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 19 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.10251562500000000.1	x^16 - 4x^15 + 6x^14 + 9x^13 - 52x^12 + 91x^11 - 36x^10 - 163x^9 + 403x^8 - 489x^7 + 356x^6 - 143x^5 + 13x^4 + 12x^3 - x^2 - 3x + 1	\( 2^{8}\cdot 3^{8}\cdot 5^{14} \)	$(C_8:C_2):C_2$ (as 16T16)	Trivial
16.0.32400000000000000.1	x^16 - 2x^15 + 2x^14 + 4x^13 + x^12 - 12x^11 + 15x^10 + 32x^9 - 21x^8 + 6x^7 + 20x^6 - 34x^5 - 4x^4 + 22x^3 - 2x^2 - 4x + 1	\( 2^{16}\cdot 3^{4}\cdot 5^{14} \)	$(C_8:C_2):C_2$ (as 16T16)	Trivial
16.0.96148443603515625.1	x^16 - 5x^15 + 19x^14 - 50x^13 + 112x^12 - 205x^11 + 337x^10 - 470x^9 + 600x^8 - 655x^7 + 673x^6 - 550x^5 + 472x^4 - 260x^3 + 186x^2 - 55x + 31	\( 3^{8}\cdot 5^{14}\cdot 7^{4} \)	$(C_8:C_2):C_2$ (as 16T16)	Trivial
16.0.164025000000000000.1	x^16 - 5x^15 + 19x^14 - 50x^13 + 107x^12 - 180x^11 + 237x^10 - 225x^9 + 150x^8 - 25x^7 + 13x^6 + 40x^5 + 37x^4 + 35x^3 + 21x^2 + 5x + 1	\( 2^{12}\cdot 3^{8}\cdot 5^{14} \)	$(C_8:C_2):C_2$ (as 16T16)	Trivial
16.0.960400000000000000.1	x^16 - 2x^15 + 8x^14 - 24x^13 + 70x^12 - 194x^11 + 423x^10 - 722x^9 + 1006x^8 - 1150x^7 + 1075x^6 - 840x^5 + 570x^4 - 330x^3 + 145x^2 - 40x + 5	\( 2^{16}\cdot 5^{14}\cdot 7^{4} \)	$(C_8:C_2):C_2$ (as 16T16)	Trivial
16.0.2624400000000000000.1	x^16 - 10x^14 + 50x^12 - 145x^10 + 270x^8 - 300x^6 + 150x^4 - 25x^2 + 25	\( 2^{16}\cdot 3^{8}\cdot 5^{14} \)	$(C_8:C_2):C_2$ (as 16T16)	Trivial
16.8.2624400000000000000.1	x^16 - 8x^15 + 29x^14 - 58x^13 + 48x^12 + 62x^11 - 234x^10 + 306x^9 - 172x^8 - 68x^7 + 239x^6 - 314x^5 + 313x^4 - 206x^3 + 76x^2 - 14x + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{14} \)	$(C_8:C_2):C_2$ (as 16T16)	Trivial
16.0.2850029791259765625.1	x^16 - 5x^15 + 16x^14 - 25x^13 + 27x^12 - 35x^11 + 48x^10 - 90x^9 + 165x^8 - 195x^7 + 247x^6 - 190x^5 + 157x^4 - 80x^3 + 39x^2 - 10x + 1	\( 3^{4}\cdot 5^{14}\cdot 7^{8} \)	$(C_8:C_2):C_2$ (as 16T16)	Trivial
16.0.8294400000000000000.1	x^16 - 6x^15 + 9x^14 + 4x^13 + 11x^12 - 58x^11 - 29x^10 + 32x^9 + 162x^8 + 98x^7 - 54x^6 - 182x^5 - 119x^4 + 6x^3 + 69x^2 + 46x + 11	\( 2^{24}\cdot 3^{4}\cdot 5^{14} \)	$(C_8:C_2):C_2$ (as 16T16)	Trivial
16.0.8294400000000000000.2	x^16 - 2x^15 + 12x^14 - 6x^13 + 26x^12 + 68x^11 - 30x^10 + 222x^9 + 199x^8 - 224x^7 + 1210x^6 - 994x^5 + 1546x^4 - 698x^3 + 778x^2 - 184x + 181	\( 2^{24}\cdot 3^{4}\cdot 5^{14} \)	$(C_8:C_2):C_2$ (as 16T16)	$[2]$
16.0.9007501562500000000.1	x^16 - x^15 - 4x^14 + 6x^13 + 3x^12 - 26x^11 + 24x^10 + 93x^9 - 212x^8 + 54x^7 + 316x^6 - 497x^5 + 373x^4 - 227x^3 + 154x^2 - 67x + 11	\( 2^{8}\cdot 5^{14}\cdot 7^{8} \)	$(C_8:C_2):C_2$ (as 16T16)	Trivial
16.8.230852413092041015625.1	x^16 - 6x^15 + 8x^14 + 13x^13 - 39x^12 + 29x^11 + 15x^10 - 81x^9 + 89x^8 + 38x^7 - 100x^6 + 2x^5 + 46x^4 + x^3 - 23x^2 + 7x + 1	\( 3^{8}\cdot 5^{14}\cdot 7^{8} \)	$(C_8:C_2):C_2$ (as 16T16)	Trivial (GRH)
16.8.671846400000000000000.1	x^16 - 8x^15 + 22x^14 - 14x^13 - 79x^12 + 232x^11 - 105x^10 - 502x^9 + 679x^8 + 344x^7 - 1165x^6 + 464x^5 + 526x^4 - 562x^3 + 193x^2 - 26x + 1	\( 2^{24}\cdot 3^{8}\cdot 5^{14} \)	$(C_8:C_2):C_2$ (as 16T16)	Trivial (GRH)
16.8.671846400000000000000.2	x^16 - 2x^15 - 6x^14 - 2x^13 + 23x^12 + 48x^11 - 34x^10 + 34x^9 - 12x^8 - 232x^7 - 356x^6 + 44x^5 + 378x^4 + 216x^3 + 66x^2 + 14x + 1	\( 2^{24}\cdot 3^{8}\cdot 5^{14} \)	$(C_8:C_2):C_2$ (as 16T16)	Trivial (GRH)
16.8.2305920400000000000000.1	x^16 - 8x^15 + 24x^14 - 28x^13 - 37x^12 + 172x^11 - 194x^10 - 104x^9 + 503x^8 - 388x^7 - 321x^6 + 666x^5 - 57x^4 - 386x^3 + 91x^2 + 66x - 19	\( 2^{16}\cdot 5^{14}\cdot 7^{8} \)	$(C_8:C_2):C_2$ (as 16T16)	Trivial (GRH)
16.0.6301184400000000000000.1	x^16 + 19x^14 - 20x^13 + 142x^12 - 260x^11 + 617x^10 - 1100x^9 + 1585x^8 - 1750x^7 + 1398x^6 - 600x^5 + 202x^4 - 680x^3 + 1256x^2 - 750x + 181	\( 2^{16}\cdot 3^{8}\cdot 5^{14}\cdot 7^{4} \)	$(C_8:C_2):C_2$ (as 16T16)	$[2, 2]$
16.0.59098217751562500000000.1	x^16 - 4x^15 + 13x^14 - 18x^13 + 16x^12 - 9x^11 - 120x^10 + 136x^9 + 189x^8 - 228x^7 + 165x^6 + 283x^5 - 49x^4 + 659x^3 + 1222x^2 + 708x + 631	\( 2^{8}\cdot 3^{8}\cdot 5^{14}\cdot 7^{8} \)	$(C_8:C_2):C_2$ (as 16T16)	$[2, 2]$
16.16.6127097573297673637724160000.1	x^16 - 96x^14 + 2760x^12 - 31392x^10 + 173268x^8 - 509760x^6 + 810000x^4 - 648000x^2 + 202500	\( 2^{64}\cdot 3^{12}\cdot 5^{4} \)	$(C_8:C_2):C_2$ (as 16T16)	Trivial (GRH)
16.16.957358995827761505894400000000.1	x^16 - 48x^14 + 936x^12 - 9504x^10 + 53460x^8 - 163296x^6 + 244944x^4 - 139968x^2 + 324	\( 2^{62}\cdot 3^{12}\cdot 5^{8} \)	$(C_8:C_2):C_2$ (as 16T16)	Trivial (GRH)