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 60)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.6788091008176384.1	x^16 - 2x^14 - 4x^12 + 10x^10 + 3x^8 - 12x^6 - x^4 + 5x^2 + 1	\( 2^{8}\cdot 47^{2}\cdot 331^{4} \)	16T1852	Trivial
16.0.30037248999755776.2	x^16 + x^12 + 4x^10 + 6x^8 + 9x^6 + 6x^4 + x^2 + 1	\( 2^{12}\cdot 41^{2}\cdot 257^{4} \)	16T1852	Trivial
16.0.33765262030653696.1	x^16 - 5x^15 + 16x^14 - 36x^13 + 67x^12 - 106x^11 + 150x^10 - 196x^9 + 235x^8 - 246x^7 + 220x^6 - 167x^5 + 107x^4 - 56x^3 + 22x^2 - 6x + 1	\( 2^{8}\cdot 3^{2}\cdot 73^{2}\cdot 229^{4} \)	16T1852	Trivial
16.0.37440324312760576.1	x^16 + 5x^14 + 10x^12 + 14x^10 + 19x^8 + 18x^6 + 10x^4 + 5x^2 + 1	\( 2^{8}\cdot 151^{2}\cdot 283^{4} \)	16T1852	Trivial
16.0.121485239855939584.5	x^16 + 4x^14 + 8x^12 + 12x^10 + 13x^8 + 10x^6 + 7x^4 + 3x^2 + 1	\( 2^{16}\cdot 17^{2}\cdot 283^{4} \)	16T1852	Trivial
16.0.121485239855939584.6	x^16 - 4x^14 + 8x^12 - 12x^10 + 13x^8 - 10x^6 + 7x^4 - 3x^2 + 1	\( 2^{16}\cdot 17^{2}\cdot 283^{4} \)	16T1852	Trivial
16.4.202963613851988224.1	x^16 - 5x^14 + 7x^12 + 2x^10 - 11x^8 + 8x^6 - 6x^4 + 4x^2 + 1	\( 2^{8}\cdot 257^{2}\cdot 331^{4} \)	16T1852	Trivial
16.4.1454550543311110144.3	x^16 - 4x^14 + 11x^12 - 17x^10 + 18x^8 - 10x^6 - 2x^4 + x^2 + 1	\( 2^{16}\cdot 43^{2}\cdot 331^{4} \)	16T1852	Trivial
16.4.1454550543311110144.4	x^16 - 7x^14 + 21x^12 - 34x^10 + 30x^8 - 13x^6 + 3x^4 - 3x^2 + 1	\( 2^{16}\cdot 43^{2}\cdot 331^{4} \)	16T1852	Trivial
16.4.8294667542637416704.1	x^16 + 4x^14 + 3x^12 - 3x^10 - 4x^8 - 13x^6 - 23x^4 - 9x^2 + 1	\( 2^{8}\cdot 19^{4}\cdot 47^{2}\cdot 103^{4} \)	16T1852	Trivial
16.8.8294667542637416704.1	x^16 - x^14 - 11x^12 + 12x^10 + 25x^8 - 40x^6 + 18x^4 - 4x^2 + 1	\( 2^{8}\cdot 19^{4}\cdot 47^{2}\cdot 103^{4} \)	16T1852	Trivial
16.4.8294667542637416704.2	x^16 - 13x^12 - 13x^10 + 36x^8 + 71x^6 + 43x^4 + 11x^2 + 1	\( 2^{8}\cdot 19^{4}\cdot 47^{2}\cdot 103^{4} \)	16T1852	Trivial
16.0.15336535719789789184.1	x^16 + 2x^14 + 2x^12 + 9x^10 + 26x^8 + 41x^6 + 34x^4 + 11x^2 + 1	\( 2^{16}\cdot 37^{2}\cdot 643^{4} \)	16T1852	Trivial
16.4.15336535719789789184.2	x^16 + 2x^14 - 4x^12 - 8x^10 - 13x^8 - 17x^6 - 9x^4 + 1	\( 2^{16}\cdot 37^{2}\cdot 643^{4} \)	16T1852	Trivial
16.8.15336535719789789184.2	x^16 - 2x^14 + 2x^12 - 9x^10 + 26x^8 - 41x^6 + 34x^4 - 11x^2 + 1	\( 2^{16}\cdot 37^{2}\cdot 643^{4} \)	16T1852	Trivial (GRH)
16.4.15336535719789789184.3	x^16 - 2x^14 - 4x^12 + 8x^10 - 13x^8 + 17x^6 - 9x^4 + 1	\( 2^{16}\cdot 37^{2}\cdot 643^{4} \)	16T1852	Trivial
16.4.15336535719789789184.4	x^16 - x^14 - 7x^12 + 11x^10 + 9x^8 - 18x^6 + 9x^4 - 4x^2 + 1	\( 2^{16}\cdot 37^{2}\cdot 643^{4} \)	16T1852	Trivial
16.4.15589904002433941504.3	x^16 + 2x^14 - 2x^12 - 19x^10 - 31x^8 - 8x^6 + x^4 - 9x^2 + 1	\( 2^{18}\cdot 2777^{4} \)	16T1852	Trivial
16.4.15589904002433941504.4	x^16 + 3x^14 - 2x^12 - 21x^10 - 34x^8 - 17x^6 + 13x^4 + 16x^2 + 4	\( 2^{18}\cdot 2777^{4} \)	16T1852	Trivial
16.0.17464833213656006656.1	x^16 + x^14 - 7x^12 - 5x^10 + 18x^8 + 20x^6 + 11x^4 + 7x^2 + 1	\( 2^{16}\cdot 149^{2}\cdot 331^{4} \)	16T1852	Trivial
16.8.17464833213656006656.2	x^16 - x^14 - 7x^12 + 5x^10 + 18x^8 - 20x^6 + 11x^4 - 7x^2 + 1	\( 2^{16}\cdot 149^{2}\cdot 331^{4} \)	16T1852	Trivial (GRH)
16.0.57585340506288295936.2	x^16 - 3x^15 + 14x^14 - 32x^13 + 78x^12 - 140x^11 + 226x^10 - 305x^9 + 338x^8 - 305x^7 + 226x^6 - 140x^5 + 78x^4 - 32x^3 + 14x^2 - 3x + 1	\( 2^{12}\cdot 10889^{4} \)	16T1852	$[2]$
16.0.57585340506288295936.3	x^16 - 3x^15 + 9x^14 - 12x^13 + 18x^12 - 9x^11 + 21x^9 - 2x^8 - 51x^7 + 92x^6 - 86x^5 + 54x^4 - 27x^3 + 13x^2 - 5x + 1	\( 2^{12}\cdot 10889^{4} \)	16T1852	$[2]$
16.8.128860300270118047744.2	x^16 - 2x^14 - 8x^12 + 14x^10 + 16x^8 - 13x^6 - 20x^4 - 5x^2 + 1	\( 2^{12}\cdot 23^{2}\cdot 2777^{4} \)	16T1852	Trivial (GRH)
16.0.495957167475659939344.1	x^16 - 5x^15 + 11x^14 - 11x^13 - x^12 + 8x^11 - 8x^10 + 8x^9 + 10x^8 + 8x^7 - 8x^6 + 8x^5 - x^4 - 11x^3 + 11x^2 - 5x + 1	\( 2^{4}\cdot 17^{2}\cdot 18097^{4} \)	16T1852	$[2]$
16.4.495957167475659939344.1	x^16 - 6x^15 + 12x^14 - 6x^13 - 18x^12 + 46x^11 - 29x^10 - 34x^9 + 64x^8 - 34x^7 - 29x^6 + 46x^5 - 18x^4 - 6x^3 + 12x^2 - 6x + 1	\( 2^{4}\cdot 17^{2}\cdot 18097^{4} \)	16T1852	Trivial
16.0.2349361115135565595024.1	x^16 + 10x^14 + 43x^12 + 127x^10 + 287x^8 + 466x^6 + 541x^4 + 412x^2 + 144	\( 2^{4}\cdot 37^{2}\cdot 18097^{4} \)	16T1852	$[2]$
16.4.2349361115135565595024.1	x^16 + x^14 + 2x^12 - 18x^10 - 51x^8 - 5x^6 + 17x^4 + 4x^2 + 1	\( 2^{4}\cdot 37^{2}\cdot 18097^{4} \)	16T1852	Trivial (GRH)
16.8.3685461792402450939904.1	x^16 + 2x^14 - 12x^12 + 9x^10 - 11x^8 + 8x^6 + 19x^4 - 13x^2 + 1	\( 2^{18}\cdot 10889^{4} \)	16T1852	Trivial (GRH)
16.4.3685461792402450939904.2	x^16 - 2x^14 - 12x^12 - 9x^10 - 11x^8 - 8x^6 + 19x^4 + 13x^2 + 1	\( 2^{18}\cdot 10889^{4} \)	16T1852	Trivial (GRH)
16.8.3685461792402450939904.2	x^16 - 10x^14 + 30x^12 - 35x^10 - 6x^8 + 60x^6 - 43x^4 + 4	\( 2^{18}\cdot 10889^{4} \)	16T1852	Trivial (GRH)
16.4.3685461792402450939904.3	x^16 - 5x^14 + 18x^12 - 56x^10 + 90x^8 - 52x^6 + 16x^4 - 57x^2 + 49	\( 2^{18}\cdot 10889^{4} \)	16T1852	$[2]$ (GRH)
16.4.3685461792402450939904.4	x^16 + 10x^14 + 30x^12 + 35x^10 - 6x^8 - 60x^6 - 43x^4 + 4	\( 2^{18}\cdot 10889^{4} \)	16T1852	Trivial
16.4.3685461792402450939904.5	x^16 - 4x^12 - 14x^10 + 43x^8 - 64x^6 + 57x^4 - 24x^2 + 4	\( 2^{18}\cdot 10889^{4} \)	16T1852	$[2]$
16.12.7206433125125089460224.1	x^16 - 7x^14 + 2x^12 + 99x^10 - 319x^8 + 393x^6 - 175x^4 + x^2 + 1	\( 2^{16}\cdot 43^{2}\cdot 2777^{4} \)	16T1852	Trivial (GRH)
16.4.7206433125125089460224.1	x^16 + 2x^14 - 20x^12 - 69x^10 - 22x^8 + 150x^6 + 193x^4 + 72x^2 + 4	\( 2^{16}\cdot 43^{2}\cdot 2777^{4} \)	16T1852	Trivial
16.8.7206433125125089460224.1	x^16 + 5x^14 - 11x^12 - 51x^10 + 35x^8 + 57x^6 - 44x^4 + 3x^2 + 1	\( 2^{16}\cdot 43^{2}\cdot 2777^{4} \)	16T1852	Trivial (GRH)
16.12.7206433125125089460224.2	x^16 - 2x^14 - 20x^12 + 69x^10 - 22x^8 - 150x^6 + 193x^4 - 72x^2 + 4	\( 2^{16}\cdot 43^{2}\cdot 2777^{4} \)	16T1852	Trivial (GRH)
16.4.7206433125125089460224.2	x^16 + 7x^14 + 2x^12 - 99x^10 - 319x^8 - 393x^6 - 175x^4 - x^2 + 1	\( 2^{16}\cdot 43^{2}\cdot 2777^{4} \)	16T1852	Trivial
16.8.7206433125125089460224.2	x^16 + 3x^14 - 23x^12 - 49x^10 + 62x^8 + 56x^6 - 55x^4 + 8x^2 + 1	\( 2^{16}\cdot 43^{2}\cdot 2777^{4} \)	16T1852	Trivial (GRH)
16.12.18322920601686053499136.1	x^16 - 4x^15 - 11x^14 + 57x^13 + 2x^12 - 200x^11 + 158x^10 + 177x^9 - 514x^8 + 210x^7 + 825x^6 - 263x^5 - 674x^4 - 126x^3 + 140x^2 + 69x + 9	\( 2^{8}\cdot 19^{4}\cdot 47^{4}\cdot 103^{4} \)	16T1852	Trivial (GRH)
16.8.42300512875804643061904.1	x^16 - 2x^15 - 13x^14 + 32x^13 + 43x^12 - 151x^11 - 65x^10 + 291x^9 + 45x^8 - 206x^7 + 48x^6 + 69x^5 - 19x^4 - 21x^3 - 59x^2 - 36x - 4	\( 2^{4}\cdot 157^{2}\cdot 18097^{4} \)	16T1852	Trivial (GRH)
16.12.48364778475442110726144.1	x^16 - 4x^15 - 4x^14 + 34x^13 - 32x^12 - 58x^11 + 222x^10 - 274x^9 - 406x^8 + 1314x^7 - 26x^6 - 2180x^5 + 792x^4 + 1620x^3 - 724x^2 - 452x + 173	\( 2^{20}\cdot 3^{2}\cdot 8461^{4} \)	16T1852	Trivial (GRH)
16.0.66600697967345628325264.1	x^16 - 6x^14 + 19x^12 - 65x^10 + 215x^8 - 466x^6 + 601x^4 - 436x^2 + 144	\( 2^{4}\cdot 197^{2}\cdot 18097^{4} \)	16T1852	$[4]$ (GRH)
16.8.66600697967345628325264.1	x^16 - 4x^15 - 6x^14 + 49x^13 - 65x^12 - 61x^11 + 281x^10 - 310x^9 - 36x^8 + 407x^7 - 447x^6 + 151x^5 + 141x^4 - 152x^3 + 47x^2 - 2x - 1	\( 2^{4}\cdot 197^{2}\cdot 18097^{4} \)	16T1852	Trivial (GRH)
16.0.66600697967345628325264.2	x^16 - x^15 + 7x^14 - 2x^13 + 7x^12 + 6x^11 + 12x^10 - 27x^9 + 132x^8 - 32x^7 - 143x^6 - 115x^5 + 69x^4 + 135x^3 + 100x^2 + 36x + 7	\( 2^{4}\cdot 197^{2}\cdot 18097^{4} \)	16T1852	$[4]$ (GRH)
16.0.68167098842892447256576.1	x^16 + 19x^14 + 167x^12 + 890x^10 + 2773x^8 + 4949x^6 + 4942x^4 + 2553x^2 + 529	\( 2^{12}\cdot 23^{4}\cdot 2777^{4} \)	16T1852	$[3]$ (GRH)
16.0.112467297327629238009856.1	x^16 + 16x^14 + 110x^12 + 424x^10 + 981x^8 + 1320x^6 + 908x^4 + 240x^2 + 16	\( 2^{20}\cdot 18097^{4} \)	16T1852	$[2, 2]$ (GRH)
16.8.54271542302331817400394304.1	x^16 - 2x^15 - 2x^14 + 2x^13 - 147x^12 + 439x^11 - 786x^10 + 1408x^9 + 1789x^8 - 3682x^7 - 1926x^6 - 844x^5 + 3809x^4 - 8402x^3 + 7592x^2 + 812x - 1682	\( 2^{6}\cdot 43^{2}\cdot 2777^{6} \)	16T1852	Trivial (GRH)
16.8.54271542302331817400394304.2	x^16 + 9x^14 - 29x^13 - 182x^12 - 103x^11 - 289x^10 + 2096x^9 + 43x^8 - 6952x^7 + 13569x^6 - 5247x^5 - 5567x^4 + 7585x^3 - 9021x^2 + 1450x + 1439	\( 2^{6}\cdot 43^{2}\cdot 2777^{6} \)	16T1852	Trivial (GRH)