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 87)

Label	Polynomial	Discriminant	Galois group	Class group
12.4.972292630401.1	x^12 - 4x^11 + 5x^10 + 3x^9 - 20x^8 + 30x^7 - 12x^6 - 24x^5 + 43x^4 - 30x^3 + 8x^2 + 2x - 1	\( 3^{4}\cdot 331^{4} \)	$C_4^2:C_3:C_2$ (as 12T62)	Trivial
12.4.1642047467776.1	x^12 - 6x^10 + 16x^8 - 25x^6 + 23x^4 - 11x^2 + 1	\( 2^{8}\cdot 283^{4} \)	$C_4^2:C_3:C_2$ (as 12T62)	Trivial
12.4.4694952902656.1	x^12 - 4x^8 - 4x^6 + 11x^4 - 6x^2 + 1	\( 2^{24}\cdot 23^{4} \)	$C_4^2:C_3:C_2$ (as 12T62)	Trivial
12.4.11866206109696.1	x^12 - 7x^10 + 17x^8 - 16x^6 + x^4 + 5x^2 + 1	\( 2^{24}\cdot 29^{4} \)	$C_4^2:C_3:C_2$ (as 12T62)	Trivial
12.4.14667743362801.1	x^12 - 3x^11 + x^10 - x^8 + 3x^7 - 3x^6 + 3x^5 - x^4 + x^2 - 3x + 1	\( 19^{4}\cdot 103^{4} \)	$C_4^2:C_3:C_2$ (as 12T62)	Trivial
12.4.15494111297536.2	x^12 - 2x^10 - 2x^6 - 7x^4 - 2x^2 + 1	\( 2^{24}\cdot 31^{4} \)	$C_4^2:C_3:C_2$ (as 12T62)	Trivial
12.4.59470764169441.1	x^12 - x^10 - 14x^8 + 5x^6 + 48x^4 + 24x^2 + 1	\( 2777^{4} \)	$C_4^2:C_3:C_2$ (as 12T62)	Trivial
12.4.62882616180736.2	x^12 - 4x^10 + 9x^8 - 12x^6 - x^4 + 4x^2 + 1	\( 2^{32}\cdot 11^{4} \)	$C_4^2:C_3:C_2$ (as 12T62)	Trivial
12.4.559724432982016.1	x^12 - 7x^8 - 12x^6 - 13x^4 - 8x^2 + 1	\( 2^{32}\cdot 19^{4} \)	$C_4^2:C_3:C_2$ (as 12T62)	Trivial
12.4.759437191020544.4	x^12 - 2x^10 - 12x^8 - 24x^6 - 11x^4 + 6x^2 + 4	\( 2^{30}\cdot 29^{4} \)	$C_4^2:C_3:C_2$ (as 12T62)	Trivial
12.4.2282521714753536.12	x^12 + 3x^8 - 4x^6 - 15x^4 + 9	\( 2^{32}\cdot 3^{12} \)	$C_4^2:C_3:C_2$ (as 12T62)	Trivial
12.4.3596345248055296.7	x^12 - 3x^10 - 12x^9 - 9x^8 + 24x^7 + 38x^6 + 40x^5 - 12x^4 - 72x^3 - 42x^2 - 16x + 2	\( 2^{24}\cdot 11^{8} \)	$C_4^2:C_3:C_2$ (as 12T62)	Trivial
12.12.4239150758955121.1	x^12 - 5x^11 - 3x^10 + 42x^9 - 25x^8 - 102x^7 + 97x^6 + 68x^5 - 70x^4 - 21x^3 + 17x^2 + 3x - 1	\( 8069^{4} \)	$C_4^2:C_3:C_2$ (as 12T62)	Trivial
12.4.11555266180939776.7	x^12 - 6x^10 + 9x^8 - 16x^6 + 9x^4 + 18x^2 + 9	\( 2^{28}\cdot 3^{16} \)	$C_4^2:C_3:C_2$ (as 12T62)	Trivial
12.4.14624633760251904.10	x^12 - 6x^10 - 12x^8 + 4x^6 + 24x^4 + 12x^2 + 4	\( 2^{22}\cdot 3^{20} \)	$C_4^2:C_3:C_2$ (as 12T62)	Trivial
12.4.46221064723759104.16	x^12 + 6x^10 - 104x^6 + 93x^4 - 18x^2 + 4	\( 2^{30}\cdot 3^{16} \)	$C_4^2:C_3:C_2$ (as 12T62)	Trivial
12.12.60079076814032896.1	x^12 - 13x^10 + 59x^8 - 109x^6 + 73x^4 - 16x^2 + 1	\( 2^{12}\cdot 19^{4}\cdot 103^{4} \)	$C_4^2:C_3:C_2$ (as 12T62)	Trivial
12.4.125612606403641344.1	x^12 - 12x^10 + 58x^8 - 144x^6 + 186x^4 - 104x^2 + 4	\( 2^{42}\cdot 13^{4} \)	$C_4^2:C_3:C_2$ (as 12T62)	Trivial
12.4.125612606403641344.4	x^12 - 8x^8 - 80x^6 + 250x^4 - 112x^2 + 16	\( 2^{42}\cdot 13^{4} \)	$C_4^2:C_3:C_2$ (as 12T62)	Trivial
12.4.218971048064843776.9	x^12 - 5x^10 + 5x^8 - 20x^6 + 45x^4 - 41x^2 + 1	\( 2^{28}\cdot 13^{8} \)	$C_4^2:C_3:C_2$ (as 12T62)	$[3]$
12.4.230166095875538944.8	x^12 + 6x^10 - 16x^8 - 192x^6 - 496x^4 - 416x^2 + 256	\( 2^{30}\cdot 11^{8} \)	$C_4^2:C_3:C_2$ (as 12T62)	$[2]$
12.4.284936905588473856.18	x^12 + 9x^10 + 26x^8 + 2x^6 - 91x^4 - 75x^2 + 64	\( 2^{24}\cdot 19^{8} \)	$C_4^2:C_3:C_2$ (as 12T62)	$[3]$
12.4.573157819373584384.2	x^12 - 12x^10 + 46x^8 - 48x^6 - 30x^4 - 8x^2 + 4	\( 2^{42}\cdot 19^{4} \)	$C_4^2:C_3:C_2$ (as 12T62)	$[2]$
12.4.573157819373584384.8	x^12 - 16x^10 + 76x^8 - 160x^6 + 218x^4 - 304x^2 + 400	\( 2^{42}\cdot 19^{4} \)	$C_4^2:C_3:C_2$ (as 12T62)	$[2]$
12.4.578220423796228096.2	x^12 - x^11 + 15x^10 + 14x^9 + 132x^8 + 244x^7 + 288x^6 + 264x^5 - 59x^4 - 113x^3 - 53x^2 - 26x - 4	\( 2^{22}\cdot 13^{10} \)	$C_4^2:C_3:C_2$ (as 12T62)	$[2]$
12.4.875884192259375104.50	x^12 - 10x^10 + 32x^8 - 32x^6 - 59x^4 + 198x^2 + 196	\( 2^{30}\cdot 13^{8} \)	$C_4^2:C_3:C_2$ (as 12T62)	$[3]$
12.4.920664383502155776.17	x^12 - 11x^8 - 1452x^6 + 1815x^4 + 10648x^2 + 14641	\( 2^{32}\cdot 11^{8} \)	$C_4^2:C_3:C_2$ (as 12T62)	Trivial (GRH)
12.4.935976560656121856.35	x^12 - 6x^10 - 30x^8 + 28x^6 + 60x^4 - 168x^2 + 16	\( 2^{28}\cdot 3^{20} \)	$C_4^2:C_3:C_2$ (as 12T62)	Trivial
12.4.935976560656121856.70	x^12 + 6x^10 - 6x^8 - 124x^6 - 324x^4 - 216x^2 + 144	\( 2^{28}\cdot 3^{20} \)	$C_4^2:C_3:C_2$ (as 12T62)	$[2]$
12.4.1313840315232157696.11	x^12 + 2x^10 - 10x^8 - 100x^6 - 228x^4 - 160x^2 + 16	\( 2^{24}\cdot 23^{8} \)	$C_4^2:C_3:C_2$ (as 12T62)	Trivial
12.4.1313840315232157696.12	x^12 + 10x^10 + 22x^8 - 76x^6 + 60x^4 - 64x^2 + 16	\( 2^{24}\cdot 23^{8} \)	$C_4^2:C_3:C_2$ (as 12T62)	Trivial
12.4.1313840315232157696.19	x^12 - 46x^10 + 805x^8 - 5290x^6 + 4232x^4 - 24334x^2 + 279841	\( 2^{24}\cdot 23^{8} \)	$C_4^2:C_3:C_2$ (as 12T62)	Trivial (GRH)
12.4.1717986918400000000.3	x^12 + 4x^10 + 50x^8 - 280x^4 - 416x^2 + 16	\( 2^{42}\cdot 5^{8} \)	$C_4^2:C_3:C_2$ (as 12T62)	Trivial (GRH)
12.4.1717986918400000000.4	x^12 - 12x^10 + 58x^8 - 144x^6 + 210x^4 - 200x^2 + 100	\( 2^{42}\cdot 5^{8} \)	$C_4^2:C_3:C_2$ (as 12T62)	Trivial
12.4.2312881695184912384.31	x^12 - 6x^11 + 10x^10 - 8x^9 + 100x^8 - 392x^7 + 168x^6 + 1696x^5 - 4040x^4 + 4688x^3 - 2960x^2 - 960x + 2432	\( 2^{24}\cdot 13^{10} \)	$C_4^2:C_3:C_2$ (as 12T62)	$[4]$
12.4.2337302235907620864.14	x^12 + 36x^8 + 64x^6 - 198x^4 - 432x^2 + 16	\( 2^{42}\cdot 3^{12} \)	$C_4^2:C_3:C_2$ (as 12T62)	$[4]$
12.4.2337302235907620864.22	x^12 - 12x^10 + 54x^8 - 112x^6 + 114x^4 - 72x^2 + 36	\( 2^{42}\cdot 3^{12} \)	$C_4^2:C_3:C_2$ (as 12T62)	$[2]$
12.4.8392742123471896576.21	x^12 - 5x^11 - 11x^10 + 81x^9 - 201x^8 - 384x^7 + 1880x^6 + 3960x^5 - 5019x^4 - 24649x^3 + 34321x^2 - 70035x + 113963	\( 2^{24}\cdot 29^{8} \)	$C_4^2:C_3:C_2$ (as 12T62)	$[2]$ (GRH)
12.4.11832592569282330624.3	x^12 - 12x^10 - 104x^6 - 186x^4 - 72x^2 + 4	\( 2^{38}\cdot 3^{16} \)	$C_4^2:C_3:C_2$ (as 12T62)	Trivial (GRH)
12.4.11832592569282330624.4	x^12 - 12x^10 + 36x^8 - 104x^6 + 390x^4 - 72x^2 + 4	\( 2^{38}\cdot 3^{16} \)	$C_4^2:C_3:C_2$ (as 12T62)	Trivial
12.4.11832592569282330624.18	x^12 - 24x^10 + 204x^8 - 704x^6 + 744x^4 + 192x^2 + 64	\( 2^{38}\cdot 3^{16} \)	$C_4^2:C_3:C_2$ (as 12T62)	Trivial
12.4.11832592569282330624.22	x^12 - 24x^10 + 222x^8 - 992x^6 + 2202x^4 - 2256x^2 + 784	\( 2^{38}\cdot 3^{16} \)	$C_4^2:C_3:C_2$ (as 12T62)	Trivial (GRH)
12.4.14309137159611744256.57	x^12 - 465x^8 - 1922x^6 + 9610x^4 - 417074x^2 + 923521	\( 2^{24}\cdot 31^{8} \)	$C_4^2:C_3:C_2$ (as 12T62)	Trivial (GRH)
12.4.14975624970497949696.71	x^12 - 12x^10 + 66x^8 - 232x^6 + 432x^4 - 216x^2 + 36	\( 2^{32}\cdot 3^{20} \)	$C_4^2:C_3:C_2$ (as 12T62)	Trivial (GRH)
12.4.18235961957662326784.26	x^12 - 10x^10 + 64x^8 - 188x^6 + 289x^4 - 246x^2 + 64	\( 2^{30}\cdot 19^{8} \)	$C_4^2:C_3:C_2$ (as 12T62)	$[3]$
12.4.21021445043714523136.9	x^12 + 11x^10 + 57x^8 + 140x^6 + 56x^4 - 292x^2 + 4	\( 2^{28}\cdot 23^{8} \)	$C_4^2:C_3:C_2$ (as 12T62)	$[2]$
12.4.21021445043714523136.18	x^12 - 13x^10 + 53x^8 - 176x^6 + 304x^4 - 576x^2 + 64	\( 2^{28}\cdot 23^{8} \)	$C_4^2:C_3:C_2$ (as 12T62)	$[2]$
12.4.58922520544137969664.1	x^12 + 4x^10 + 68x^8 + 88x^6 - 210x^4 - 296x^2 + 4	\( 2^{38}\cdot 11^{8} \)	$C_4^2:C_3:C_2$ (as 12T62)	$[2]$ (GRH)
12.4.58922520544137969664.4	x^12 + 4x^10 + 36x^8 - 408x^6 + 1006x^4 - 776x^2 + 36	\( 2^{38}\cdot 11^{8} \)	$C_4^2:C_3:C_2$ (as 12T62)	$[2]$
12.4.58922520544137969664.6	x^12 - 24x^10 + 204x^8 - 704x^6 + 904x^4 - 1088x^2 + 64	\( 2^{38}\cdot 11^{8} \)	$C_4^2:C_3:C_2$ (as 12T62)	$[2]$ (GRH)