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 2724)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.46716936381.1	x^12 - 4x^11 + 9x^10 - 15x^9 + 23x^8 - 33x^7 + 44x^6 - 50x^5 + 45x^4 - 29x^3 + 13x^2 - 4x + 1	\( 3^{6}\cdot 23^{4}\cdot 229 \)	12T193	Trivial
12.0.63853279857.1	x^12 - 4x^11 + 9x^10 - 13x^9 + 17x^8 - 21x^7 + 25x^6 - 27x^5 + 26x^4 - 20x^3 + 12x^2 - 5x + 1	\( 3^{6}\cdot 23^{4}\cdot 313 \)	12T193	Trivial
12.2.257978421875.1	x^12 - 2x^11 + 2x^9 - 5x^7 + 10x^6 - 16x^5 + 20x^4 - 19x^3 + 12x^2 - 5x + 1	\( -\,5^{6}\cdot 23^{4}\cdot 59 \)	12T193	Trivial
12.2.566636000000.1	x^12 - 4x^10 - x^9 + 7x^8 + 4x^7 - 5x^6 - 8x^5 + x^4 + 7x^3 - x^2 - 3x + 1	\( -\,2^{8}\cdot 5^{6}\cdot 7^{4}\cdot 59 \)	12T193	Trivial
12.0.651504828125.1	x^12 - 4x^11 + 4x^10 + 3x^9 - 3x^8 - 9x^7 + 9x^6 + 3x^5 - x^4 - 4x^3 - x^2 + 2x + 1	\( 5^{6}\cdot 23^{4}\cdot 149 \)	12T193	Trivial
12.0.1430996000000.1	x^12 - x^11 - x^10 - x^9 + 3x^8 + x^6 - 6x^5 + 5x^4 - x^3 + 1	\( 2^{8}\cdot 5^{6}\cdot 7^{4}\cdot 149 \)	12T193	Trivial
12.0.1483275763712.1	x^12 - 4x^10 + 5x^8 - 4x^6 + 7x^4 - 6x^2 + 2	\( 2^{21}\cdot 29^{4} \)	12T193	Trivial
12.4.2278080640625.1	x^12 - x^11 - x^10 + 3x^9 - 4x^8 - 6x^7 + 7x^6 + 6x^5 - 4x^4 - 3x^3 - x^2 + x + 1	\( 5^{6}\cdot 23^{4}\cdot 521 \)	12T193	Trivial
12.0.2688437321728.1	x^12 - 2x^11 + 3x^10 - 4x^9 + 3x^8 - 4x^7 + 15x^6 - 34x^5 + 47x^4 - 38x^3 + 20x^2 - 6x + 1	\( 2^{17}\cdot 29^{5} \)	12T193	Trivial
12.4.3304473578125.1	x^12 - x^11 - 3x^10 + 2x^9 + 5x^8 - 8x^7 - 9x^6 + 4x^5 + 7x^4 - 3x^3 + 5x^2 + 2x - 1	\( 5^{6}\cdot 31^{4}\cdot 229 \)	12T193	Trivial
12.2.5061276073984.2	x^12 - 3x^10 + x^8 + 3x^4 + 3x^2 - 1	\( -\,2^{20}\cdot 13^{6} \)	12T193	Trivial
12.0.7860327022592.1	x^12 - 4x^10 + 10x^8 - 14x^6 + 14x^4 - 8x^2 + 2	\( 2^{29}\cdot 11^{4} \)	12T193	Trivial
12.0.7860327022592.4	x^12 - 2x^8 - 2x^6 + 6x^4 - 4x^2 + 2	\( 2^{29}\cdot 11^{4} \)	12T193	Trivial
12.2.8745694265344.2	x^12 - 6x^6 + 6x^4 + 4x^2 - 1	\( -\,2^{26}\cdot 19^{4} \)	12T193	Trivial
12.0.8886803708997.1	x^12 - 2x^11 + 4x^10 - 2x^9 - 6x^8 + 17x^7 - 20x^6 + 8x^5 + 22x^4 - 45x^3 + 36x^2 - 15x + 3	\( 3^{7}\cdot 31\cdot 107^{4} \)	12T193	Trivial
12.2.10240000000000.2	x^12 + 7x^10 + 20x^8 + 25x^6 + 10x^4 - 3x^2 - 1	\( -\,2^{20}\cdot 5^{10} \)	12T193	Trivial
12.0.15045919506432.3	x^12 - 3x^10 + 9x^8 - 12x^6 + 15x^4 - 9x^2 + 3	\( 2^{20}\cdot 3^{15} \)	12T193	Trivial
12.2.20245104295936.1	x^12 + x^10 + x^8 - 4x^6 - 12x^4 - 12x^2 - 4	\( -\,2^{22}\cdot 13^{6} \)	12T193	Trivial
12.0.20421060067328.1	x^12 - 2x^11 - 3x^10 + 4x^9 + 9x^8 - 10x^7 - 6x^6 + 10x^5 + 9x^4 - 4x^3 - 3x^2 + 2x + 1	\( 2^{19}\cdot 79^{4} \)	12T193	Trivial
12.0.23732412219392.1	x^12 - 2x^10 + 5x^8 - 10x^6 + 11x^4 - 6x^2 + 2	\( 2^{25}\cdot 29^{4} \)	12T193	Trivial
12.0.24917051441152.3	x^12 - 6x^11 + 20x^10 - 44x^9 + 76x^8 - 108x^7 + 120x^6 - 104x^5 + 78x^4 - 52x^3 + 32x^2 - 16x + 4	\( 2^{26}\cdot 13^{5} \)	12T193	Trivial
12.2.34982777061376.1	x^12 - 2x^10 - x^8 + 2x^4 + 8x^2 - 4	\( -\,2^{28}\cdot 19^{4} \)	12T193	Trivial
12.2.34982777061376.2	x^12 + 6x^6 + 6x^4 - 4x^2 - 1	\( -\,2^{28}\cdot 19^{4} \)	12T193	Trivial
12.2.35664401793024.2	x^12 - 6x^8 + 2x^6 + 24x^4 + 12x^2 - 1	\( -\,2^{26}\cdot 3^{12} \)	12T193	Trivial
12.0.37559623221248.4	x^12 - 8x^10 + 28x^8 - 44x^6 + 28x^4 - 8x^2 + 8	\( 2^{27}\cdot 23^{4} \)	12T193	Trivial
12.0.37559623221248.9	x^12 - 4x^10 + 12x^8 - 4x^6 + 12x^4 + 24x^2 + 8	\( 2^{27}\cdot 23^{4} \)	12T193	Trivial
12.2.40960000000000.2	x^12 + x^10 - 5x^8 - 10x^6 - 10x^4 - 4x^2 - 4	\( -\,2^{22}\cdot 5^{10} \)	12T193	Trivial
12.0.43014997147648.1	x^12 - 6x^10 - 4x^9 + 19x^8 + 28x^7 - 24x^6 - 68x^5 + 3x^4 + 92x^3 + 78x^2 + 16x + 1	\( 2^{21}\cdot 29^{5} \)	12T193	Trivial
12.0.43014997147648.2	x^12 - 10x^10 + 44x^8 - 104x^6 + 137x^4 - 110x^2 + 58	\( 2^{21}\cdot 29^{5} \)	12T193	Trivial
12.0.43014997147648.3	x^12 - 6x^10 + 40x^6 - 19x^4 - 58x^2 + 58	\( 2^{21}\cdot 29^{5} \)	12T193	Trivial
12.2.51200000000000.1	x^12 + 5x^10 + 5x^8 - 5x^4 - 5x^2 - 5	\( -\,2^{20}\cdot 5^{11} \)	12T193	Trivial
12.0.60183678025728.4	x^12 + 9x^10 + 33x^8 + 60x^6 + 60x^4 + 36x^2 + 12	\( 2^{22}\cdot 3^{15} \)	12T193	Trivial
12.2.61334280470528.2	x^12 - 2x^10 + 3x^8 - 4x^6 - 8x^4 + 8x^2 - 2	\( -\,2^{31}\cdot 13^{4} \)	12T193	Trivial
12.2.61334280470528.3	x^12 + 2x^10 + 11x^8 - 4x^6 + 8x^4 + 16x^2 - 2	\( -\,2^{31}\cdot 13^{4} \)	12T193	Trivial
12.0.61334280470528.2	x^12 + 2x^10 + x^8 - 2x^6 - 3x^4 + 2	\( 2^{31}\cdot 13^{4} \)	12T193	Trivial
12.0.61334280470528.3	x^12 - 2x^10 + x^8 + 2x^6 - 3x^4 + 2	\( 2^{31}\cdot 13^{4} \)	12T193	Trivial
12.0.61334280470528.4	x^12 - 2x^10 + 3x^8 + 4x^6 + 2	\( 2^{31}\cdot 13^{4} \)	12T193	Trivial
12.0.61334280470528.9	x^12 - 6x^10 + 17x^8 - 28x^6 + 28x^4 - 16x^2 + 8	\( 2^{31}\cdot 13^{4} \)	12T193	Trivial
12.2.65796588961792.1	x^12 + 7x^10 + 16x^8 + 5x^6 - 30x^4 - 39x^2 - 13	\( -\,2^{20}\cdot 13^{7} \)	12T193	Trivial
12.0.69965554122752.1	x^12 - 2x^10 + 4x^8 - 10x^6 + 14x^4 - 8x^2 + 2	\( 2^{29}\cdot 19^{4} \)	12T193	Trivial
12.0.69965554122752.6	x^12 - 2x^10 - 2x^6 + 6x^4 + 4x^2 + 2	\( 2^{29}\cdot 19^{4} \)	12T193	Trivial
12.0.77964682330112.1	x^12 - 2x^11 + 5x^10 + 6x^9 - 4x^8 + 16x^7 + 37x^6 + 8x^5 - 5x^4 + 28x^3 + 40x^2 + 16x + 2	\( 2^{17}\cdot 29^{6} \)	12T193	Trivial
12.0.77964682330112.2	x^12 - 4x^11 + 5x^10 + 8x^9 - 35x^8 + 48x^7 - 16x^6 - 80x^5 + 202x^4 - 264x^3 + 232x^2 - 128x + 32	\( 2^{17}\cdot 29^{6} \)	12T193	Trivial
12.2.80980417183744.2	x^12 + 3x^10 + x^8 + 3x^4 - 3x^2 - 1	\( -\,2^{24}\cdot 13^{6} \)	12T193	Trivial
12.0.94929648877568.3	x^12 - 4x^8 - 12x^6 + 40x^4 - 32x^2 + 8	\( 2^{27}\cdot 29^{4} \)	12T193	Trivial
12.0.94929648877568.7	x^12 - 4x^10 + 12x^8 - 12x^6 + 24x^4 + 8	\( 2^{27}\cdot 29^{4} \)	12T193	Trivial
12.0.99668205764608.3	x^12 + 3x^8 - 16x^6 + 31x^4 + 13	\( 2^{28}\cdot 13^{5} \)	12T193	Trivial
12.0.99668205764608.5	x^12 - 6x^10 + 19x^8 - 4x^6 + 15x^4 + 26x^2 + 13	\( 2^{28}\cdot 13^{5} \)	12T193	Trivial
12.0.123952890380288.2	x^12 - 6x^10 + 18x^8 - 28x^6 + 40x^4 - 16x^2 + 8	\( 2^{27}\cdot 31^{4} \)	12T193	Trivial
12.0.123952890380288.8	x^12 - 6x^10 + 18x^8 - 20x^6 - 8x^4 + 16x^2 + 8	\( 2^{27}\cdot 31^{4} \)	12T193	Trivial