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 1434)

Label	Polynomial	Discriminant	Galois group	Class group
12.2.1676496367616.1	x^12 - 2x^11 + x^10 + 2x^9 - 8x^8 + 20x^7 - 30x^6 + 32x^5 - 22x^4 + 12x^3 - 10x^2 + 6x - 1	\( -\,2^{12}\cdot 7^{8}\cdot 71 \)	12T188	Trivial
12.2.2998803361792.1	x^12 + 2x^10 - 2x^9 - 4x^8 - 12x^7 - 20x^6 - 14x^5 - 6x^4 + 6x^3 + 3x^2 - 2x - 1	\( -\,2^{12}\cdot 7^{8}\cdot 127 \)	12T188	Trivial
12.0.8901959585792.1	x^12 - 2x^11 + 5x^10 - 4x^9 + 6x^8 - 4x^7 + 3x^6 - 18x^5 + 27x^4 - 34x^3 + 42x^2 - 28x + 7	\( 2^{12}\cdot 7^{8}\cdot 13\cdot 29 \)	12T188	Trivial
12.0.8901959585792.2	x^12 + 3x^10 - 2x^9 + 9x^8 - 4x^7 + 5x^6 - 10x^5 + 10x^4 - 4x^2 - 8x + 8	\( 2^{12}\cdot 7^{8}\cdot 13\cdot 29 \)	12T188	Trivial
12.4.20802722533376.1	x^12 - 2x^11 - x^10 + 7x^8 - 8x^7 - 14x^6 + 10x^5 + 28x^4 + 14x^3 - 3x^2 - 4x - 1	\( 2^{12}\cdot 7^{8}\cdot 881 \)	12T188	Trivial
12.4.22125029527552.1	x^12 - 6x^11 + 13x^10 - 10x^9 - 11x^8 + 38x^7 - 49x^6 + 38x^5 - 15x^4 - 2x^3 - x^2 + 4x - 1	\( 2^{12}\cdot 7^{8}\cdot 937 \)	12T188	Trivial
12.4.18596122216516017.1	x^12 - 6x^11 + 15x^10 - 6x^9 - 78x^8 + 276x^7 - 550x^6 + 795x^5 - 936x^4 + 969x^3 - 729x^2 + 243x + 9	\( 3^{16}\cdot 17\cdot 71^{4} \)	12T188	Trivial
12.8.18596122216516017.1	x^12 - 30x^8 + 54x^6 + 21x^4 - 54x^2 + 17	\( 3^{16}\cdot 17\cdot 71^{4} \)	12T188	Trivial
12.8.19902528501900005.1	x^12 - 7x^10 + x^8 + 81x^6 - 151x^4 - 19x^2 + 125	\( 5\cdot 13^{8}\cdot 47^{4} \)	12T188	Trivial
12.4.19902528501900005.1	x^12 - 6x^11 + 16x^10 - 25x^9 + 6x^8 + 60x^7 - 143x^6 + 180x^5 - 81x^4 - 51x^3 + 146x^2 - 103x + 31	\( 5\cdot 13^{8}\cdot 47^{4} \)	12T188	Trivial
12.6.20783901300812019.1	x^12 - 3x^11 - 9x^10 + 10x^9 + 12x^8 - 13x^6 + 12x^4 + 10x^3 - 9x^2 - 3x + 1	\( -\,3^{16}\cdot 19\cdot 71^{4} \)	12T188	Trivial
12.6.20783901300812019.2	x^12 - 6x^10 - 14x^9 - 33x^8 - 9x^7 + 38x^6 + 69x^5 + 42x^4 - 85x^3 + 12x^2 - 36x + 24	\( -\,3^{16}\cdot 19\cdot 71^{4} \)	12T188	Trivial
12.2.55895067029733376.1	x^12 + x^10 - 9x^8 + 3x^6 + 28x^4 - 24x^2 - 256	\( -\,2^{16}\cdot 31^{8} \)	12T188	$[2]$
12.2.55895067029733376.7	x^12 + 6x^10 + 19x^8 + 36x^6 + 34x^4 + 12x^2 - 16	\( -\,2^{16}\cdot 31^{8} \)	12T188	$[2]$
12.2.55895067029733376.8	x^12 + 7x^10 + 10x^8 - 18x^6 - 28x^4 + 40x^2 - 16	\( -\,2^{16}\cdot 31^{8} \)	12T188	$[2]$
12.2.55895067029733376.17	x^12 + 9x^10 + 5x^8 + 81x^6 - 78x^4 + 50x^2 - 4	\( -\,2^{16}\cdot 31^{8} \)	12T188	$[2]$
12.2.55895067029733376.19	x^12 - 5x^11 + 11x^10 - 6x^9 - 9x^8 + 29x^7 - 55x^6 + 64x^5 - 66x^4 + 30x^3 + 66x^2 + 28x + 4	\( -\,2^{16}\cdot 31^{8} \)	12T188	$[2]$
12.2.55895067029733376.20	x^12 - 2x^10 - 16x^9 + 18x^8 - 20x^7 + 72x^6 - 116x^5 + 205x^4 - 396x^3 + 234x^2 + 68x + 16	\( -\,2^{16}\cdot 31^{8} \)	12T188	$[2]$
12.2.55895067029733376.21	x^12 - 5x^11 + 12x^10 - 28x^9 + 60x^8 - 84x^7 + 96x^6 - 168x^5 + 240x^4 - 224x^3 + 192x^2 - 160x + 64	\( -\,2^{16}\cdot 31^{8} \)	12T188	$[2]$
12.2.55895067029733376.22	x^12 + 2x^10 - 2x^9 + 9x^8 + 18x^7 - 18x^6 + 44x^5 - 138x^4 + 172x^3 - 168x^2 - 72x + 216	\( -\,2^{16}\cdot 31^{8} \)	12T188	$[2]$
12.6.98148720350720000.1	x^12 - 2x^11 - 5x^10 + 24x^9 + 24x^8 - 98x^7 - 110x^6 + 124x^5 + 143x^4 - 92x^3 - 57x^2 + 40x - 5	\( -\,2^{12}\cdot 5^{4}\cdot 13^{8}\cdot 47 \)	12T188	Trivial
12.6.98148720350720000.2	x^12 - 6x^11 + 9x^10 - 2x^9 + 5x^8 - 4x^7 - 7x^6 - 4x^5 + 5x^4 - 2x^3 + 9x^2 - 6x + 1	\( -\,2^{12}\cdot 5^{4}\cdot 13^{8}\cdot 47 \)	12T188	Trivial
12.8.111790134059466752.1	x^12 - 12x^10 - 3x^9 + 46x^8 + 24x^7 - 76x^6 - 75x^5 + 71x^4 + 76x^3 - 28x^2 - 22x + 2	\( 2^{17}\cdot 31^{8} \)	12T188	Trivial
12.4.111790134059466752.2	x^12 - x^11 - 11x^10 + 9x^9 + 56x^8 - 25x^7 - 178x^6 - 39x^5 + 259x^4 + 212x^3 - 19x^2 - 40x - 8	\( 2^{17}\cdot 31^{8} \)	12T188	Trivial
12.10.117046181009836107.1	x^12 - 6x^11 + 54x^9 - 66x^8 - 138x^7 + 298x^6 + 69x^5 - 459x^4 + 129x^3 + 225x^2 - 108x + 9	\( -\,3^{16}\cdot 71^{4}\cdot 107 \)	12T188	Trivial
12.2.117046181009836107.1	x^12 - 10x^9 + 3x^8 - 3x^7 - 4x^6 + 48x^5 + 120x^4 + 287x^3 + 135x^2 + 285x + 361	\( -\,3^{16}\cdot 71^{4}\cdot 107 \)	12T188	Trivial
12.10.192805163391176203.1	x^12 - 2x^11 - 11x^10 + 17x^9 + 14x^8 + 80x^7 - 56x^6 - 524x^5 + 459x^4 + 433x^3 - 458x^2 + 80x + 8	\( -\,7^{8}\cdot 43\cdot 167^{4} \)	12T188	Trivial
12.2.192805163391176203.1	x^12 - x^11 - 4x^10 + x^9 + 33x^8 + x^7 - 54x^6 - 36x^5 + 138x^4 + 538x^3 - 690x^2 - 41x + 1681	\( -\,7^{8}\cdot 43\cdot 167^{4} \)	12T188	Trivial
12.2.216593384740216832.4	x^12 + 9x^10 - 4x^8 + 58x^6 - 31x^4 + 93x^2 - 62	\( -\,2^{13}\cdot 31^{9} \)	12T188	$[2]$
12.2.216593384740216832.6	x^12 - 5x^11 + x^10 + 4x^9 + 19x^8 + 21x^7 + 23x^6 - 92x^5 - 156x^4 - 284x^3 - 276x^2 - 112x - 16	\( -\,2^{13}\cdot 31^{9} \)	12T188	$[2]$
12.2.216593384740216832.7	x^12 - 3x^11 + 2x^10 + 18x^9 - 80x^8 + 282x^7 - 671x^6 + 729x^5 - 130x^4 - 496x^3 + 538x^2 - 142x + 16	\( -\,2^{13}\cdot 31^{9} \)	12T188	$[2]$
12.2.216593384740216832.8	x^12 - 3x^11 + 3x^10 + 27x^9 - 35x^8 + 17x^7 + 179x^6 + 79x^5 + 34x^4 + 286x^3 + 734x^2 + 442x + 188	\( -\,2^{13}\cdot 31^{9} \)	12T188	$[2]$
12.0.216593384740216832.1	x^12 - 5x^11 + 13x^10 - 16x^9 + 33x^8 - 37x^7 + 38x^6 - 37x^5 + 33x^4 - 16x^3 + 13x^2 - 5x + 1	\( 2^{13}\cdot 31^{9} \)	12T188	$[2]$
12.4.216593384740216832.2	x^12 - 6x^11 + 14x^10 - 14x^9 - 54x^8 + 188x^7 - 215x^6 - 114x^5 + 490x^4 - 152x^3 - 66x^2 + 16x + 4	\( 2^{13}\cdot 31^{9} \)	12T188	$[2]$
12.4.216593384740216832.3	x^12 - 5x^11 + 6x^10 + 4x^9 - 21x^8 + 37x^7 + 24x^6 - 78x^5 - 78x^4 + 118x^3 - 108x^2 + 20x + 16	\( 2^{13}\cdot 31^{9} \)	12T188	$[2]$
12.0.216593384740216832.3	x^12 - 3x^11 - x^10 - 7x^9 + 15x^8 + 57x^7 + 92x^6 + 88x^5 + 170x^4 + 190x^3 + 16x^2 - 80x + 16	\( 2^{13}\cdot 31^{9} \)	12T188	$[2]$
12.0.216593384740216832.4	x^12 + 5x^10 - 7x^9 + 9x^8 - 13x^7 + 45x^6 + 5x^5 - 50x^4 - 11x^3 + 134x^2 - 70x + 16	\( 2^{13}\cdot 31^{9} \)	12T188	$[2]$
12.4.216593384740216832.4	x^12 + 3x^10 + 3x^8 - 61x^6 - 124x^4 - 62x^2 + 992	\( 2^{13}\cdot 31^{9} \)	12T188	$[2]$
12.4.216593384740216832.5	x^12 + x^10 - 21x^9 + 14x^8 + 17x^7 + 93x^6 - 142x^5 - 273x^4 + 537x^3 - 445x + 202	\( 2^{13}\cdot 31^{9} \)	12T188	$[2]$
12.0.216593384740216832.6	x^12 + 7x^10 + 37x^8 + 77x^6 + 186x^4 + 372x^2 + 248	\( 2^{13}\cdot 31^{9} \)	12T188	$[2]$ (GRH)
12.2.223580268118933504.1	x^12 - x^10 - 9x^8 - 3x^6 + 28x^4 + 24x^2 - 256	\( -\,2^{18}\cdot 31^{8} \)	12T188	$[4]$
12.2.223580268118933504.2	x^12 + 16x^10 + 94x^8 + 212x^6 + 120x^4 - 240x^2 - 64	\( -\,2^{18}\cdot 31^{8} \)	12T188	$[2]$
12.2.223580268118933504.4	x^12 - 7x^10 + 25x^8 - 21x^6 - 38x^4 - 112x^2 - 64	\( -\,2^{18}\cdot 31^{8} \)	12T188	$[2]$ (GRH)
12.2.223580268118933504.12	x^12 - 7x^10 + 10x^8 + 18x^6 - 28x^4 - 40x^2 - 16	\( -\,2^{18}\cdot 31^{8} \)	12T188	$[4]$
12.2.223580268118933504.14	x^12 - 6x^10 + 19x^8 - 36x^6 + 34x^4 - 12x^2 - 16	\( -\,2^{18}\cdot 31^{8} \)	12T188	$[4]$
12.2.223580268118933504.18	x^12 + 5x^10 + 33x^8 - 5x^6 - 18x^4 + 64x^2 - 16	\( -\,2^{18}\cdot 31^{8} \)	12T188	$[4]$
12.2.223580268118933504.19	x^12 - 9x^10 + 5x^8 - 81x^6 - 78x^4 - 50x^2 - 4	\( -\,2^{18}\cdot 31^{8} \)	12T188	$[2]$ (GRH)
12.2.223580268118933504.29	x^12 - 2x^11 - 8x^10 + 28x^9 + 2x^8 - 66x^7 + 79x^6 + 78x^5 - 160x^4 + 128x^3 - 42x^2 + 12x + 4	\( -\,2^{18}\cdot 31^{8} \)	12T188	$[2]$
12.8.447160536237867008.1	x^12 - 2x^10 - 45x^8 + 112x^6 - 18x^4 - 40x^2 + 8	\( 2^{19}\cdot 31^{8} \)	12T188	Trivial
12.4.447160536237867008.16	x^12 - 3x^10 - 33x^8 - 22x^6 + 86x^4 + 64x^2 + 8	\( 2^{19}\cdot 31^{8} \)	12T188	Trivial