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 17 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.4540317078515625.1	x^16 - 3x^15 + 4x^14 - 3x^13 + 11x^10 - 24x^9 + 29x^8 - 24x^7 + 11x^6 - 3x^3 + 4x^2 - 3x + 1	\( 3^{8}\cdot 5^{8}\cdot 11^{6} \)	$D_4:D_4$ (as 16T141)	Trivial
16.0.8084777718513664.1	x^16 - 4x^15 + 6x^14 - 14x^12 + 24x^11 - 18x^10 + 15x^8 - 20x^7 + 22x^6 - 24x^5 + 24x^4 - 20x^3 + 12x^2 - 4x + 1	\( 2^{36}\cdot 7^{6} \)	$D_4:D_4$ (as 16T141)	Trivial
16.0.103670069459943424.3	x^16 - 4x^13 - 3x^12 + 8x^10 + 4x^9 + 4x^8 - 4x^7 + 8x^6 - 3x^4 + 4x^3 + 1	\( 2^{32}\cdot 17^{6} \)	$D_4:D_4$ (as 16T141)	Trivial
16.0.219809187453515625.2	x^16 - x^15 + 4x^13 + 11x^12 - 6x^11 + x^10 + 23x^9 + 6x^8 + 14x^7 + 25x^6 + 24x^5 + 29x^4 + 22x^3 + 12x^2 + 5x + 1	\( 3^{14}\cdot 5^{8}\cdot 7^{6} \)	$D_4:D_4$ (as 16T141)	Trivial
16.0.396154108207169536.5	x^16 - 2x^14 + 7x^12 - 22x^10 + 34x^8 - 22x^6 + 7x^4 - 2x^2 + 1	\( 2^{36}\cdot 7^{8} \)	$D_4:D_4$ (as 16T141)	Trivial
16.0.555307587640295424.2	x^16 - 6x^15 + 14x^14 - 12x^13 + x^12 + 2x^10 + 18x^9 - 20x^8 + 18x^7 + 2x^6 + x^4 - 12x^3 + 14x^2 - 6x + 1	\( 2^{16}\cdot 3^{14}\cdot 11^{6} \)	$D_4:D_4$ (as 16T141)	Trivial
16.0.3428140926314458809.1	x^16 - 5x^15 + 21x^14 - 49x^13 + 103x^12 - 148x^11 + 218x^10 - 240x^9 + 279x^8 - 240x^7 + 218x^6 - 148x^5 + 103x^4 - 49x^3 + 21x^2 - 5x + 1	\( 3^{6}\cdot 7^{8}\cdot 13^{8} \)	$D_4:D_4$ (as 16T141)	Trivial
16.0.6871947673600000000.1	x^16 - 4x^15 + 12x^14 - 36x^13 + 74x^12 - 116x^11 + 180x^10 - 180x^9 + 238x^8 - 180x^7 + 180x^6 - 116x^5 + 74x^4 - 36x^3 + 12x^2 - 4x + 1	\( 2^{44}\cdot 5^{8} \)	$D_4:D_4$ (as 16T141)	Trivial
16.0.6871947673600000000.12	x^16 - 4x^15 + 8x^14 - 12x^13 + 20x^12 - 40x^11 + 68x^10 - 20x^9 - 153x^8 + 360x^7 - 328x^6 - 12x^5 + 372x^4 - 436x^3 + 256x^2 - 80x + 11	\( 2^{44}\cdot 5^{8} \)	$D_4:D_4$ (as 16T141)	Trivial
16.0.19411551302151307264.1	x^16 - 4x^15 + 4x^14 - 8x^13 + 40x^12 - 60x^11 + 88x^10 - 224x^9 + 258x^8 - 340x^7 + 460x^6 - 344x^5 + 512x^4 - 108x^3 + 304x^2 - 32x + 1	\( 2^{36}\cdot 7^{10} \)	$D_4:D_4$ (as 16T141)	$[2]$
16.0.277679415031471163529.2	x^16 + 6x^14 - 21x^12 - 19x^10 + 159x^8 + 282x^6 + 190x^4 + 60x^2 + 9	\( 3^{10}\cdot 7^{8}\cdot 13^{8} \)	$D_4:D_4$ (as 16T141)	$[2]$
16.8.31130283153817600000000.2	x^16 - 2x^15 - 5x^14 - 6x^13 + 30x^12 + 70x^11 - 91x^10 - 106x^9 - 269x^8 + 1044x^7 + 510x^6 - 3352x^5 + 4x^4 + 3616x^3 + 256x^2 - 1280x - 256	\( 2^{24}\cdot 5^{8}\cdot 41^{6} \)	$D_4:D_4$ (as 16T141)	$[2]$ (GRH)
16.16.189537365823025172265625.1	x^16 - 7x^15 - 3x^14 + 103x^13 - 98x^12 - 476x^11 + 526x^10 + 1093x^9 - 951x^8 - 1407x^7 + 639x^6 + 946x^5 - 49x^4 - 241x^3 - 54x^2 + 2x + 1	\( 5^{8}\cdot 13^{8}\cdot 29^{6} \)	$D_4:D_4$ (as 16T141)	Trivial (GRH)
16.8.3257016588442009600000000.1	x^16 - 4x^15 + 6x^14 + 24x^13 - 165x^12 + 340x^11 - 206x^10 - 1148x^9 + 3479x^8 - 2192x^7 - 3546x^6 + 5220x^5 - 975x^4 - 1844x^3 + 1396x^2 - 396x + 41	\( 2^{24}\cdot 5^{8}\cdot 89^{6} \)	$D_4:D_4$ (as 16T141)	Trivial (GRH)
16.0.9316515344280166632259584.1	x^16 - 4x^15 + 8x^14 + 14x^12 - 32x^11 + 184x^10 - 120x^9 + 310x^8 - 192x^7 + 592x^6 - 40x^5 + 1196x^4 - 240x^3 + 1136x^2 - 176x + 484	\( 2^{40}\cdot 3^{14}\cdot 11^{6} \)	$D_4:D_4$ (as 16T141)	$[2, 4, 4]$ (GRH)
16.16.9316515344280166632259584.1	x^16 - 4x^15 - 16x^14 + 60x^13 + 92x^12 - 296x^11 - 260x^10 + 624x^9 + 367x^8 - 624x^7 - 260x^6 + 296x^5 + 92x^4 - 60x^3 - 16x^2 + 4x + 1	\( 2^{40}\cdot 3^{14}\cdot 11^{6} \)	$D_4:D_4$ (as 16T141)	Trivial (GRH)
16.0.10461504735757671642169344.1	x^16 - 8x^15 + 24x^14 - 12x^13 - 68x^12 + 52x^11 + 312x^10 - 264x^9 - 831x^8 + 892x^7 + 2596x^6 + 24x^5 - 5388x^4 - 476x^3 + 16696x^2 + 9876x + 3303	\( 2^{44}\cdot 3^{6}\cdot 13^{8} \)	$D_4:D_4$ (as 16T141)	$[3, 6]$ (GRH)