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 112)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.567013518009.1	x^12 - 2x^8 - x^7 + 2x^6 + 4x^4 - 2x^3 - x^2 - x + 1	\( 3^{6}\cdot 167^{4} \)	12T183	Trivial
12.0.5006007982921.1	x^12 - x^11 + 2x^10 + x^9 - x^8 + 2x^7 + x^6 + 2x^5 - x^4 + x^3 + 2x^2 - x + 1	\( 11^{6}\cdot 41^{4} \)	12T183	Trivial
12.0.10083952674576.1	x^12 - 3x^11 + 12x^9 - 15x^8 - 9x^7 + 31x^6 - 9x^5 - 15x^4 + 12x^3 - 3x + 1	\( 2^{4}\cdot 3^{16}\cdot 11^{4} \)	12T183	Trivial
12.4.10497600000000.1	x^12 - 4x^11 + 11x^10 - 20x^9 + 33x^8 - 46x^7 + 46x^6 - 34x^5 + 7x^4 + 14x^3 - 10x^2 + 1	\( 2^{12}\cdot 3^{8}\cdot 5^{8} \)	12T183	Trivial
12.4.20794740015625.1	x^12 - 2x^11 + 2x^10 + 2x^9 - 9x^8 + 9x^7 - 5x^6 + x^5 - 8x^4 + 21x^3 - 20x^2 + 10x - 1	\( 5^{6}\cdot 191^{4} \)	12T183	Trivial
12.0.342648531949824.1	x^12 - x^11 + 5x^10 - 10x^9 + 19x^8 - 25x^7 + 62x^6 - 13x^5 + 55x^4 - 34x^3 + 21x^2 - 5x + 1	\( 2^{8}\cdot 3^{14}\cdot 23^{4} \)	12T183	Trivial
12.4.722204136308736.11	x^12 + 6x^10 + 9x^8 - 14x^6 - 18x^4 + 9	\( 2^{24}\cdot 3^{16} \)	12T183	Trivial
12.4.1283918464548864.10	x^12 - 4x^11 + 2x^10 + 12x^9 - 6x^8 - 20x^7 - 32x^6 + 108x^5 + 24x^4 - 48x^3 - 108x^2 - 72x + 90	\( 2^{28}\cdot 3^{14} \)	12T183	Trivial
12.4.2888816545234944.4	x^12 - 6x^10 + 21x^8 - 48x^6 + 48x^4 - 24x^2 + 4	\( 2^{26}\cdot 3^{16} \)	12T183	Trivial
12.4.11555266180939776.6	x^12 - 6x^10 + 3x^8 - 8x^6 - 9x^4 - 18x^2 + 9	\( 2^{28}\cdot 3^{16} \)	12T183	Trivial
12.4.11555266180939776.8	x^12 - 6x^10 + 27x^8 - 80x^6 + 63x^4 + 54x^2 + 9	\( 2^{28}\cdot 3^{16} \)	12T183	Trivial
12.4.14624633760251904.5	x^12 + 3x^8 - 46x^6 - 9x^4 - 6x^2 + 1	\( 2^{22}\cdot 3^{20} \)	12T183	Trivial
12.0.14624633760251904.47	x^12 - 6x^11 + 18x^10 - 28x^9 + 72x^7 - 120x^6 + 216x^4 - 112x^3 - 48x^2 + 288x + 160	\( 2^{22}\cdot 3^{20} \)	12T183	$[2]$
12.4.16384000000000000.3	x^12 - 10x^8 - 60x^6 + 265x^4 - 260x^2 + 100	\( 2^{26}\cdot 5^{12} \)	12T183	$[2]$
12.4.46221064723759104.4	x^12 - 6x^10 - 24x^9 + 48x^7 + 176x^6 + 192x^5 + 153x^4 + 56x^3 - 150x^2 - 144x - 28	\( 2^{30}\cdot 3^{16} \)	12T183	Trivial
12.4.46221064723759104.5	x^12 - 16x^9 - 24x^8 - 48x^7 + 24x^6 + 24x^5 + 207x^4 + 56x^3 + 156x^2 - 48x - 4	\( 2^{30}\cdot 3^{16} \)	12T183	Trivial
12.0.46221064723759104.33	x^12 + 9x^8 - 24x^7 + 28x^6 - 24x^5 + 15x^4 - 24x^3 + 60x^2 + 72x + 55	\( 2^{30}\cdot 3^{16} \)	12T183	$[2]$
12.0.58498535041007616.1	x^12 - 4x^9 + 27x^8 - 24x^7 + 8x^6 + 75x^4 - 104x^3 + 72x^2 - 12x + 1	\( 2^{24}\cdot 3^{20} \)	12T183	$[2]$
12.4.58498535041007616.1	x^12 - 6x^11 + 21x^10 - 44x^9 + 48x^8 - 12x^7 - 24x^6 - 48x^5 + 105x^4 + 22x^3 - 219x^2 + 156x - 28	\( 2^{24}\cdot 3^{20} \)	12T183	Trivial
12.4.58498535041007616.9	x^12 - 6x^10 - 4x^9 + 6x^8 - 10x^6 - 12x^5 + 3x^4 + 28x^3 + 12x^2 + 12x + 1	\( 2^{24}\cdot 3^{20} \)	12T183	Trivial
12.0.58498535041007616.21	x^12 + 12x^10 - 4x^9 + 63x^8 - 60x^7 + 172x^6 - 252x^5 + 297x^4 - 432x^3 + 342x^2 + 72x + 12	\( 2^{24}\cdot 3^{20} \)	12T183	Trivial
12.4.58498535041007616.23	x^12 - 6x^10 - 16x^9 - 12x^8 + 32x^6 + 96x^5 + 192x^4 + 256x^3 + 192x^2 + 192x + 16	\( 2^{24}\cdot 3^{20} \)	12T183	Trivial
12.4.58498535041007616.24	x^12 - 6x^10 - 20x^9 - 42x^8 - 72x^7 - 56x^6 + 96x^5 + 348x^4 + 480x^3 + 360x^2 + 144x + 24	\( 2^{24}\cdot 3^{20} \)	12T183	Trivial
12.4.58498535041007616.26	x^12 - 6x^10 + 27x^8 - 52x^6 + 3x^4 + 18x^2 + 25	\( 2^{24}\cdot 3^{20} \)	12T183	Trivial
12.4.65536000000000000.2	x^12 - 4x^11 - 6x^10 + 20x^9 + 15x^8 + 24x^7 - 116x^6 - 24x^5 + 15x^4 - 20x^3 - 6x^2 + 4x + 1	\( 2^{28}\cdot 5^{12} \)	12T183	$[2]$
12.4.117033789351264256.1	x^12 - 6x^11 + 6x^10 + 16x^9 - 14x^8 - 12x^7 - 8x^6 - 80x^5 + 41x^4 + 106x^3 + 10x^2 - 8	\( 2^{24}\cdot 17^{8} \)	12T183	Trivial
12.4.131621703842267136.28	x^12 - 6x^10 + 51x^8 - 164x^6 + 123x^4 - 222x^2 + 25	\( 2^{22}\cdot 3^{22} \)	12T183	Trivial
12.4.160000000000000000.6	x^12 + 8x^10 + 25x^8 - 100x^4 - 50x^2 + 100	\( 2^{20}\cdot 5^{16} \)	12T183	Trivial
12.4.184884258895036416.7	x^12 - 6x^10 - 8x^9 - 15x^8 - 24x^7 - 40x^6 - 24x^5 - 15x^4 - 8x^3 - 6x^2 + 1	\( 2^{32}\cdot 3^{16} \)	12T183	Trivial
12.4.184884258895036416.8	x^12 - 6x^10 - 16x^9 - 3x^8 + 48x^7 + 8x^6 - 48x^5 - 3x^4 + 16x^3 - 6x^2 + 1	\( 2^{32}\cdot 3^{16} \)	12T183	Trivial
12.4.218971048064843776.7	x^12 - 4x^11 - 4x^10 + 40x^9 - 48x^8 - 36x^7 + 106x^6 - 36x^5 - 48x^4 + 40x^3 - 4x^2 - 4x + 1	\( 2^{28}\cdot 13^{8} \)	12T183	Trivial
12.4.218971048064843776.16	x^12 + 6x^10 - 22x^8 - 136x^6 + 153x^4 - 38x^2 + 4	\( 2^{28}\cdot 13^{8} \)	12T183	Trivial
12.12.226890864312890625.1	x^12 - 2x^11 - 14x^10 + 31x^9 + 58x^8 - 153x^7 - 56x^6 + 266x^5 - 63x^4 - 105x^3 + 26x^2 + 13x - 1	\( 3^{8}\cdot 5^{8}\cdot 97^{4} \)	12T183	Trivial (GRH)
12.4.233994140164030464.1	x^12 - 6x^10 - 16x^9 + 27x^8 + 48x^7 + 10x^6 - 72x^5 - 90x^4 - 48x^3 + 180x^2 - 12	\( 2^{26}\cdot 3^{20} \)	12T183	Trivial
12.4.233994140164030464.15	x^12 - 6x^10 - 3x^8 - 32x^6 + 24x^4 - 24x^2 + 4	\( 2^{26}\cdot 3^{20} \)	12T183	Trivial
12.4.233994140164030464.35	x^12 + 6x^10 + 27x^8 - 60x^6 + 27x^4 - 162x^2 + 81	\( 2^{26}\cdot 3^{20} \)	12T183	Trivial
12.4.262144000000000000.2	x^12 - 4x^11 + 4x^10 - 20x^9 + 75x^8 - 48x^7 - 48x^6 + 8x^5 - 10x^4 + 16x^2 + 16x + 4	\( 2^{30}\cdot 5^{12} \)	12T183	$[2]$
12.4.262144000000000000.5	x^12 - 10x^10 - 30x^8 - 80x^6 - 15x^4 - 110x^2 + 100	\( 2^{30}\cdot 5^{12} \)	12T183	$[2]$
12.12.390577501444000000.1	x^12 - 3x^11 - 21x^10 + 82x^9 + 43x^8 - 499x^7 + 609x^6 + 50x^5 - 521x^4 + 295x^3 - 15x^2 - 24x + 4	\( 2^{8}\cdot 5^{6}\cdot 13^{4}\cdot 43^{4} \)	12T183	Trivial (GRH)
12.0.415989582513831936.68	x^12 + 6x^10 - 8x^9 + 33x^8 - 48x^7 + 124x^6 - 168x^5 + 276x^4 - 240x^3 + 288x^2 - 144x + 132	\( 2^{30}\cdot 3^{18} \)	12T183	$[2]$
12.0.526486815369068544.59	x^12 - 6x^10 + 51x^8 - 108x^7 + 154x^6 - 180x^5 + 321x^4 - 540x^3 + 552x^2 - 288x + 64	\( 2^{24}\cdot 3^{22} \)	12T183	Trivial (GRH)
12.4.640000000000000000.1	x^12 - 6x^11 + 11x^10 - 35x^8 + 74x^7 - 59x^6 - 16x^5 + 190x^4 - 300x^3 - 124x^2 + 264x - 4	\( 2^{22}\cdot 5^{16} \)	12T183	Trivial
12.4.935976560656121856.2	x^12 - 18x^10 - 12x^9 + 87x^8 + 156x^7 + 52x^6 - 360x^5 - 738x^4 - 816x^3 - 528x^2 - 192x - 32	\( 2^{28}\cdot 3^{20} \)	12T183	Trivial
12.4.935976560656121856.44	x^12 + 12x^10 - 16x^9 + 69x^8 - 144x^7 + 260x^6 - 336x^5 + 300x^4 - 416x^3 + 48x^2 + 192x + 16	\( 2^{28}\cdot 3^{20} \)	12T183	Trivial
12.4.935976560656121856.67	x^12 - 6x^11 + 3x^10 + 38x^9 - 63x^8 - 48x^7 + 248x^6 + 48x^5 - 612x^4 + 592x^3 - 24x^2 - 912x + 712	\( 2^{28}\cdot 3^{20} \)	12T183	Trivial
12.4.2105947261476274176.19	x^12 - 6x^10 - 3x^8 - 8x^6 + 24x^4 - 24x^2 + 4	\( 2^{26}\cdot 3^{22} \)	12T183	Trivial
12.4.2105947261476274176.26	x^12 - 6x^11 + 3x^10 + 10x^9 + 45x^8 - 72x^6 - 36x^5 - 18x^4 - 44x^3 - 6x^2 + 12x + 10	\( 2^{26}\cdot 3^{22} \)	12T183	Trivial (GRH)
12.0.2560000000000000000.4	x^12 - 4x^11 + 4x^10 + 20x^9 + 35x^8 - 24x^7 - 64x^6 + 24x^5 + 35x^4 - 20x^3 + 4x^2 + 4x + 1	\( 2^{24}\cdot 5^{16} \)	12T183	$[6]$
12.0.2560000000000000000.16	x^12 - 2x^11 + 11x^10 + 10x^9 + 45x^8 + 104x^7 + 222x^6 + 324x^5 + 570x^4 + 640x^3 + 394x^2 + 172x + 94	\( 2^{24}\cdot 5^{16} \)	12T183	$[6]$
12.4.3743906242624487424.2	x^12 + 6x^10 - 16x^9 + 72x^8 + 240x^6 - 864x^5 - 279x^4 - 40x^3 + 3006x^2 - 1752x - 392	\( 2^{30}\cdot 3^{20} \)	12T183	Trivial