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 246)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.166933642578125.1	x^12 - 3x^11 + 8x^10 - 5x^9 + 17x^7 - 11x^6 + x^5 + 15x^4 - 10x^3 - 9x^2 + 2x + 3	\( 5^{11}\cdot 43^{4} \)	$A_5:C_4$ (as 12T124)	Trivial
12.0.166933642578125.2	x^12 - 6x^11 + 19x^10 - 35x^9 + 35x^8 - 16x^7 - 9x^6 + 11x^5 + 5x^4 + x^2 + 14x + 9	\( 5^{11}\cdot 43^{4} \)	$A_5:C_4$ (as 12T124)	Trivial
12.4.500000000000000.1	x^12 - 6x^11 + 16x^10 - 20x^9 - 5x^8 + 48x^7 - 78x^6 + 48x^5 - 5x^4 - 20x^3 + 16x^2 - 6x + 1	\( 2^{14}\cdot 5^{15} \)	$A_5:C_4$ (as 12T124)	Trivial
12.4.500000000000000.2	x^12 - 10x^10 + 35x^8 - 60x^6 + 55x^4 - 42x^2 + 5	\( 2^{14}\cdot 5^{15} \)	$A_5:C_4$ (as 12T124)	Trivial
12.0.3276800000000000.2	x^12 + 10x^10 + 35x^8 + 40x^6 - 5x^4 - 18x^2 + 5	\( 2^{26}\cdot 5^{11} \)	$A_5:C_4$ (as 12T124)	Trivial
12.4.3276800000000000.3	x^12 - 2x^10 - 5x^8 + 35x^4 - 30x^2 + 5	\( 2^{26}\cdot 5^{11} \)	$A_5:C_4$ (as 12T124)	Trivial
12.0.3276800000000000.3	x^12 + 2x^10 - 5x^8 + 35x^4 + 30x^2 + 5	\( 2^{26}\cdot 5^{11} \)	$A_5:C_4$ (as 12T124)	Trivial
12.4.3276800000000000.4	x^12 - 10x^10 + 35x^8 - 40x^6 - 5x^4 + 18x^2 + 5	\( 2^{26}\cdot 5^{11} \)	$A_5:C_4$ (as 12T124)	Trivial
12.4.4882812500000000.1	x^12 - 3x^11 + 5x^10 - 5x^9 + 5x^8 + 14x^7 - 47x^6 + 30x^5 + 15x^4 - 65x^3 + 24x^2 + 68x - 35	\( 2^{8}\cdot 5^{19} \)	$A_5:C_4$ (as 12T124)	Trivial
12.4.4882812500000000.2	x^12 - 6x^11 + 14x^10 - 15x^9 + 5x^8 + 4x^7 - 29x^6 + 76x^5 - 75x^4 + 25x^3 - 25x^2 + 25x + 25	\( 2^{8}\cdot 5^{19} \)	$A_5:C_4$ (as 12T124)	Trivial
12.0.8000000000000000.1	x^12 - 2x^10 + 35x^8 - 20x^6 - 25x^4 + 10x^2 + 5	\( 2^{18}\cdot 5^{15} \)	$A_5:C_4$ (as 12T124)	Trivial
12.0.8000000000000000.2	x^12 + 10x^10 + 35x^8 + 60x^6 + 55x^4 + 42x^2 + 5	\( 2^{18}\cdot 5^{15} \)	$A_5:C_4$ (as 12T124)	Trivial
12.4.13107200000000000.1	x^12 - 20x^6 + 16x^2 + 20	\( 2^{28}\cdot 5^{11} \)	$A_5:C_4$ (as 12T124)	Trivial
12.0.13107200000000000.3	x^12 + 20x^6 - 16x^2 + 20	\( 2^{28}\cdot 5^{11} \)	$A_5:C_4$ (as 12T124)	Trivial
12.4.13107200000000000.5	x^12 - 10x^10 + 35x^8 - 60x^6 + 95x^4 - 170x^2 + 125	\( 2^{28}\cdot 5^{11} \)	$A_5:C_4$ (as 12T124)	Trivial
12.0.13107200000000000.13	x^12 + 10x^10 + 35x^8 + 60x^6 + 95x^4 + 170x^2 + 125	\( 2^{28}\cdot 5^{11} \)	$A_5:C_4$ (as 12T124)	Trivial
12.0.32000000000000000.1	x^12 - 6x^11 + 9x^10 + 10x^7 + 10x^6 - 90x^5 + 150x^4 - 140x^3 + 77x^2 - 22x + 3	\( 2^{20}\cdot 5^{15} \)	$A_5:C_4$ (as 12T124)	Trivial
12.0.32000000000000000.2	x^12 - 8x^10 - 10x^9 + 25x^8 + 36x^7 + 5x^6 - 48x^5 - 5x^4 + 9x^2 - 10x + 23	\( 2^{20}\cdot 5^{15} \)	$A_5:C_4$ (as 12T124)	Trivial
12.0.128000000000000000.3	x^12 + 14x^10 + 55x^8 + 110x^6 + 125x^4 + 80x^2 + 20	\( 2^{22}\cdot 5^{15} \)	$A_5:C_4$ (as 12T124)	Trivial
12.4.128000000000000000.4	x^12 - 14x^10 + 55x^8 - 110x^6 + 125x^4 - 80x^2 + 20	\( 2^{22}\cdot 5^{15} \)	$A_5:C_4$ (as 12T124)	Trivial
12.0.128000000000000000.6	x^12 + 50x^6 + 100x^2 + 125	\( 2^{22}\cdot 5^{15} \)	$A_5:C_4$ (as 12T124)	Trivial
12.4.128000000000000000.7	x^12 - 50x^6 - 100x^2 + 125	\( 2^{22}\cdot 5^{15} \)	$A_5:C_4$ (as 12T124)	Trivial
12.4.312500000000000000.1	x^12 - 4x^11 - 2x^10 + 20x^9 + 15x^8 + 2x^7 - 108x^6 - 94x^5 + 45x^4 - 60x^3 - 24x^2 - 4x - 17	\( 2^{14}\cdot 5^{19} \)	$A_5:C_4$ (as 12T124)	Trivial
12.0.312500000000000000.1	x^12 + 10x^10 + 35x^8 + 10x^6 - 95x^4 - 24x^2 + 80	\( 2^{14}\cdot 5^{19} \)	$A_5:C_4$ (as 12T124)	Trivial (GRH)
12.0.312500000000000000.2	x^12 + 50x^6 + 20x^2 + 125	\( 2^{14}\cdot 5^{19} \)	$A_5:C_4$ (as 12T124)	Trivial (GRH)
12.4.312500000000000000.2	x^12 + 10x^10 + 35x^8 + 60x^6 + 55x^4 - 74x^2 + 5	\( 2^{14}\cdot 5^{19} \)	$A_5:C_4$ (as 12T124)	Trivial
12.0.512000000000000000.2	x^12 - 4x^10 + 15x^8 + 40x^6 - 25x^4 + 30x^2 + 5	\( 2^{24}\cdot 5^{15} \)	$A_5:C_4$ (as 12T124)	Trivial
12.4.512000000000000000.3	x^12 + 4x^10 + 15x^8 - 40x^6 - 25x^4 - 30x^2 + 5	\( 2^{24}\cdot 5^{15} \)	$A_5:C_4$ (as 12T124)	Trivial
12.0.512000000000000000.5	x^12 - 20x^6 + 136x^2 + 20	\( 2^{24}\cdot 5^{15} \)	$A_5:C_4$ (as 12T124)	Trivial
12.4.512000000000000000.6	x^12 + 20x^6 - 136x^2 + 20	\( 2^{24}\cdot 5^{15} \)	$A_5:C_4$ (as 12T124)	Trivial
12.4.512000000000000000.8	x^12 + 10x^10 + 35x^8 + 10x^6 - 95x^4 - 368x^2 + 80	\( 2^{24}\cdot 5^{15} \)	$A_5:C_4$ (as 12T124)	Trivial
12.4.512000000000000000.14	x^12 - 2x^10 - 40x^8 + 80x^6 + 400x^4 - 890x^2 + 405	\( 2^{24}\cdot 5^{15} \)	$A_5:C_4$ (as 12T124)	Trivial
12.4.1024000000000000000.1	x^12 - 5x^11 + 3x^10 - 5x^9 + 10x^8 + 84x^7 - 20x^6 - 68x^5 + 140x^4 + 220x^3 + 44x^2 - 20x - 8	\( 2^{25}\cdot 5^{15} \)	$A_5:C_4$ (as 12T124)	Trivial (GRH)
12.4.1024000000000000000.3	x^12 - 5x^11 + 14x^10 - 45x^9 + 40x^8 + 71x^7 - 80x^6 - 71x^5 + 40x^4 + 45x^3 + 14x^2 + 5x + 1	\( 2^{25}\cdot 5^{15} \)	$A_5:C_4$ (as 12T124)	Trivial
12.4.1024000000000000000.4	x^12 - 6x^11 + 14x^10 - 10x^9 - 5x^8 + 116x^7 - 116x^6 - 116x^5 - 5x^4 + 10x^3 + 14x^2 + 6x + 1	\( 2^{25}\cdot 5^{15} \)	$A_5:C_4$ (as 12T124)	Trivial
12.4.1024000000000000000.5	x^12 - 6x^11 + 14x^10 - 10x^9 - 5x^8 - 108x^7 + 108x^6 + 108x^5 - 5x^4 + 10x^3 + 14x^2 + 6x + 1	\( 2^{25}\cdot 5^{15} \)	$A_5:C_4$ (as 12T124)	Trivial
12.0.1250000000000000000.3	x^12 - 10x^10 + 35x^8 - 60x^6 + 55x^4 + 54x^2 + 5	\( 2^{16}\cdot 5^{19} \)	$A_5:C_4$ (as 12T124)	$[2]$
12.0.1250000000000000000.6	x^12 - 4x^11 + 4x^10 - 20x^7 - 20x^6 + 120x^5 + 100x^4 - 120x^2 - 120x + 220	\( 2^{16}\cdot 5^{19} \)	$A_5:C_4$ (as 12T124)	$[2]$
12.4.1677721600000000000.26	x^12 - 8x^10 + 30x^8 - 60x^6 + 65x^4 - 100x^2 + 40	\( 2^{35}\cdot 5^{11} \)	$A_5:C_4$ (as 12T124)	Trivial
12.0.1677721600000000000.29	x^12 + 8x^10 + 30x^8 + 60x^6 + 65x^4 + 100x^2 + 40	\( 2^{35}\cdot 5^{11} \)	$A_5:C_4$ (as 12T124)	Trivial (GRH)
12.4.1677721600000000000.47	x^12 - 10x^10 + 20x^8 + 40x^6 - 35x^4 - 374x^2 + 250	\( 2^{35}\cdot 5^{11} \)	$A_5:C_4$ (as 12T124)	Trivial (GRH)
12.4.1677721600000000000.48	x^12 - 6x^10 + 40x^8 - 200x^6 + 325x^4 - 250x^2 + 250	\( 2^{35}\cdot 5^{11} \)	$A_5:C_4$ (as 12T124)	Trivial
12.4.1677721600000000000.49	x^12 - 10x^10 + 20x^8 + 125x^4 + 50x^2 + 250	\( 2^{35}\cdot 5^{11} \)	$A_5:C_4$ (as 12T124)	Trivial
12.0.1677721600000000000.59	x^12 + 10x^10 + 20x^8 + 125x^4 - 50x^2 + 250	\( 2^{35}\cdot 5^{11} \)	$A_5:C_4$ (as 12T124)	Trivial (GRH)
12.0.1677721600000000000.61	x^12 + 6x^10 + 40x^8 + 200x^6 + 325x^4 + 250x^2 + 250	\( 2^{35}\cdot 5^{11} \)	$A_5:C_4$ (as 12T124)	Trivial (GRH)
12.0.1677721600000000000.62	x^12 + 10x^10 + 20x^8 - 40x^6 - 35x^4 + 374x^2 + 250	\( 2^{35}\cdot 5^{11} \)	$A_5:C_4$ (as 12T124)	Trivial (GRH)
12.4.2048000000000000000.7	x^12 - 10x^10 + 35x^8 - 100x^6 + 175x^4 - 370x^2 + 125	\( 2^{26}\cdot 5^{15} \)	$A_5:C_4$ (as 12T124)	Trivial (GRH)
12.0.2048000000000000000.7	x^12 + 10x^10 + 35x^8 + 100x^6 + 175x^4 + 370x^2 + 125	\( 2^{26}\cdot 5^{15} \)	$A_5:C_4$ (as 12T124)	Trivial (GRH)
12.0.2048000000000000000.8	x^12 - 10x^10 + 35x^8 + 40x^6 - 245x^4 + 274x^2 + 405	\( 2^{26}\cdot 5^{15} \)	$A_5:C_4$ (as 12T124)	Trivial (GRH)
12.4.2048000000000000000.10	x^12 + 10x^10 + 35x^8 - 40x^6 - 245x^4 - 274x^2 + 405	\( 2^{26}\cdot 5^{15} \)	$A_5:C_4$ (as 12T124)	Trivial (GRH)