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 428)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.28455140560896.1	x^12 - 3x^10 - 4x^9 + 3x^8 + 6x^7 - 12x^6 + 12x^5 + 33x^4 - 4x^3 - 6x^2 + 1	\( 2^{12}\cdot 3^{10}\cdot 7^{6} \)	$C_2\times S_5$ (as 12T123)	Trivial
12.0.29160000000000.1	x^12 - 4x^11 + 4x^10 + 2x^7 - 3x^6 - 2x^5 + 4x^2 + 4x + 1	\( 2^{12}\cdot 3^{6}\cdot 5^{10} \)	$C_2\times S_5$ (as 12T123)	Trivial
12.0.47608675209216.1	x^12 - 2x^11 - 5x^10 + 16x^9 - x^8 - 38x^7 + 40x^6 + 20x^5 - 58x^4 + 14x^3 + 25x^2 - 10x + 1	\( 2^{12}\cdot 3^{8}\cdot 11^{6} \)	$C_2\times S_5$ (as 12T123)	Trivial
12.0.163840000000000.1	x^12 + 4x^10 - 20x^6 + 16x^2 + 4	\( 2^{24}\cdot 5^{10} \)	$C_2\times S_5$ (as 12T123)	Trivial
12.0.475549784866816.3	x^12 - 4x^11 + 10x^10 - 12x^9 + 8x^8 + 4x^7 + 8x^6 - 80x^5 + 246x^4 - 416x^3 + 434x^2 - 264x + 73	\( 2^{28}\cdot 11^{6} \)	$C_2\times S_5$ (as 12T123)	Trivial
12.0.475549784866816.6	x^12 + 2x^10 + 2x^8 - 16x^7 + 8x^6 - 12x^5 + 12x^3 + 10x^2 + 4x + 1	\( 2^{28}\cdot 11^{6} \)	$C_2\times S_5$ (as 12T123)	Trivial
12.0.475549784866816.9	x^12 + 3x^10 - 5x^8 + 2x^6 + 35x^4 - 29x^2 + 9	\( 2^{28}\cdot 11^{6} \)	$C_2\times S_5$ (as 12T123)	Trivial
12.0.475549784866816.24	x^12 - 3x^10 + 4x^8 - 24x^6 + 80x^4 - 48x^2 + 64	\( 2^{28}\cdot 11^{6} \)	$C_2\times S_5$ (as 12T123)	Trivial
12.0.655360000000000.3	x^12 - 4x^11 + 4x^10 + 4x^2 + 4x + 1	\( 2^{26}\cdot 5^{10} \)	$C_2\times S_5$ (as 12T123)	Trivial
12.0.729000000000000.1	x^12 - 6x^11 + 19x^10 - 40x^9 + 70x^8 - 106x^7 + 141x^6 - 154x^5 + 155x^4 - 130x^3 + 94x^2 - 44x + 31	\( 2^{12}\cdot 3^{6}\cdot 5^{12} \)	$C_2\times S_5$ (as 12T123)	$[2]$
12.0.899086312013824.4	x^12 - 3x^11 + 9x^10 - 26x^9 + 67x^8 - 127x^7 + 177x^6 - 190x^5 + 169x^4 - 125x^3 + 69x^2 - 24x + 4	\( 2^{22}\cdot 11^{8} \)	$C_2\times S_5$ (as 12T123)	Trivial
12.0.899086312013824.9	x^12 - 3x^11 + x^10 + 6x^9 - 7x^8 - 5x^7 + 11x^6 - 42x^5 + 125x^4 - 121x^3 + 53x^2 - 28x + 12	\( 2^{22}\cdot 11^{8} \)	$C_2\times S_5$ (as 12T123)	Trivial
12.0.1184787066781696.2	x^12 - 5x^11 + 13x^10 - 26x^9 + 51x^8 - 69x^7 + 83x^6 - 100x^5 + 78x^4 - 58x^3 + 54x^2 - 8x + 8	\( 2^{22}\cdot 7^{10} \)	$C_2\times S_5$ (as 12T123)	$[3]$
12.0.1547476985184256.1	x^12 - 2x^11 + 3x^10 + 2x^9 + 3x^8 + 4x^7 + 18x^6 - 4x^5 + 3x^4 - 2x^3 + 3x^2 + 2x + 1	\( 2^{28}\cdot 7^{8} \)	$C_2\times S_5$ (as 12T123)	Trivial
12.4.1600000000000000.1	x^12 - 6x^11 + 21x^10 - 50x^9 + 90x^8 - 126x^7 + 131x^6 - 96x^5 + 25x^4 + 30x^3 - 56x^2 + 36x - 1	\( 2^{18}\cdot 5^{14} \)	$C_2\times S_5$ (as 12T123)	Trivial
12.0.1600000000000000.2	x^12 - 4x^11 + 8x^10 + 4x^7 - 16x^6 - 8x^5 + 8x^2 + 8x + 4	\( 2^{18}\cdot 5^{14} \)	$C_2\times S_5$ (as 12T123)	Trivial
12.4.1902199139467264.1	x^12 - 2x^11 - 5x^10 + 10x^9 + x^8 - 4x^6 + 8x^5 + 9x^4 - 34x^3 - 13x^2 + 2x - 7	\( 2^{30}\cdot 11^{6} \)	$C_2\times S_5$ (as 12T123)	Trivial
12.0.1902199139467264.5	x^12 - 2x^11 - x^10 + 8x^9 - 22x^8 + 16x^7 + 44x^6 - 72x^5 + 25x^4 + 22x^3 - 33x^2 + 22	\( 2^{30}\cdot 11^{6} \)	$C_2\times S_5$ (as 12T123)	Trivial
12.0.2494869834563584.3	x^12 - 2x^11 + 5x^10 - 6x^9 + 20x^8 - 2x^7 + 29x^6 + 2x^5 + 20x^4 + 6x^3 + 5x^2 + 2x + 1	\( 2^{22}\cdot 29^{6} \)	$C_2\times S_5$ (as 12T123)	Trivial
12.4.2621440000000000.2	x^12 - 4x^11 + 4x^10 + 12x^7 - 18x^6 - 12x^5 + 4x^2 + 4x + 1	\( 2^{28}\cdot 5^{10} \)	$C_2\times S_5$ (as 12T123)	Trivial
12.0.2621440000000000.2	x^12 - 4x^11 + 6x^10 - 20x^8 + 4x^7 + 44x^6 + 4x^5 - 20x^4 + 6x^2 - 4x + 1	\( 2^{28}\cdot 5^{10} \)	$C_2\times S_5$ (as 12T123)	Trivial
12.4.2621440000000000.3	x^12 - 8x^10 + 20x^8 - 60x^6 + 100x^4 - 88x^2 + 4	\( 2^{28}\cdot 5^{10} \)	$C_2\times S_5$ (as 12T123)	Trivial
12.0.2621440000000000.5	x^12 - 8x^10 + 25x^8 - 4x^7 - 20x^6 - 8x^5 + 20x^4 - 4x^2 + 2	\( 2^{28}\cdot 5^{10} \)	$C_2\times S_5$ (as 12T123)	Trivial
12.0.2621440000000000.10	x^12 + 4x^10 - 10x^8 - 20x^6 + 25x^4 + 16x^2 + 4	\( 2^{28}\cdot 5^{10} \)	$C_2\times S_5$ (as 12T123)	Trivial (GRH)
12.0.2621440000000000.13	x^12 + 8x^10 + 20x^8 + 60x^6 + 100x^4 + 88x^2 + 4	\( 2^{28}\cdot 5^{10} \)	$C_2\times S_5$ (as 12T123)	Trivial
12.0.2621440000000000.19	x^12 - 2x^10 + 10x^8 - 8x^7 - 20x^6 + 56x^5 - 15x^4 - 40x^3 + 54x^2 - 40x + 12	\( 2^{28}\cdot 5^{10} \)	$C_2\times S_5$ (as 12T123)	Trivial
12.0.2621440000000000.26	x^12 - 4x^11 + 12x^10 - 20x^9 + 25x^8 + 12x^7 - 28x^6 + 24x^5 + 60x^4 + 4x^2 + 24x + 18	\( 2^{28}\cdot 5^{10} \)	$C_2\times S_5$ (as 12T123)	Trivial
12.0.3722460239233024.1	x^12 - 4x^11 + 4x^10 + 23x^8 + 4x^7 + 36x^6 - 4x^5 + 23x^4 + 4x^2 + 4x + 1	\( 2^{22}\cdot 31^{6} \)	$C_2\times S_5$ (as 12T123)	Trivial
12.0.4096000000000000.1	x^12 - 2x^11 + x^10 + 10x^9 + 10x^8 - 58x^7 + 121x^6 - 58x^5 + 10x^4 + 10x^3 + x^2 - 2x + 1	\( 2^{24}\cdot 5^{12} \)	$C_2\times S_5$ (as 12T123)	Trivial
12.0.4096000000000000.3	x^12 - 4x^11 + 4x^10 + 5x^8 + 30x^6 - 20x^5 - 5x^4 + 50x^2 + 20x + 5	\( 2^{24}\cdot 5^{12} \)	$C_2\times S_5$ (as 12T123)	$[2]$
12.0.4739148267126784.9	x^12 - 2x^11 - x^10 + 8x^9 - 7x^8 - 14x^7 + 35x^6 + 4x^5 - 50x^4 - 4x^3 + 18x^2 + 28	\( 2^{24}\cdot 7^{10} \)	$C_2\times S_5$ (as 12T123)	Trivial
12.0.6189907940737024.1	x^12 + 6x^10 + 25x^8 + 20x^6 + 12x^4 + 4	\( 2^{30}\cdot 7^{8} \)	$C_2\times S_5$ (as 12T123)	$[2]$
12.0.6400000000000000.1	x^12 - 2x^11 + 2x^10 - 10x^9 + 6x^7 + 38x^6 + 2x^5 - 10x^3 + 18x^2 - 6x + 1	\( 2^{20}\cdot 5^{14} \)	$C_2\times S_5$ (as 12T123)	Trivial
12.0.9934520342020096.3	x^12 - 4x^11 + 8x^10 - 4x^9 + x^8 - 32x^7 + 148x^6 - 300x^5 + 388x^4 - 280x^3 + 88x^2 + 24x + 52	\( 2^{26}\cdot 23^{6} \)	$C_2\times S_5$ (as 12T123)	Trivial
12.0.10485760000000000.6	x^12 - 4x^11 + 14x^10 - 20x^9 + 25x^8 + 25x^4 + 20x^3 + 14x^2 + 4x + 1	\( 2^{30}\cdot 5^{10} \)	$C_2\times S_5$ (as 12T123)	$[2]$
12.4.10485760000000000.10	x^12 - 8x^10 + 25x^8 + 40x^6 - 40x^4 - 32x^2 + 16	\( 2^{30}\cdot 5^{10} \)	$C_2\times S_5$ (as 12T123)	Trivial
12.0.10485760000000000.16	x^12 - 4x^11 + 8x^10 + 10x^8 - 16x^7 - 16x^6 - 8x^5 + 25x^4 + 20x^3 + 8x^2 + 8x + 4	\( 2^{30}\cdot 5^{10} \)	$C_2\times S_5$ (as 12T123)	$[2]$
12.0.10485760000000000.17	x^12 - 2x^10 + 10x^8 - 4x^7 - 20x^6 + 28x^5 - 15x^4 - 20x^3 + 42x^2 - 20x + 6	\( 2^{30}\cdot 5^{10} \)	$C_2\times S_5$ (as 12T123)	$[2]$
12.0.16384000000000000.1	x^12 - 6x^10 + 15x^8 + 40x^6 + 35x^4 + 14x^2 + 1	\( 2^{26}\cdot 5^{12} \)	$C_2\times S_5$ (as 12T123)	$[4]$
12.0.16384000000000000.2	x^12 - 6x^11 + 19x^10 - 30x^9 + 20x^8 + 6x^7 + 29x^6 - 6x^5 + 20x^4 + 30x^3 + 19x^2 + 6x + 1	\( 2^{26}\cdot 5^{12} \)	$C_2\times S_5$ (as 12T123)	Trivial
12.4.16384000000000000.2	x^12 - 2x^11 - 4x^10 - 35x^8 + 26x^7 + 48x^6 - 44x^5 + 25x^4 - 30x^3 - 6x^2 + 12x + 4	\( 2^{26}\cdot 5^{12} \)	$C_2\times S_5$ (as 12T123)	Trivial
12.0.16384000000000000.3	x^12 - 4x^11 + 6x^10 - 20x^8 + 24x^7 + 34x^6 - 96x^5 + 90x^4 - 60x^3 + 32x^2 - 8x + 2	\( 2^{26}\cdot 5^{12} \)	$C_2\times S_5$ (as 12T123)	$[4]$
12.4.16384000000000000.4	x^12 + 10x^8 - 100x^6 + 185x^4 - 180x^2 + 100	\( 2^{26}\cdot 5^{12} \)	$C_2\times S_5$ (as 12T123)	Trivial
12.0.18956593068507136.1	x^12 - 4x^11 + 10x^10 - 12x^9 + 18x^8 + 12x^7 + 14x^6 + 52x^5 + 9x^4 + 16x^3 + 20x^2 - 16x + 8	\( 2^{26}\cdot 7^{10} \)	$C_2\times S_5$ (as 12T123)	$[2]$
12.4.25600000000000000.1	x^12 - 2x^11 + 11x^10 - 10x^9 + 30x^8 + 22x^7 - 49x^6 + 162x^5 - 160x^4 - 170x^3 + 121x^2 - 22x + 1	\( 2^{22}\cdot 5^{14} \)	$C_2\times S_5$ (as 12T123)	$[2]$
12.0.25600000000000000.1	x^12 - 2x^11 + 9x^10 + 10x^9 - 10x^8 - 2x^7 + 9x^6 + 2x^5 - 10x^4 - 10x^3 + 9x^2 + 2x + 1	\( 2^{22}\cdot 5^{14} \)	$C_2\times S_5$ (as 12T123)	Trivial
12.4.25600000000000000.4	x^12 - 6x^11 + 9x^10 + 10x^9 - 40x^8 + 34x^7 + x^6 - 14x^5 + 20x^4 - 30x^3 + 69x^2 - 54x + 31	\( 2^{22}\cdot 5^{14} \)	$C_2\times S_5$ (as 12T123)	$[2]$
12.0.25600000000000000.4	x^12 + 5x^10 + 45x^8 + 180x^6 + 200x^4 + 20x^2 + 100	\( 2^{22}\cdot 5^{14} \)	$C_2\times S_5$ (as 12T123)	$[2]$
12.0.25999348907114496.24	x^12 + 15x^10 - 4x^9 + 87x^8 - 24x^7 + 226x^6 - 48x^5 + 267x^4 - 72x^3 + 135x^2 - 108x + 21	\( 2^{26}\cdot 3^{18} \)	$C_2\times S_5$ (as 12T123)	$[3]$
12.0.39738081368080384.1	x^12 - 2x^11 - x^10 + 6x^9 + 3x^8 - 28x^7 + 16x^6 + 60x^5 - 23x^4 - 110x^3 + 23x^2 + 66x + 27	\( 2^{28}\cdot 23^{6} \)	$C_2\times S_5$ (as 12T123)	Trivial (GRH)