Global number field search results

Further refine search

Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying all 35 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.115422332637413376.3	x^16 - 8x^14 + 24x^12 - 32x^10 + 30x^8 - 56x^6 + 56x^4 + 1	\( 2^{44}\cdot 3^{8} \)	$C_2^2:D_4$ (as 16T34)	Trivial
16.0.168110601127133184.1	x^16 - 6x^15 + 20x^14 - 46x^13 + 71x^12 - 66x^11 + 38x^10 - 30x^9 + 31x^8 - 18x^7 + 10x^6 + 4x^5 - 9x^4 - 8x^3 + 4x^2 + 4x + 1	\( 2^{16}\cdot 3^{12}\cdot 13^{6} \)	$C_2^2:D_4$ (as 16T34)	Trivial
16.0.217678233600000000.2	x^16 - 5x^14 + 8x^12 + 4x^10 - 17x^8 - 4x^6 + 32x^4 - x^2 + 1	\( 2^{20}\cdot 3^{12}\cdot 5^{8} \)	$C_2^2:D_4$ (as 16T34)	Trivial
16.0.1048970301636870144.3	x^16 - 2x^15 - 5x^14 + 14x^13 - 7x^12 + 22x^11 - 28x^10 - 148x^9 + 403x^8 - 406x^7 + 158x^6 + 64x^5 - 94x^4 + 20x^3 + 16x^2 - 8x + 1	\( 2^{24}\cdot 3^{12}\cdot 7^{6} \)	$C_2^2:D_4$ (as 16T34)	Trivial
16.4.1846757322198614016.1	x^16 - 8x^14 - 8x^13 + 24x^12 + 40x^11 - 4x^10 - 56x^9 - 66x^8 - 48x^7 - 8x^6 + 40x^5 + 48x^4 + 16x^3 - 8x^2 - 8x - 2	\( 2^{48}\cdot 3^{8} \)	$C_2^2:D_4$ (as 16T34)	Trivial
16.4.3482851737600000000.1	x^16 - 6x^14 - 2x^13 + 23x^12 + 6x^11 - 54x^10 + 18x^9 + 90x^8 - 38x^7 - 114x^6 - 18x^5 + 60x^4 + 32x^3 - 12x^2 + 2x + 1	\( 2^{24}\cdot 3^{12}\cdot 5^{8} \)	$C_2^2:D_4$ (as 16T34)	Trivial (GRH)
16.0.9349208943630483456.11	x^16 - 8x^14 + 38x^12 - 116x^10 + 271x^8 - 460x^6 + 470x^4 - 244x^2 + 49	\( 2^{44}\cdot 3^{12} \)	$C_2^2:D_4$ (as 16T34)	Trivial
16.0.9349208943630483456.14	x^16 - 4x^14 + 14x^12 - 76x^10 + 163x^8 + 4x^6 - 298x^4 + 88x^2 + 169	\( 2^{44}\cdot 3^{12} \)	$C_2^2:D_4$ (as 16T34)	Trivial
16.0.9766449236141015625.2	x^16 - x^15 - 7x^14 + 15x^13 + 12x^12 - 47x^11 + 52x^10 + 41x^9 - 35x^8 + 18x^7 + 63x^6 + 26x^5 - 3x^4 + 15x^3 + 22x^2 + 8x + 1	\( 3^{12}\cdot 5^{8}\cdot 19^{6} \)	$C_2^2:D_4$ (as 16T34)	Trivial
16.0.15227477017600000000.2	x^16 - 6x^15 + 17x^14 - 26x^13 + 24x^12 - 6x^11 - 16x^10 + 38x^9 - 23x^8 + 30x^7 + 32x^6 + 8x^5 + 32x^4 + 22x^3 + 31x^2 + 10x + 1	\( 2^{16}\cdot 5^{8}\cdot 29^{6} \)	$C_2^2:D_4$ (as 16T34)	Trivial
16.4.28410691590485508096.1	x^16 - 6x^15 + 19x^14 - 46x^13 + 72x^12 - 72x^11 + 16x^10 + 132x^9 - 242x^8 + 358x^7 - 225x^6 + 158x^5 + 52x^4 - 24x^3 + 54x^2 + 12x - 3	\( 2^{16}\cdot 3^{12}\cdot 13^{8} \)	$C_2^2:D_4$ (as 16T34)	Trivial (GRH)
16.4.37396835774521933824.1	x^16 - 4x^14 - 4x^12 - 40x^10 - 116x^8 - 104x^6 - 16x^4 + 16x^2 + 4	\( 2^{46}\cdot 3^{12} \)	$C_2^2:D_4$ (as 16T34)	Trivial
16.4.51399544780206637056.4	x^16 + 2x^14 - 13x^12 - 40x^10 - 143x^8 - 152x^6 - 13x^4 - 26x^2 + 1	\( 2^{24}\cdot 3^{12}\cdot 7^{8} \)	$C_2^2:D_4$ (as 16T34)	Trivial
16.0.55725627801600000000.3	x^16 - 10x^14 + 50x^12 - 136x^10 + 193x^8 - 110x^6 - 16x^4 + 16x^2 + 16	\( 2^{28}\cdot 3^{12}\cdot 5^{8} \)	$C_2^2:D_4$ (as 16T34)	Trivial
16.4.109951162777600000000.5	x^16 - 4x^14 - 4x^12 - 16x^10 + 23x^8 + 32x^6 + 34x^4 + 12x^2 + 1	\( 2^{48}\cdot 5^{8} \)	$C_2^2:D_4$ (as 16T34)	Trivial (GRH)
16.0.109951162777600000000.7	x^16 - 4x^14 + 8x^12 - 24x^10 + 83x^8 - 96x^6 + 38x^4 + 4x^2 + 1	\( 2^{48}\cdot 5^{8} \)	$C_2^2:D_4$ (as 16T34)	Trivial (GRH)
16.4.118192468620711297024.1	x^16 - 16x^14 - 8x^13 + 84x^12 + 64x^11 - 184x^10 - 224x^9 + 124x^8 + 352x^7 - 256x^5 - 64x^4 + 96x^3 + 64x^2 - 8	\( 2^{54}\cdot 3^{8} \)	$C_2^2:D_4$ (as 16T34)	Trivial (GRH)
16.0.118192468620711297024.9	x^16 - 16x^14 - 24x^13 + 88x^12 + 240x^11 - 8x^10 - 576x^9 - 420x^8 + 384x^7 + 608x^6 + 240x^5 + 112x^4 + 96x^3 + 16x^2 + 4	\( 2^{54}\cdot 3^{8} \)	$C_2^2:D_4$ (as 16T34)	$[2]$
16.0.136048896000000000000.3	x^16 - 8x^15 + 37x^14 - 104x^13 + 218x^12 - 320x^11 + 361x^10 - 232x^9 + 28x^8 + 96x^7 - 101x^6 - 12x^5 + 103x^4 - 8x^3 + 28x^2 + 48x + 16	\( 2^{20}\cdot 3^{12}\cdot 5^{12} \)	$C_2^2:D_4$ (as 16T34)	$[2]$ (GRH)
16.0.149587343098087735296.11	x^16 - 8x^15 + 24x^14 - 24x^13 - 40x^12 + 144x^11 - 124x^10 - 152x^9 + 498x^8 - 400x^7 - 160x^6 + 432x^5 - 16x^4 - 144x^3 + 48x^2 + 56x + 10	\( 2^{48}\cdot 3^{12} \)	$C_2^2:D_4$ (as 16T34)	$[2]$
16.0.482071511786234904576.1	x^16 - 4x^15 + 19x^14 - 56x^13 + 181x^12 - 508x^11 + 1214x^10 - 2380x^9 + 3877x^8 - 5180x^7 + 5536x^6 - 4606x^5 + 2908x^4 - 1350x^3 + 438x^2 - 90x + 9	\( 2^{16}\cdot 3^{12}\cdot 7^{12} \)	$C_2^2:D_4$ (as 16T34)	$[2]$ (GRH)
16.4.482071511786234904576.1	x^16 - 52x^12 - 210x^10 - 330x^8 - 168x^6 - 31x^4 - 42x^2 + 1	\( 2^{16}\cdot 3^{12}\cdot 7^{12} \)	$C_2^2:D_4$ (as 16T34)	Trivial (GRH)
16.4.598349372392350941184.1	x^16 - 8x^12 + 18x^8 - 104x^4 + 1	\( 2^{50}\cdot 3^{12} \)	$C_2^2:D_4$ (as 16T34)	Trivial (GRH)
16.0.598349372392350941184.2	x^16 + 8x^12 + 18x^8 + 104x^4 + 1	\( 2^{50}\cdot 3^{12} \)	$C_2^2:D_4$ (as 16T34)	$[2]$ (GRH)
16.4.891610044825600000000.2	x^16 - 4x^14 - 4x^12 + 20x^10 - 50x^8 + 40x^6 - 19x^4 + 4x^2 + 1	\( 2^{32}\cdot 3^{12}\cdot 5^{8} \)	$C_2^2:D_4$ (as 16T34)	Trivial (GRH)
16.4.2176782336000000000000.1	x^16 - 6x^15 + 16x^14 - 16x^13 - 41x^12 + 204x^11 - 356x^10 + 78x^9 + 829x^8 - 1592x^7 + 1084x^6 + 620x^5 - 2008x^4 + 1952x^3 - 1040x^2 + 320x - 44	\( 2^{24}\cdot 3^{12}\cdot 5^{12} \)	$C_2^2:D_4$ (as 16T34)	$[2]$ (GRH)
16.4.3525688174246906640625.1	x^16 + 2x^14 - 31x^12 - 19x^10 - 14x^8 + 79x^6 - 61x^4 + 13x^2 + 1	\( 3^{12}\cdot 5^{8}\cdot 19^{8} \)	$C_2^2:D_4$ (as 16T34)	Trivial (GRH)
16.0.19456426971136000000000000.1	x^16 - 2x^15 + 13x^14 - 90x^13 + 230x^12 - 568x^11 + 1529x^10 - 1080x^9 - 4251x^8 + 7280x^7 + 2021x^6 - 7456x^5 - 3460x^4 + 2490x^3 + 13617x^2 - 10314x + 5751	\( 2^{24}\cdot 5^{12}\cdot 41^{6} \)	$C_2^2:D_4$ (as 16T34)	$[4, 4]$ (GRH)
16.16.19456426971136000000000000.1	x^16 - 2x^15 - 45x^14 + 78x^13 + 759x^12 - 1218x^11 - 5980x^10 + 10232x^9 + 22641x^8 - 47290x^7 - 31370x^6 + 109240x^5 - 26870x^4 - 88500x^3 + 80550x^2 - 24300x + 2025	\( 2^{24}\cdot 5^{12}\cdot 41^{6} \)	$C_2^2:D_4$ (as 16T34)	Trivial (GRH)
16.0.25576314038393241600000000.1	x^16 - 4x^15 + 8x^14 - 48x^13 + 157x^12 - 272x^11 + 474x^10 - 844x^9 + 398x^8 + 2536x^7 + 12568x^6 + 7572x^5 + 1049x^4 + 9020x^3 + 34230x^2 + 32200x + 8875	\( 2^{24}\cdot 3^{8}\cdot 5^{8}\cdot 29^{6} \)	$C_2^2:D_4$ (as 16T34)	$[30]$ (GRH)
16.0.25576314038393241600000000.2	x^16 - 2x^15 - 15x^14 + 80x^13 + 2x^12 - 494x^11 + 590x^10 + 590x^9 + 6773x^8 - 30706x^7 + 62980x^6 - 59650x^5 + 40752x^4 - 13132x^3 + 11617x^2 + 414x + 529	\( 2^{24}\cdot 3^{8}\cdot 5^{8}\cdot 29^{6} \)	$C_2^2:D_4$ (as 16T34)	$[6]$ (GRH)
16.0.25576314038393241600000000.3	x^16 + 14x^14 + 101x^12 + 158x^10 + 964x^8 - 4406x^6 + 14549x^4 - 19430x^2 + 21025	\( 2^{24}\cdot 3^{8}\cdot 5^{8}\cdot 29^{6} \)	$C_2^2:D_4$ (as 16T34)	$[10]$ (GRH)
16.0.118460853639390732666015625.3	x^16 - 4x^15 + 6x^14 - 24x^13 + 159x^12 - 704x^11 + 2729x^10 - 9468x^9 + 25319x^8 - 48408x^7 + 63469x^6 - 58860x^5 + 48622x^4 - 33452x^3 + 23275x^2 - 9660x + 5836	\( 5^{12}\cdot 13^{8}\cdot 29^{6} \)	$C_2^2:D_4$ (as 16T34)	$[2, 28]$ (GRH)
16.16.273386361958931260426420224.1	x^16 - 8x^15 - 16x^14 + 232x^13 - 96x^12 - 2320x^11 + 2956x^10 + 8816x^9 - 16042x^8 - 8056x^7 + 22088x^6 + 368x^5 - 8264x^4 + 272x^3 + 864x^2 - 24x - 2	\( 2^{48}\cdot 3^{8}\cdot 23^{6} \)	$C_2^2:D_4$ (as 16T34)	Trivial (GRH)
16.0.860387204251548647424000000.1	x^16 - 6x^15 + 25x^14 - 134x^13 + 804x^12 - 3360x^11 + 9353x^10 - 17224x^9 + 21523x^8 - 20452x^7 + 19291x^6 - 17876x^5 + 13448x^4 - 8278x^3 + 4363x^2 - 1646x + 313	\( 2^{24}\cdot 3^{8}\cdot 5^{6}\cdot 29^{8} \)	$C_2^2:D_4$ (as 16T34)	$[6]$ (GRH)