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 all 30 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.3100665090835456.1	x^16 + 2x^14 + 4x^12 + 6x^10 + 8x^8 + 7x^6 + 5x^4 + 3x^2 + 1	\( 2^{10}\cdot 1740113^{2} \)	16T1945	Trivial
16.0.3571460308796416.1	x^16 - 2x^14 + 4x^10 - 4x^8 + x^6 + 3x^4 - 3x^2 + 1	\( 2^{10}\cdot 1867553^{2} \)	16T1945	Trivial
16.4.105970624024377025.1	x^16 - x^15 - 2x^14 + 7x^13 - 12x^12 + 10x^11 - x^10 - 10x^9 + 15x^8 - 10x^7 - x^6 + 10x^5 - 12x^4 + 7x^3 - 2x^2 - x + 1	\( 5^{2}\cdot 89^{2}\cdot 731531^{2} \)	16T1945	Trivial
16.4.233622440259572809.1	x^16 - 2x^15 + 2x^14 - x^13 - x^12 + 2x^11 - 2x^10 + x^9 - x^8 + x^7 - 2x^6 + 2x^5 - x^4 - x^3 + 2x^2 - 2x + 1	\( 483345053^{2} \)	16T1945	Trivial
16.4.467930136224664481.1	x^16 - 7x^15 + 25x^14 - 61x^13 + 111x^12 - 164x^11 + 206x^10 - 230x^9 + 239x^8 - 230x^7 + 206x^6 - 164x^5 + 111x^4 - 61x^3 + 25x^2 - 7x + 1	\( 43^{4}\cdot 369959^{2} \)	16T1945	Trivial
16.4.500266405165487689.1	x^16 - x^15 - 2x^14 + 4x^13 - x^12 - 5x^11 + 5x^10 + 2x^9 - 7x^8 + 2x^7 + 5x^6 - 5x^5 - x^4 + 4x^3 - 2x^2 - x + 1	\( 9973^{2}\cdot 70921^{2} \)	16T1945	Trivial
16.4.1209626064094560256.1	x^16 - 5x^12 - x^10 + 8x^8 + 3x^6 - 4x^4 - 2x^2 + 1	\( 2^{16}\cdot 199^{2}\cdot 21589^{2} \)	16T1945	Trivial
16.0.1209626064094560256.2	x^16 + 2x^14 + 2x^12 + 4x^10 + 8x^8 + 12x^6 + 9x^4 + 4x^2 + 1	\( 2^{16}\cdot 199^{2}\cdot 21589^{2} \)	16T1945	Trivial
16.4.1209626064094560256.2	x^16 + x^14 - 3x^10 - 4x^8 - 2x^6 + 2x^4 + 3x^2 + 1	\( 2^{16}\cdot 199^{2}\cdot 21589^{2} \)	16T1945	Trivial
16.0.1209626064094560256.3	x^16 - 2x^14 - x^12 + 3x^10 + 2x^8 - 3x^6 - 2x^4 + 2x^2 + 1	\( 2^{16}\cdot 199^{2}\cdot 21589^{2} \)	16T1945	Trivial
16.4.16585326883515203584.1	x^16 + x^14 - 5x^12 - 15x^10 - 23x^8 - 19x^6 - 8x^4 + 1	\( 2^{16}\cdot 43^{2}\cdot 369959^{2} \)	16T1945	Trivial
16.8.16585326883515203584.1	x^16 - 7x^14 + 17x^12 - 13x^10 - 9x^8 + 14x^6 + 2x^4 - 5x^2 + 1	\( 2^{16}\cdot 43^{2}\cdot 369959^{2} \)	16T1945	Trivial
16.0.16585326883515203584.2	x^16 + 7x^14 + 17x^12 + 13x^10 - 9x^8 - 14x^6 + 2x^4 + 5x^2 + 1	\( 2^{16}\cdot 43^{2}\cdot 369959^{2} \)	16T1945	Trivial
16.8.16585326883515203584.2	x^16 - 6x^14 + 13x^12 - 17x^10 + 16x^8 - 9x^6 + 8x^4 - 8x^2 + 1	\( 2^{16}\cdot 43^{2}\cdot 369959^{2} \)	16T1945	Trivial
16.0.16585326883515203584.3	x^16 + 6x^14 + 13x^12 + 17x^10 + 16x^8 + 9x^6 + 8x^4 + 8x^2 + 1	\( 2^{16}\cdot 43^{2}\cdot 369959^{2} \)	16T1945	Trivial
16.4.39883104057814537129.1	x^16 - x^15 - 3x^14 - 8x^13 + 3x^12 + 24x^11 - 4x^10 - 6x^9 - 51x^8 + 63x^7 + 10x^6 - 39x^5 - 9x^4 + 43x^3 - 30x^2 + 9x - 1	\( 89^{2}\cdot 97^{2}\cdot 731531^{2} \)	16T1945	Trivial
16.8.140363026479679031809.1	x^16 - 8x^15 + 25x^14 - 31x^13 - 21x^12 + 119x^11 - 140x^10 + 37x^9 + 21x^8 + 44x^7 - 45x^6 - 62x^5 + 69x^4 + 22x^3 - 25x^2 - 6x + 1	\( 11^{4}\cdot 97913143^{2} \)	16T1945	Trivial
16.8.140363026479679031809.2	x^16 - 3x^15 + 5x^13 - 4x^12 + 10x^11 - 17x^10 + 18x^9 - 21x^8 + 18x^7 - 17x^6 + 10x^5 - 4x^4 + 5x^3 - 3x + 1	\( 11^{4}\cdot 97913143^{2} \)	16T1945	Trivial
16.12.277795632642462908416.1	x^16 - 7x^14 + 14x^12 + 2x^10 - 27x^8 + x^6 + 35x^4 - 19x^2 + 1	\( 2^{16}\cdot 89^{2}\cdot 731531^{2} \)	16T1945	Trivial (GRH)
16.8.277795632642462908416.1	x^16 - 5x^14 + 3x^12 + 21x^10 - 45x^8 + 36x^6 - 11x^4 - 2x^2 + 1	\( 2^{16}\cdot 89^{2}\cdot 731531^{2} \)	16T1945	Trivial
16.0.277795632642462908416.2	x^16 + 7x^14 + 14x^12 - 2x^10 - 27x^8 - x^6 + 35x^4 + 19x^2 + 1	\( 2^{16}\cdot 89^{2}\cdot 731531^{2} \)	16T1945	Trivial
16.8.277795632642462908416.2	x^16 - 4x^14 + 8x^12 - 15x^10 + 13x^8 + 7x^6 - 10x^4 + 1	\( 2^{16}\cdot 89^{2}\cdot 731531^{2} \)	16T1945	Trivial
16.12.307463056776831238144.1	x^16 - 5x^14 + 23x^10 - 11x^8 - 28x^6 + 30x^4 - 10x^2 + 1	\( 2^{16}\cdot 811^{2}\cdot 84457^{2} \)	16T1945	Trivial (GRH)
16.0.307463056776831238144.2	x^16 + 5x^14 - 23x^10 - 11x^8 + 28x^6 + 30x^4 + 10x^2 + 1	\( 2^{16}\cdot 811^{2}\cdot 84457^{2} \)	16T1945	Trivial
16.12.15310680244851363610624.1	x^16 - 8x^14 + 19x^12 + x^10 - 65x^8 + 90x^6 - 42x^4 + 4x^2 + 1	\( 2^{16}\cdot 483345053^{2} \)	16T1945	Trivial (GRH)
16.16.15310680244851363610624.1	x^16 - 15x^14 + 86x^12 - 242x^10 + 360x^8 - 281x^6 + 107x^4 - 18x^2 + 1	\( 2^{16}\cdot 483345053^{2} \)	16T1945	Trivial (GRH)
16.0.15310680244851363610624.2	x^16 + 15x^14 + 86x^12 + 242x^10 + 360x^8 + 281x^6 + 107x^4 + 18x^2 + 1	\( 2^{16}\cdot 483345053^{2} \)	16T1945	$[12]$
16.12.15310680244851363610624.2	x^16 - 7x^14 + 3x^12 + 49x^10 - 47x^8 - 26x^6 + 36x^4 - 11x^2 + 1	\( 2^{16}\cdot 483345053^{2} \)	16T1945	Trivial (GRH)
16.0.16983926204041162848889.1	x^16 - 5x^15 + 13x^14 - 14x^13 - 4x^12 + 35x^11 + 11x^10 - 210x^9 + 632x^8 - 1187x^7 + 1795x^6 - 2086x^5 + 1854x^4 - 1180x^3 + 566x^2 - 197x + 49	\( 11^{6}\cdot 97913143^{2} \)	16T1945	$[2, 2]$
16.16.16983926204041162848889.1	x^16 - 6x^15 - 3x^14 + 78x^13 - 82x^12 - 345x^11 + 620x^10 + 535x^9 - 1592x^8 + 56x^7 + 1563x^6 - 582x^5 - 517x^4 + 249x^3 + 50x^2 - 27x + 1	\( 11^{6}\cdot 97913143^{2} \)	16T1945	Trivial (GRH)