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 18 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.447821316305142784.1	x^16 + 4x^12 - 3x^10 + 7x^8 - 6x^6 + 6x^4 - 3x^2 + 1	\( 2^{10}\cdot 17^{4}\cdot 269^{4} \)	16T1938	Trivial
16.0.1247561325698351104.1	x^16 - 2x^12 - 3x^10 + 2x^8 + 2x^6 + 2x^4 + x^2 + 1	\( 2^{18}\cdot 7^{4}\cdot 211^{4} \)	16T1938	Trivial
16.4.13493350820422352896.1	x^16 - 4x^12 + 2x^10 - 14x^8 - 8x^6 + 29x^4 + 22x^2 + 1	\( 2^{24}\cdot 947^{4} \)	16T1938	Trivial
16.4.13493350820422352896.2	x^16 - 4x^12 - 2x^10 - 14x^8 + 8x^6 + 29x^4 - 22x^2 + 1	\( 2^{24}\cdot 947^{4} \)	16T1938	Trivial
16.0.442421811294226366464.1	x^16 + 8x^14 + 27x^12 + 58x^10 + 84x^8 + 62x^6 + 22x^4 + 5x^2 + 1	\( 2^{14}\cdot 3^{4}\cdot 4273^{4} \)	16T1938	Trivial
16.8.442421811294226366464.1	x^16 - 12x^14 + 62x^12 - 174x^10 + 265x^8 - 201x^6 + 76x^4 - 14x^2 + 1	\( 2^{14}\cdot 3^{4}\cdot 4273^{4} \)	16T1938	Trivial
16.0.442421811294226366464.2	x^16 + 5x^14 + 10x^12 + 11x^10 + 7x^8 + 10x^6 + 18x^4 + 9x^2 + 1	\( 2^{14}\cdot 3^{4}\cdot 4273^{4} \)	16T1938	Trivial
16.8.1375792611276761399296.1	x^16 - 11x^10 - 3x^8 + 20x^4 - 9x^2 + 1	\( 2^{16}\cdot 12037^{4} \)	16T1938	Trivial (GRH)
16.12.2177548341958822306321.1	x^16 - 3x^15 - 9x^14 + 43x^13 - 20x^12 - 151x^11 + 298x^10 + 15x^9 - 703x^8 + 626x^7 + 437x^6 - 763x^5 + 67x^4 + 221x^3 - 56x^2 - 8x + 1	\( 17^{4}\cdot 97^{4}\cdot 131^{4} \)	16T1938	Trivial
16.4.2177548341958822306321.1	x^16 - 8x^15 + 38x^14 - 126x^13 + 308x^12 - 574x^11 + 781x^10 - 693x^9 + 133x^8 + 744x^7 - 1399x^6 + 1411x^5 - 730x^4 + 14x^3 + 361x^2 - 261x + 100	\( 17^{4}\cdot 97^{4}\cdot 131^{4} \)	16T1938	$[2]$
16.8.2177548341958822306321.1	x^16 - 2x^15 - 6x^14 + 17x^13 - 19x^12 + 11x^11 + 16x^10 - 46x^9 + 57x^8 - 46x^7 + 16x^6 + 11x^5 - 19x^4 + 17x^3 - 6x^2 - 2x + 1	\( 17^{4}\cdot 97^{4}\cdot 131^{4} \)	16T1938	Trivial
16.8.18816282527049267019776.1	x^16 - 6x^15 + 12x^14 + 2x^13 - 50x^12 + 76x^11 - 36x^10 + 68x^9 - 189x^8 + 152x^7 - 32x^6 - 60x^5 + 300x^4 - 462x^3 + 306x^2 - 90x + 9	\( 2^{24}\cdot 3^{8}\cdot 643^{4} \)	16T1938	Trivial
16.12.106699868755982293009729.1	x^16 - 2x^15 - 17x^14 + 26x^13 + 113x^12 - 126x^11 - 364x^10 + 334x^9 + 624x^8 - 585x^7 - 682x^6 + 570x^5 + 492x^4 - 237x^3 - 184x^2 + 23x + 19	\( 7^{2}\cdot 17^{4}\cdot 97^{4}\cdot 131^{4} \)	16T1938	Trivial
16.4.106699868755982293009729.1	x^16 - 2x^15 - 7x^14 + 12x^13 + 22x^12 + 8x^11 - 191x^10 + 251x^9 - 25x^8 - 201x^7 + 177x^6 - 49x^5 - 27x^4 - 2x^3 + 3x^2 - 5x - 1	\( 7^{2}\cdot 17^{4}\cdot 97^{4}\cdot 131^{4} \)	16T1938	$[2]$
16.0.35676952034653344666763264.1	x^16 + 20x^14 + 152x^12 + 557x^10 + 1035x^8 + 960x^6 + 454x^4 + 104x^2 + 9	\( 2^{14}\cdot 17^{4}\cdot 97^{4}\cdot 131^{4} \)	16T1938	$[2, 30]$
16.16.35676952034653344666763264.1	x^16 - 23x^14 + 197x^12 - 784x^10 + 1498x^8 - 1361x^6 + 578x^4 - 101x^2 + 4	\( 2^{14}\cdot 17^{4}\cdot 97^{4}\cdot 131^{4} \)	16T1938	Trivial (GRH)
16.0.35676952034653344666763264.2	x^16 + 18x^14 + 129x^12 + 478x^10 + 990x^8 + 1154x^6 + 726x^4 + 223x^2 + 25	\( 2^{14}\cdot 17^{4}\cdot 97^{4}\cdot 131^{4} \)	16T1938	$[2, 60]$
16.16.142707808138613378667053056.1	x^16 - 20x^14 + 152x^12 - 557x^10 + 1035x^8 - 960x^6 + 454x^4 - 104x^2 + 9	\( 2^{16}\cdot 17^{4}\cdot 97^{4}\cdot 131^{4} \)	16T1938	Trivial (GRH)