \)	$C_4:S_4$ (as 12T54)	$[2]$
12.0.1376479908724736.15	x^12 - 10x^10 + 27x^8 - 18x^6 + 66x^4 - 108x^2 + 116	\( 2^{26}\cdot 29^{5} \)	$C_4:S_4$ (as 12T54)	$[2]$
12.0.1711891286065152.7	x^12 + 12x^8 - 8x^6 + 36x^4 - 48x^2 + 48	\( 2^{30}\cdot 3^{13} \)	$C_4:S_4$ (as 12T54)	Trivial
12.0.1711891286065152.8	x^12 + 12x^8 + 8x^6 + 36x^4 + 48x^2 + 48	\( 2^{30}\cdot 3^{13} \)	$C_4:S_4$ (as 12T54)	Trivial
12.2.2049009307488256.1	x^12 - 4x^11 + 14x^10 - 42x^9 + 86x^8 - 172x^7 + 245x^6 - 322x^5 + 317x^4 - 254x^3 + 153x^2 - 52x + 7	\( -\,2^{12}\cdot 29^{8} \)	$C_4:S_4$ (as 12T54)	Trivial
12.2.2494869834563584.5	x^12 - 7x^10 + 15x^8 - 16x^6 + 2x^4 + 8x^2 - 4	\( -\,2^{22}\cdot 29^{6} \)	$C_4:S_4$ (as 12T54)	Trivial
12.2.2494869834563584.9	x^12 - 6x^10 + 13x^8 - 2x^6 - 26x^4 + 20x^2 - 4	\( -\,2^{22}\cdot 29^{6} \)	$C_4:S_4$ (as 12T54)	Trivial
12.2.2567836929097728.1	x^12 - 9x^8 - 24x^7 - 20x^6 - 12x^5 - 24x^4 - 24x^3 - 24x^2 - 24x - 2	\( -\,2^{29}\cdot 3^{14} \)	$C_4:S_4$ (as 12T54)	Trivial
12.2.2567836929097728.12	x^12 + 9x^8 - 28x^6 - 72x^5 - 87x^4 - 48x^3 - 12x^2 + 1	\( -\,2^{29}\cdot 3^{14} \)	$C_4:S_4$ (as 12T54)	Trivial
12.0.2658691056664576.9	x^12 - 10x^10 + 37x^8 - 52x^6 + 23x^4 - 10x^2 + 19	\( 2^{30}\cdot 19^{5} \)	$C_4:S_4$ (as 12T54)	Trivial
12.0.2658691056664576.12	x^12 + 10x^10 + 37x^8 + 52x^6 + 23x^4 + 10x^2 + 19	\( 2^{30}\cdot 19^{5} \)	$C_4:S_4$ (as 12T54)	Trivial
12.0.3189382584467456.6	x^12 - 10x^10 + 34x^8 - 48x^6 + 65x^4 - 42x^2 + 26	\( 2^{33}\cdot 13^{5} \)	$C_4:S_4$ (as 12T54)	Trivial
12.0.3189382584467456.9	x^12 - 2x^10 + 18x^8 + 16x^6 - 31x^4 - 2x^2 + 26	\( 2^{33}\cdot 13^{5} \)	$C_4:S_4$ (as 12T54)	Trivial
12.0.3189382584467456.18	x^12 - 6x^10 + 14x^8 - 24x^6 + 76x^4 - 152x^2 + 104	\( 2^{33}\cdot 13^{5} \)	$C_4:S_4$ (as 12T54)	Trivial
12.0.3189382584467456.20	x^12 - 2x^10 + 6x^8 - 24x^6 + 60x^4 - 72x^2 + 104	\( 2^{33}\cdot 13^{5} \)	$C_4:S_4$ (as 12T54)	Trivial
12.0.3355443200000000.6	x^12 - 2x^10 + 2x^8 + 4x^6 + x^4 + 2x^2 + 2	\( 2^{33}\cdot 5^{8} \)	$C_4:S_4$ (as 12T54)	Trivial
12.0.3355443200000000.11	x^12 - 4x^10 + 8x^8 - 8x^6 + x^4 + 4x^2 + 8	\( 2^{33}\cdot 5^{8} \)	$C_4:S_4$ (as 12T54)	Trivial
12.2.3792912694161408.2	x^12 - 2x^10 - 8x^9 + 15x^8 - 6x^7 + 4x^6 - 42x^5 + 103x^4 - 106x^3 + 6x^2 - 14x + 1	\( -\,2^{12}\cdot 3^{9}\cdot 19^{6} \)	$C_4:S_4$ (as 12T54)	$[2]$
12.2.4874877920083968.2	x^12 + 6x^8 + 9x^4 - 12	\( -\,2^{22}\cdot 3^{19} \)	$C_4:S_4$ (as 12T54)	Trivial
12.0.4874877920083968.14	x^12 - 3x^10 + 3x^8 - 48x^6 - 18x^4 + 288x^2 + 588	\( 2^{22}\cdot 3^{19} \)	$C_4:S_4$ (as 12T54)	Trivial
12.0.4874877920083968.15	x^12 - 9x^10 + 39x^8 - 108x^6 + 216x^4 - 288x^2 + 192	\( 2^{22}\cdot 3^{19} \)	$C_4:S_4$ (as 12T54)	Trivial
12.2.5182746699759616.4	x^12 + 4x^8 - 40x^6 + 4x^4 - 80x^2 - 16	\( -\,2^{30}\cdot 13^{6} \)	$C_4:S_4$ (as 12T54)	$[2]$
12.2.5182746699759616.7	x^12 - 4x^10 + 22x^8 - 16x^6 - 63x^4 - 28x^2 - 4	\( -\,2^{30}\cdot 13^{6} \)	$C_4:S_4$ (as 12T54)	$[2]$
12.0.5242880000000000.5	x^12 - 10x^10 + 50x^8 - 80x^6 + 100x^4 - 200x^2 + 200	\( 2^{29}\cdot 5^{10} \)	$C_4:S_4$ (as 12T54)	$[2]$
12.0.5533670223904768.10	x^12 - 8x^8 - 12x^6 + 48x^4 - 8x^2 + 22	\( 2^{35}\cdot 11^{5} \)	$C_4:S_4$ (as 12T54)	Trivial
12.0.5533670223904768.17	x^12 - 8x^8 + 12x^6 + 48x^4 + 8x^2 + 22	\( 2^{35}\cdot 11^{5} \)	$C_4:S_4$ (as 12T54)	Trivial
12.2.6710886400000000.9	x^12 - 2x^10 + 11x^8 + 32x^6 + 16x^4 + 8x^2 - 4	\( -\,2^{34}\cdot 5^{8} \)	$C_4:S_4$ (as 12T54)	Trivial
12.2.6710886400000000.11	x^12 - 2x^10 + 15x^8 - 15x^4 - 2x^2 - 1	\( -\,2^{34}\cdot 5^{8} \)	$C_4:S_4$ (as 12T54)	Trivial
12.2.9979479338254336.9	x^12 - 10x^10 + 26x^8 + 4x^6 - 52x^4 + 48x^2 - 16	\( -\,2^{24}\cdot 29^{6} \)	$C_4:S_4$ (as 12T54)	Trivial
12.2.9979479338254336.10	x^12 - 4x^10 - 2x^8 + 32x^6 - 60x^4 + 56x^2 - 16	\( -\,2^{24}\cdot 29^{6} \)	$C_4:S_4$ (as 12T54)	Trivial
12.2.10485760000000000.2	x^12 - 10x^10 + 5x^8 - 20x^6 - 125x^4 - 50x^2 - 25	\( -\,2^{30}\cdot 5^{10} \)	$C_4:S_4$ (as 12T54)	$[2]$