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 20 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.6298009600000000.1	x^16 - 4x^15 + 8x^14 - 10x^13 + 11x^12 - 12x^11 + 10x^10 - 4x^9 + x^8 - 4x^7 + 10x^6 - 12x^5 + 11x^4 - 10x^3 + 8x^2 - 4x + 1	\( 2^{24}\cdot 5^{8}\cdot 31^{2} \)	$D_4^2.C_2$ (as 16T396)	Trivial
16.0.12687769600000000.1	x^16 - 6x^15 + 14x^14 - 12x^13 - 8x^12 + 22x^11 - 2x^10 - 30x^9 + 31x^8 - 6x^7 - 6x^6 - 2x^5 + 10x^4 - 8x^3 + 4x^2 - 2x + 1	\( 2^{28}\cdot 5^{8}\cdot 11^{2} \)	$D_4^2.C_2$ (as 16T396)	Trivial
16.0.28968410356383744.1	x^16 - 2x^15 + 2x^14 - 4x^12 + 8x^11 - 8x^10 + 6x^9 - 2x^8 - 6x^7 + 16x^6 - 20x^5 + 17x^4 - 12x^3 + 8x^2 - 4x + 1	\( 2^{24}\cdot 3^{14}\cdot 19^{2} \)	$D_4^2.C_2$ (as 16T396)	Trivial
16.0.29572464740663296.1	x^16 - 4x^14 + 14x^12 - 28x^10 + 43x^8 - 44x^6 + 10x^4 + 8x^2 + 1	\( 2^{44}\cdot 41^{2} \)	$D_4^2.C_2$ (as 16T396)	Trivial
16.0.51911065600000000.1	x^16 - 2x^15 + 2x^14 + 2x^12 - 10x^11 + 16x^10 - 18x^9 + 19x^8 - 18x^7 + 16x^6 - 10x^5 + 2x^4 + 2x^2 - 2x + 1	\( 2^{24}\cdot 5^{8}\cdot 89^{2} \)	$D_4^2.C_2$ (as 16T396)	Trivial
16.0.51911065600000000.2	x^16 - 2x^15 + 2x^14 - 4x^13 + 3x^12 + 2x^11 - 2x^10 + 4x^9 - 7x^8 + 4x^7 - 2x^6 + 2x^5 + 3x^4 - 4x^3 + 2x^2 - 2x + 1	\( 2^{24}\cdot 5^{8}\cdot 89^{2} \)	$D_4^2.C_2$ (as 16T396)	Trivial
16.4.9575028998081640625.1	x^16 - x^15 - 9x^14 + 24x^13 - 16x^12 - 19x^11 + 30x^10 + 8x^9 - 37x^8 + 8x^7 + 30x^6 - 19x^5 - 16x^4 + 24x^3 - 9x^2 - x + 1	\( 5^{8}\cdot 7^{2}\cdot 29^{8} \)	$D_4^2.C_2$ (as 16T396)	Trivial
16.0.19778710400363659264.1	x^16 - 4x^15 + 14x^14 - 42x^13 + 105x^12 - 224x^11 + 403x^10 - 622x^9 + 826x^8 - 936x^7 + 903x^6 - 724x^5 + 484x^4 - 256x^3 + 112x^2 - 32x + 8	\( 2^{24}\cdot 13^{2}\cdot 17^{8} \)	$D_4^2.C_2$ (as 16T396)	Trivial
16.4.23644459362609765625.1	x^16 - 2x^15 + 5x^14 - 11x^13 + 23x^12 - 19x^11 - 3x^10 - 30x^9 - 53x^8 + 30x^7 - 3x^6 + 19x^5 + 23x^4 + 11x^3 + 5x^2 + 2x + 1	\( 5^{8}\cdot 11^{2}\cdot 29^{8} \)	$D_4^2.C_2$ (as 16T396)	Trivial (GRH)
16.8.33024079605628515625.1	x^16 - 4x^15 + 4x^14 + 6x^13 - 29x^12 + 58x^11 - 74x^10 + 43x^9 + 84x^8 - 212x^7 + 151x^6 + 28x^5 - 81x^4 + 13x^3 + 14x^2 - 2x - 1	\( 5^{8}\cdot 13^{2}\cdot 29^{8} \)	$D_4^2.C_2$ (as 16T396)	Trivial (GRH)
16.0.168996791823225585664.1	x^16 - 4x^14 + 3x^12 + 12x^10 - 37x^8 + 4x^6 + 125x^4 + 20x^2 + 4	\( 2^{26}\cdot 17^{8}\cdot 19^{2} \)	$D_4^2.C_2$ (as 16T396)	Trivial
16.8.328482117260719140625.1	x^16 - x^15 - 8x^14 + 36x^12 + 57x^11 - 77x^10 - 241x^9 - 4x^8 + 307x^7 + 67x^6 - 136x^5 - 4x^4 + 15x^3 - 12x^2 - 2x + 1	\( 5^{8}\cdot 29^{8}\cdot 41^{2} \)	$D_4^2.C_2$ (as 16T396)	Trivial (GRH)
16.8.1547832748853156640625.1	x^16 - 2x^15 - 11x^14 + 10x^13 + 37x^12 + 2x^11 - 95x^10 - 109x^9 + 219x^8 + 183x^7 - 180x^6 - 106x^5 + 32x^4 + 5x^3 - 4x^2 + x + 1	\( 5^{8}\cdot 29^{8}\cdot 89^{2} \)	$D_4^2.C_2$ (as 16T396)	Trivial (GRH)
16.8.1993364710396547265625.1	x^16 - 4x^15 + 3x^14 + 10x^13 - 58x^12 + 154x^11 + 38x^10 - 426x^9 - 74x^8 + 293x^7 + 202x^6 + 82x^5 - 3x^4 - 40x^3 - 13x^2 + 3x + 1	\( 5^{8}\cdot 29^{8}\cdot 101^{2} \)	$D_4^2.C_2$ (as 16T396)	Trivial (GRH)
16.0.2321651418902203515625.1	x^16 - 3x^15 + 7x^14 - 16x^13 + 36x^12 - 39x^11 + 37x^10 - 9x^9 - 64x^8 + 177x^7 - 131x^6 + 52x^5 + 273x^4 - 202x^3 + 391x^2 - 110x + 121	\( 5^{8}\cdot 29^{8}\cdot 109^{2} \)	$D_4^2.C_2$ (as 16T396)	$[2]$
16.12.3353409645634266015625.1	x^16 - 4x^15 - x^14 + 16x^13 - 40x^12 + 24x^11 + 229x^10 - 70x^9 - 430x^8 - 118x^7 + 155x^6 + 96x^5 + 25x^4 - 19x^3 - 15x^2 + x + 1	\( 5^{8}\cdot 29^{8}\cdot 131^{2} \)	$D_4^2.C_2$ (as 16T396)	Trivial (GRH)
16.12.3775492556570109765625.1	x^16 - 18x^14 + 97x^12 - 263x^10 + 408x^8 - 354x^6 + 153x^4 - 26x^2 + 1	\( 5^{8}\cdot 29^{8}\cdot 139^{2} \)	$D_4^2.C_2$ (as 16T396)	Trivial (GRH)
16.0.50626695670448766015625.1	x^16 - x^15 + 13x^14 + 8x^13 + 111x^12 + 210x^11 + 783x^10 + 1107x^9 + 2089x^8 + 1657x^7 + 2260x^6 + 712x^5 + 1596x^4 + 382x^3 + 376x^2 - 264x + 121	\( 5^{8}\cdot 29^{8}\cdot 509^{2} \)	$D_4^2.C_2$ (as 16T396)	$[8]$
16.16.67791400715173078515625.1	x^16 - 2x^15 - 27x^14 + 64x^13 + 219x^12 - 584x^11 - 680x^10 + 2121x^9 + 789x^8 - 3351x^7 - 148x^6 + 2148x^5 - 53x^4 - 471x^3 - 42x^2 + 14x + 1	\( 5^{8}\cdot 19^{2}\cdot 29^{8}\cdot 31^{2} \)	$D_4^2.C_2$ (as 16T396)	Trivial (GRH)
16.16.147565070882047547265625.1	x^16 - 26x^14 + 245x^12 - 1041x^10 + 1990x^8 - 1460x^6 + 452x^4 - 53x^2 + 1	\( 5^{8}\cdot 11^{2}\cdot 29^{8}\cdot 79^{2} \)	$D_4^2.C_2$ (as 16T396)	Trivial (GRH)