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 22 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.4.654015157911836164096.5	x^16 - 12x^14 - 16x^13 + 32x^12 + 104x^11 + 72x^10 - 88x^9 - 108x^8 + 304x^7 + 1068x^6 + 1736x^5 + 1864x^4 + 1400x^3 + 704x^2 + 208x + 31	\( 2^{40}\cdot 29^{6} \)	16T1048	Trivial
16.4.2604274900538516045824.1	x^16 - 4x^14 - 4x^13 - 2x^12 + 4x^10 + 64x^9 + 158x^8 - 500x^6 - 888x^5 - 792x^4 - 400x^3 - 104x^2 - 8x + 2	\( 2^{44}\cdot 23^{6} \)	16T1048	Trivial (GRH)
16.4.2604274900538516045824.2	x^16 - 4x^14 - 4x^13 - 2x^12 + 24x^11 - 20x^10 + 28x^9 - 94x^8 + 176x^7 - 240x^6 + 268x^5 - 174x^4 - 40x^3 + 152x^2 - 92x + 23	\( 2^{44}\cdot 23^{6} \)	16T1048	Trivial (GRH)
16.0.2821046020387461136384.3	x^16 - 16x^14 + 110x^12 - 414x^10 + 946x^8 - 1520x^6 + 2160x^4 - 2442x^2 + 1369	\( 2^{40}\cdot 37^{6} \)	16T1048	Trivial (GRH)
16.0.2821046020387461136384.4	x^16 + 18x^12 - 26x^10 + 210x^8 - 452x^6 + 356x^4 - 962x^2 + 1369	\( 2^{40}\cdot 37^{6} \)	16T1048	Trivial (GRH)
16.4.167427880425430058008576.5	x^16 - 16x^14 + 74x^12 - 32x^10 - 378x^8 + 928x^6 - 1102x^4 + 841	\( 2^{48}\cdot 29^{6} \)	16T1048	Trivial (GRH)
16.0.2162984691411674873266176.1	x^16 - 12x^14 - 57x^12 + 1080x^10 + 2466x^8 - 40041x^6 - 130248x^4 + 660879x^2 + 3207681	\( 2^{16}\cdot 3^{12}\cdot 199^{6} \)	16T1048	$[2]$ (GRH)
16.0.2162984691411674873266176.2	x^16 - 18x^14 + 270x^12 - 2592x^10 + 20556x^8 - 118476x^6 + 534384x^4 - 1595781x^2 + 3207681	\( 2^{16}\cdot 3^{12}\cdot 199^{6} \)	16T1048	$[2]$ (GRH)
16.8.21943454004015643378515625.1	x^16 - 2x^15 - 6x^14 + 11x^13 - 76x^12 - 70x^11 + 251x^10 - 60x^9 + 728x^8 + 4407x^7 + 5236x^6 - 3964x^5 - 14617x^4 - 24504x^3 - 49184x^2 - 27208x + 17936	\( 5^{8}\cdot 19^{6}\cdot 103^{6} \)	16T1048	Trivial (GRH)
16.0.58102542838005760000000000.3	x^16 - 2x^15 - 4x^14 - 4x^13 + 38x^12 - 128x^11 + 664x^10 - 1992x^9 + 4556x^8 - 8728x^7 + 13840x^6 - 17600x^5 + 15792x^4 - 10400x^3 + 5824x^2 - 2176x + 584	\( 2^{28}\cdot 5^{10}\cdot 53^{6} \)	16T1048	$[8]$ (GRH)
16.0.58102542838005760000000000.4	x^16 - 2x^15 + 18x^14 + 34x^13 + 148x^12 + 582x^11 + 1574x^10 + 5218x^9 + 12846x^8 + 19394x^7 + 19806x^6 + 16782x^5 + 14900x^4 + 15322x^3 + 15226x^2 + 10270x + 3281	\( 2^{28}\cdot 5^{10}\cdot 53^{6} \)	16T1048	$[8]$ (GRH)
16.0.85100355196860246401286144.3	x^16 - 45x^14 + 863x^12 - 8460x^10 + 47667x^8 - 159048x^6 + 307568x^4 - 310482x^2 + 134689	\( 2^{16}\cdot 3^{12}\cdot 367^{6} \)	16T1048	Trivial (GRH)
16.0.85100355196860246401286144.4	x^16 - 36x^14 + 581x^12 - 5364x^10 + 30546x^8 - 108174x^6 + 230375x^4 - 266442x^2 + 134689	\( 2^{16}\cdot 3^{12}\cdot 367^{6} \)	16T1048	Trivial (GRH)
16.0.1733972862707275312245243904.1	x^16 + 12x^14 - 316x^12 - 548x^10 + 43878x^8 - 291116x^6 + 873866x^4 - 1878268x^2 + 3286969	\( 2^{48}\cdot 7^{4}\cdot 37^{6} \)	16T1048	Trivial (GRH)
16.8.2163460585448341410282471424.5	x^16 - 32x^14 + 116x^12 + 1984x^10 - 3738x^8 - 49952x^6 - 82956x^4 + 49729	\( 2^{44}\cdot 223^{6} \)	16T1048	$[2]$ (GRH)
16.0.270988555121057382164053622784.1	x^16 + 16x^14 + 250x^12 + 2934x^10 + 22994x^8 + 26224x^6 + 1321320x^4 - 2068374x^2 + 20043529	\( 2^{40}\cdot 3^{8}\cdot 11^{4}\cdot 37^{6} \)	16T1048	$[2, 2]$ (GRH)
16.8.1438086201607169204454400000000.1	x^16 - 42x^14 - 704x^12 + 5182x^10 + 53472x^8 - 286134x^6 - 716159x^4 + 2821994x^2 + 3829849	\( 2^{16}\cdot 5^{8}\cdot 19^{6}\cdot 103^{6} \)	16T1048	$[2]$ (GRH)
16.8.1438086201607169204454400000000.2	x^16 - 47x^14 + 55x^12 + 15884x^10 - 49245x^8 - 536218x^6 - 114536x^4 + 3225136x^2 + 3829849	\( 2^{16}\cdot 5^{8}\cdot 19^{6}\cdot 103^{6} \)	16T1048	$[2]$ (GRH)
16.0.1438086201607169204454400000000.3	x^16 + 92x^14 + 3481x^12 + 69871x^10 + 797640x^8 + 5120439x^6 + 16818149x^4 + 21568097x^2 + 3829849	\( 2^{16}\cdot 5^{8}\cdot 19^{6}\cdot 103^{6} \)	16T1048	$[2, 4, 2424]$ (GRH)
16.16.1438086201607169204454400000000.3	x^16 - 92x^14 + 3481x^12 - 69871x^10 + 797640x^8 - 5120439x^6 + 16818149x^4 - 21568097x^2 + 3829849	\( 2^{16}\cdot 5^{8}\cdot 19^{6}\cdot 103^{6} \)	16T1048	Trivial (GRH)
16.0.15256656512850458090056729600000000.1	x^16 + 268x^14 + 29251x^12 + 1682196x^10 + 54789202x^8 + 1002211012x^6 + 9430297664x^4 + 36291649124x^2 + 40630868041	\( 2^{16}\cdot 5^{8}\cdot 19^{6}\cdot 103^{8} \)	16T1048	$[2, 2, 2, 2, 134740]$ (GRH)
16.16.15256656512850458090056729600000000.1	x^16 - 268x^14 + 29251x^12 - 1682196x^10 + 54789202x^8 - 1002211012x^6 + 9430297664x^4 - 36291649124x^2 + 40630868041	\( 2^{16}\cdot 5^{8}\cdot 19^{6}\cdot 103^{8} \)	16T1048	Trivial (GRH)