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 28 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.200779471797682176.5	x^16 - 8x^15 + 26x^14 - 42x^13 + 30x^12 + 2x^11 - 2x^10 - 56x^9 + 112x^8 - 90x^7 + 12x^6 + 40x^5 - 21x^4 - 18x^3 + 22x^2 - 8x + 1	\( 2^{16}\cdot 3^{12}\cdot 7^{8} \)	$C_2^4.C_2^3$ (as 16T392)	Trivial
16.0.254652744902639616.3	x^16 - 2x^15 - 6x^14 + 10x^13 + 21x^12 - 24x^11 - 42x^10 + 20x^9 + 93x^8 - 84x^7 - 42x^6 + 114x^5 - 31x^4 - 70x^3 + 30x^2 + 12x + 1	\( 2^{24}\cdot 3^{12}\cdot 13^{4} \)	$C_2^4.C_2^3$ (as 16T392)	Trivial
16.4.4074443918442233856.1	x^16 - 2x^15 + 4x^14 - 10x^13 + 14x^12 - 14x^11 - 4x^10 + 26x^9 - 38x^8 + 26x^7 - 4x^6 - 14x^5 + 14x^4 - 10x^3 + 4x^2 - 2x + 1	\( 2^{28}\cdot 3^{12}\cdot 13^{4} \)	$C_2^4.C_2^3$ (as 16T392)	Trivial (GRH)
16.4.4074443918442233856.2	x^16 - 8x^14 + 8x^12 - 8x^10 - 2x^8 + 8x^6 + 8x^4 + 8x^2 + 1	\( 2^{28}\cdot 3^{12}\cdot 13^{4} \)	$C_2^4.C_2^3$ (as 16T392)	Trivial
16.0.15227477017600000000.5	x^16 - 4x^15 + 7x^14 - 14x^13 + 50x^12 - 142x^11 + 278x^10 - 440x^9 + 648x^8 - 850x^7 + 907x^6 - 764x^5 + 530x^4 - 292x^3 + 128x^2 - 38x + 11	\( 2^{16}\cdot 5^{8}\cdot 29^{6} \)	$C_2^4.C_2^3$ (as 16T392)	Trivial
16.0.15227477017600000000.6	x^16 - 6x^15 + 19x^14 - 32x^13 + 14x^12 + 58x^11 - 176x^10 + 312x^9 - 339x^8 + 50x^7 + 560x^6 - 1116x^5 + 1208x^4 - 848x^3 + 392x^2 - 112x + 16	\( 2^{16}\cdot 5^{8}\cdot 29^{6} \)	$C_2^4.C_2^3$ (as 16T392)	Trivial
16.8.1622647227216566419456.3	x^16 - 8x^14 - 8x^13 + 16x^12 + 56x^11 + 20x^10 - 104x^9 - 106x^8 - 16x^7 + 216x^6 + 40x^5 - 160x^4 + 16x^3 + 40x^2 - 8x - 2	\( 2^{48}\cdot 7^{8} \)	$C_2^4.C_2^3$ (as 16T392)	Trivial (GRH)
16.0.1622647227216566419456.17	x^16 + 12x^12 - 8x^11 + 12x^10 + 64x^9 - 104x^8 + 320x^6 - 696x^5 + 1000x^4 - 920x^3 + 588x^2 - 224x + 49	\( 2^{48}\cdot 7^{8} \)	$C_2^4.C_2^3$ (as 16T392)	$[2]$
16.0.1622647227216566419456.18	x^16 - 8x^13 - 4x^12 - 8x^11 - 4x^10 - 8x^9 + 32x^8 + 128x^7 + 248x^6 + 384x^5 + 536x^4 + 616x^3 + 484x^2 + 216x + 41	\( 2^{48}\cdot 7^{8} \)	$C_2^4.C_2^3$ (as 16T392)	$[2]$
16.8.1911245314971754561536.2	x^16 - 6x^15 + 4x^14 + 46x^13 - 110x^12 - 36x^11 + 394x^10 - 306x^9 - 461x^8 + 692x^7 + 262x^6 - 962x^5 + 494x^4 + 154x^3 - 242x^2 + 88x - 11	\( 2^{24}\cdot 3^{12}\cdot 11^{8} \)	$C_2^4.C_2^3$ (as 16T392)	Trivial (GRH)
16.0.32798502387606516015625.1	x^16 - 5x^15 + 20x^14 - 59x^13 + 147x^12 - 321x^11 + 631x^10 - 1279x^9 + 2398x^8 - 4615x^7 + 8081x^6 - 11766x^5 + 14746x^4 - 13300x^3 + 8355x^2 - 2650x + 475	\( 5^{8}\cdot 29^{6}\cdot 109^{4} \)	$C_2^4.C_2^3$ (as 16T392)	$[6]$
16.0.32798502387606516015625.2	x^16 - 4x^15 + 12x^14 - 43x^13 + 112x^12 - 284x^11 + 693x^10 - 1463x^9 + 3148x^8 - 5737x^7 + 8870x^6 - 14597x^5 + 19482x^4 - 14739x^3 + 4491x^2 + 99x + 359	\( 5^{8}\cdot 29^{6}\cdot 109^{4} \)	$C_2^4.C_2^3$ (as 16T392)	$[4]$
16.0.114523100106217078515625.1	x^16 - 4x^15 - 9x^14 + 44x^13 + 54x^12 - 302x^11 - 64x^10 + 1172x^9 - 369x^8 - 2508x^7 + 1705x^6 + 2590x^5 - 2287x^4 - 30x^3 + 1078x^2 - 1378x + 1091	\( 5^{8}\cdot 29^{6}\cdot 149^{4} \)	$C_2^4.C_2^3$ (as 16T392)	$[6]$ (GRH)
16.0.114523100106217078515625.2	x^16 - 4x^15 - 9x^14 + 54x^13 + 14x^12 - 292x^11 + 126x^10 + 562x^9 + 101x^8 - 648x^7 - 1355x^6 - 260x^5 + 2983x^4 + 1860x^3 - 1032x^2 - 168x + 931	\( 5^{8}\cdot 29^{6}\cdot 149^{4} \)	$C_2^4.C_2^3$ (as 16T392)	$[8]$ (GRH)
16.0.463351970115520828515625.1	x^16 - 2x^15 + 9x^14 - 22x^13 + 41x^12 - 130x^11 + 367x^10 - 1025x^9 + 2359x^8 - 3801x^7 + 3244x^6 - 1124x^5 + 1324x^4 - 2855x^3 + 2910x^2 - 225x + 1025	\( 5^{8}\cdot 29^{4}\cdot 109^{6} \)	$C_2^4.C_2^3$ (as 16T392)	$[2, 4]$ (GRH)
16.0.463351970115520828515625.2	x^16 - 5x^15 + 21x^14 - 63x^13 + 125x^12 - 218x^11 + 387x^10 - 336x^9 + 1134x^8 - 314x^7 - 447x^6 - 2461x^5 - 689x^4 + 2225x^3 + 2865x^2 + 1700x + 475	\( 5^{8}\cdot 29^{4}\cdot 109^{6} \)	$C_2^4.C_2^3$ (as 16T392)	$[12]$ (GRH)
16.8.1103341620319083198765625.1	x^16 - 17x^14 + 60x^12 + 189x^10 - 881x^8 - 531x^6 + 2504x^4 + 515x^2 + 25	\( 5^{6}\cdot 29^{8}\cdot 109^{4} \)	$C_2^4.C_2^3$ (as 16T392)	Trivial (GRH)
16.8.1103341620319083198765625.2	x^16 - 2x^15 - 15x^14 + 10x^13 + 16x^12 - 20x^11 - 33x^10 - 124x^9 + 415x^8 - 124x^7 - 33x^6 - 20x^5 + 16x^4 + 10x^3 - 15x^2 - 2x + 1	\( 5^{6}\cdot 29^{8}\cdot 109^{4} \)	$C_2^4.C_2^3$ (as 16T392)	Trivial (GRH)
16.0.1835740554155063901159424.1	x^16 + 7x^14 - 18x^13 - 18x^12 + 76x^11 - 98x^10 + 508x^9 - 171x^8 - 896x^7 + 1779x^6 - 1906x^5 + 964x^4 - 220x^3 + 152x^2 - 136x + 104	\( 2^{22}\cdot 17^{8}\cdot 89^{4} \)	$C_2^4.C_2^3$ (as 16T392)	$[7]$ (GRH)
16.0.1835740554155063901159424.2	x^16 + 3x^14 + 5x^12 + 9x^10 + 70x^8 + 72x^6 + 320x^4 + 1536x^2 + 4096	\( 2^{22}\cdot 17^{8}\cdot 89^{4} \)	$C_2^4.C_2^3$ (as 16T392)	$[14]$ (GRH)
16.0.3023219197928805422265625.3	x^16 - 2x^15 + 13x^14 - 36x^13 + 124x^12 - 310x^11 + 880x^10 - 1475x^9 + 1639x^8 - 115x^7 - 888x^6 + 1563x^5 - 373x^4 + 1494x^3 - 1640x^2 - 160x + 2224	\( 5^{8}\cdot 29^{4}\cdot 149^{6} \)	$C_2^4.C_2^3$ (as 16T392)	$[8]$ (GRH)
16.0.3023219197928805422265625.4	x^16 - 4x^15 + 10x^14 - 60x^13 + 161x^12 - 390x^11 + 1278x^10 - 2441x^9 + 5318x^8 - 9468x^7 + 16911x^6 - 21532x^5 + 31832x^4 - 30527x^3 + 26588x^2 - 12891x + 2239	\( 5^{8}\cdot 29^{4}\cdot 149^{6} \)	$C_2^4.C_2^3$ (as 16T392)	$[6]$ (GRH)
16.0.9137400932085864255717376.1	x^16 - x^14 - 16x^12 + 48x^10 + 92x^8 - 180x^6 - 208x^4 - 1664x^2 + 4096	\( 2^{28}\cdot 17^{8}\cdot 47^{4} \)	$C_2^4.C_2^3$ (as 16T392)	$[6]$ (GRH)
16.0.20499063992254072509765625.1	x^16 - 8x^15 + 18x^14 + 14x^13 - 118x^12 + 162x^11 + 13x^10 - 263x^9 + 3320x^8 - 12208x^7 + 22491x^6 - 25211x^5 + 27907x^4 - 27846x^3 - 4192x^2 + 15920x + 16336	\( 5^{12}\cdot 29^{6}\cdot 109^{4} \)	$C_2^4.C_2^3$ (as 16T392)	$[2, 4]$ (GRH)
16.16.93659299370391914766401536.1	x^16 - 28x^14 + 272x^12 - 1116x^10 + 2126x^8 - 1860x^6 + 656x^4 - 68x^2 + 1	\( 2^{44}\cdot 7^{8}\cdot 31^{4} \)	$C_2^4.C_2^3$ (as 16T392)	Trivial (GRH)
16.16.125255372961988906944823296.1	x^16 - 4x^15 - 30x^14 + 144x^13 + 192x^12 - 1596x^11 + 1052x^10 + 5020x^9 - 9585x^8 + 5020x^7 + 1052x^6 - 1596x^5 + 192x^4 + 144x^3 - 30x^2 - 4x + 1	\( 2^{40}\cdot 3^{12}\cdot 11^{8} \)	$C_2^4.C_2^3$ (as 16T392)	Trivial (GRH)
16.0.125255372961988906944823296.2	x^16 + 28x^14 + 348x^12 + 2236x^10 + 6946x^8 + 5532x^6 - 6180x^4 - 6948x^2 + 45369	\( 2^{40}\cdot 3^{12}\cdot 11^{8} \)	$C_2^4.C_2^3$ (as 16T392)	$[2, 4, 8]$ (GRH)
16.0.182182440601540289016015625.1	x^16 - 4x^15 + 39x^14 - 104x^13 + 472x^12 - 960x^11 + 2651x^10 - 4132x^9 + 7405x^8 - 8962x^7 + 10853x^6 - 8836x^5 + 8226x^4 - 4718x^3 + 2635x^2 - 514x + 1049	\( 5^{8}\cdot 29^{6}\cdot 941^{4} \)	$C_2^4.C_2^3$ (as 16T392)	$[20]$ (GRH)