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 19 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.2624400000000000000.2	x^16 - 5x^14 + 15x^12 - 30x^10 + 45x^8 - 50x^6 + 50x^4 - 50x^2 + 25	\( 2^{16}\cdot 3^{8}\cdot 5^{14} \)	$C_2\times C_2^3.C_4$ (as 16T99)	Trivial
16.0.5856400000000000000.1	x^16 - 12x^14 + 58x^12 - 139x^10 + 185x^8 - 139x^6 + 58x^4 - 12x^2 + 1	\( 2^{16}\cdot 5^{14}\cdot 11^{4} \)	$C_2\times C_2^3.C_4$ (as 16T99)	Trivial
16.0.26214400000000000000.2	x^16 + 4x^14 + 17x^12 + 42x^10 + 50x^8 + 18x^6 - 8x^4 - 4x^2 + 1	\( 2^{32}\cdot 5^{14} \)	$C_2\times C_2^3.C_4$ (as 16T99)	Trivial
16.0.26214400000000000000.3	x^16 - 4x^14 + 17x^12 - 42x^10 + 50x^8 - 18x^6 - 8x^4 + 4x^2 + 1	\( 2^{32}\cdot 5^{14} \)	$C_2\times C_2^3.C_4$ (as 16T99)	Trivial
16.0.212576400000000000000.3	x^16 - 15x^14 + 105x^12 - 450x^10 + 1305x^8 - 2700x^6 + 4050x^4 - 4050x^2 + 2025	\( 2^{16}\cdot 3^{12}\cdot 5^{14} \)	$C_2\times C_2^3.C_4$ (as 16T99)	$[2]$
16.0.419430400000000000000.1	x^16 + 4x^14 - 8x^12 + 12x^10 + 190x^8 + 268x^6 + 152x^4 + 36x^2 + 1	\( 2^{36}\cdot 5^{14} \)	$C_2\times C_2^3.C_4$ (as 16T99)	$[2]$
16.8.419430400000000000000.1	x^16 - 4x^14 - 8x^12 - 12x^10 + 190x^8 - 268x^6 + 152x^4 - 36x^2 + 1	\( 2^{36}\cdot 5^{14} \)	$C_2\times C_2^3.C_4$ (as 16T99)	Trivial (GRH)
16.8.671846400000000000000.3	x^16 - 8x^15 + 24x^14 - 28x^13 - 12x^12 + 72x^11 - 104x^10 + 146x^9 - 172x^8 + 32x^7 + 144x^6 - 104x^5 + 33x^4 - 66x^3 + 56x^2 - 14x + 1	\( 2^{24}\cdot 3^{8}\cdot 5^{14} \)	$C_2\times C_2^3.C_4$ (as 16T99)	Trivial (GRH)
16.0.671846400000000000000.5	x^16 - 2x^15 - 6x^14 - 12x^13 - 7x^12 + 78x^11 + 366x^10 + 634x^9 + 438x^8 + 88x^7 + 24x^6 + 14x^5 - 12x^4 + 16x^3 + 6x^2 - 6x + 1	\( 2^{24}\cdot 3^{8}\cdot 5^{14} \)	$C_2\times C_2^3.C_4$ (as 16T99)	$[4]$
16.0.2294177990240478515625.3	x^16 - 26x^14 + 317x^12 - 2378x^10 + 11860x^8 - 39487x^6 + 84497x^4 - 104554x^2 + 58081	\( 3^{12}\cdot 5^{14}\cdot 29^{4} \)	$C_2\times C_2^3.C_4$ (as 16T99)	$[2, 2]$
16.0.13344870400000000000000.1	x^16 - 4x^15 + 8x^14 + 32x^13 + 6x^12 - 24x^11 + 560x^10 + 996x^9 + 939x^8 + 2952x^7 + 9480x^6 + 10748x^5 + 10406x^4 + 19284x^3 + 25992x^2 + 9348x + 1681	\( 2^{24}\cdot 5^{14}\cdot 19^{4} \)	$C_2\times C_2^3.C_4$ (as 16T99)	$[2, 2]$ (GRH)
16.0.13344870400000000000000.2	x^16 - 4x^15 + 18x^14 - 78x^13 + 256x^12 - 664x^11 + 1580x^10 - 1874x^9 + 1954x^8 - 1378x^7 - 3600x^6 + 3618x^5 - 89x^4 - 2506x^3 + 4432x^2 + 5658x + 1681	\( 2^{24}\cdot 5^{14}\cdot 19^{4} \)	$C_2\times C_2^3.C_4$ (as 16T99)	$[2, 2]$ (GRH)
16.0.170504539372564697265625.1	x^16 - 13x^14 - 5x^13 + 68x^12 + 65x^11 - 31x^10 + 180x^9 + 345x^8 - 170x^7 + 264x^6 + 2150x^5 + 1983x^4 + 185x^3 - 63x^2 - 5x + 1	\( 5^{14}\cdot 11^{8}\cdot 19^{4} \)	$C_2\times C_2^3.C_4$ (as 16T99)	$[2, 4]$ (GRH)
16.16.54660589158400000000000000.1	x^16 - 36x^14 + 502x^12 - 3468x^10 + 12675x^8 - 24612x^6 + 24162x^4 - 10664x^2 + 1681	\( 2^{36}\cdot 5^{14}\cdot 19^{4} \)	$C_2\times C_2^3.C_4$ (as 16T99)	Trivial (GRH)
16.8.54660589158400000000000000.1	x^16 - 16x^14 - 38x^12 + 472x^10 + 1915x^8 - 1472x^6 - 13398x^4 - 17464x^2 + 1681	\( 2^{36}\cdot 5^{14}\cdot 19^{4} \)	$C_2\times C_2^3.C_4$ (as 16T99)	$[2]$ (GRH)
16.8.54660589158400000000000000.2	x^16 + 4x^14 - 8x^12 - 508x^10 + 2070x^8 - 6452x^6 + 30152x^4 - 59284x^2 + 32761	\( 2^{36}\cdot 5^{14}\cdot 19^{4} \)	$C_2\times C_2^3.C_4$ (as 16T99)	$[2]$ (GRH)
16.0.54660589158400000000000000.3	x^16 + 24x^14 + 292x^12 + 2192x^10 + 10940x^8 + 36848x^6 + 80512x^4 + 95776x^2 + 55696	\( 2^{36}\cdot 5^{14}\cdot 19^{4} \)	$C_2\times C_2^3.C_4$ (as 16T99)	$[2, 4, 24]$ (GRH)
16.0.150351248768400000000000000.1	x^16 + 26x^14 + 317x^12 + 2378x^10 + 11860x^8 + 39487x^6 + 84497x^4 + 104554x^2 + 58081	\( 2^{16}\cdot 3^{12}\cdot 5^{14}\cdot 29^{4} \)	$C_2\times C_2^3.C_4$ (as 16T99)	$[2, 2, 4, 36]$ (GRH)
16.16.150351248768400000000000000.1	x^16 - 41x^14 + 677x^12 - 5843x^10 + 28585x^8 - 79537x^6 + 116702x^4 - 69544x^2 + 1	\( 2^{16}\cdot 3^{12}\cdot 5^{14}\cdot 29^{4} \)	$C_2\times C_2^3.C_4$ (as 16T99)	Trivial (GRH)