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 30 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.2.3613648921600000000.1	x^16 - 2x^15 + 2x^14 + 4x^13 - 15x^12 + 24x^11 - 6x^10 - 18x^9 + 36x^8 - 18x^7 - 6x^6 + 24x^5 - 15x^4 + 4x^3 + 2x^2 - 2x + 1	\( -\,2^{16}\cdot 5^{8}\cdot 109^{4} \)	16T1870	Trivial
16.6.3613648921600000000.1	x^16 - 11x^14 + 46x^12 - 98x^10 + 123x^8 - 90x^6 + 32x^4 - x^2 - 1	\( -\,2^{16}\cdot 5^{8}\cdot 109^{4} \)	16T1870	Trivial
16.0.8548377480396800000.1	x^16 - 6x^14 + 17x^12 - 28x^10 + 42x^8 - 58x^6 + 48x^4 - 20x^2 + 5	\( 2^{24}\cdot 5^{5}\cdot 113^{4} \)	16T1870	Trivial
16.0.8548377480396800000.2	x^16 - 4x^14 - 2x^12 - 8x^10 + 67x^8 + 32x^6 + 42x^4 + 20x^2 + 5	\( 2^{24}\cdot 5^{5}\cdot 113^{4} \)	16T1870	Trivial
16.2.57818382745600000000.1	x^16 + 6x^14 + 21x^12 + 43x^10 + 48x^8 + 25x^6 - 3x^4 - 9x^2 - 1	\( -\,2^{20}\cdot 5^{8}\cdot 109^{4} \)	16T1870	Trivial
16.6.57818382745600000000.1	x^16 - 6x^14 + 21x^12 - 43x^10 + 48x^8 - 25x^6 - 3x^4 + 9x^2 - 1	\( -\,2^{20}\cdot 5^{8}\cdot 109^{4} \)	16T1870	Trivial
16.4.4281965657233100374016.1	x^16 - 2x^15 - 3x^14 + 6x^13 - 6x^12 + 46x^11 - 83x^10 + 94x^9 - 205x^8 + 188x^7 - 50x^6 + 104x^5 + 89x^4 - 162x^3 - 47x^2 + 30x + 7	\( 2^{24}\cdot 761^{5} \)	16T1870	Trivial
16.0.274045802062918423937024.1	x^16 - 6x^15 + 17x^14 - 26x^13 - 9x^12 + 68x^11 - 60x^10 - 60x^9 + 437x^8 + 238x^7 + 255x^6 + 734x^5 + 160x^4 - 386x^3 - 137x^2 + 54x + 23	\( 2^{30}\cdot 761^{5} \)	16T1870	Trivial
16.4.274045802062918423937024.1	x^16 - 6x^15 + 19x^14 - 62x^13 + 124x^12 - 178x^11 + 263x^10 + 54x^9 + 203x^8 - 264x^7 - 772x^6 - 1228x^5 - 1695x^4 - 1398x^3 - 671x^2 - 190x - 25	\( 2^{30}\cdot 761^{5} \)	16T1870	Trivial
16.8.274045802062918423937024.1	x^16 - 6x^15 + 5x^14 + 32x^13 - 66x^12 + 4x^11 + 12x^10 + 272x^9 - 837x^8 + 1226x^7 - 217x^6 - 1480x^5 + 767x^4 + 838x^3 - 497x^2 - 68x + 46	\( 2^{30}\cdot 761^{5} \)	16T1870	Trivial
16.0.274045802062918423937024.2	x^16 - 6x^15 + 17x^14 - 20x^13 - 13x^12 + 114x^11 - 239x^10 + 192x^9 + 124x^8 - 668x^7 + 1304x^6 - 1736x^5 + 2067x^4 - 2118x^3 + 1573x^2 - 780x + 252	\( 2^{30}\cdot 761^{5} \)	16T1870	$[3]$
16.8.1096183208251673695748096.1	x^16 - 16x^14 + 154x^12 - 184x^11 - 710x^10 + 1512x^9 + 1241x^8 - 4656x^7 + 1626x^6 + 4268x^5 - 4713x^4 + 904x^3 + 1192x^2 - 748x + 127	\( 2^{32}\cdot 761^{5} \)	16T1870	Trivial
16.0.32995303182626734400000000.1	x^16 + 26x^14 + 256x^12 + 1244x^10 + 3261x^8 + 4776x^6 + 3872x^4 + 1614x^2 + 269	\( 2^{12}\cdot 5^{8}\cdot 11^{4}\cdot 269^{5} \)	16T1870	$[2, 12]$
16.8.32995303182626734400000000.1	x^16 - x^15 + 2x^14 + 42x^13 - 73x^12 - 100x^11 - 63x^10 + 135x^9 + 937x^8 - 221x^7 - 1612x^6 + 13x^5 + 1224x^4 + 95x^3 - 485x^2 + 74x + 61	\( 2^{12}\cdot 5^{8}\cdot 11^{4}\cdot 269^{5} \)	16T1870	Trivial (GRH)
16.8.32995303182626734400000000.2	x^16 - 20x^14 - 16x^13 + 124x^12 + 180x^11 - 100x^10 - 584x^9 - 1360x^8 + 752x^7 + 4608x^6 - 2112x^5 - 3344x^4 + 4064x^3 - 2336x^2 - 1216x + 704	\( 2^{12}\cdot 5^{8}\cdot 11^{4}\cdot 269^{5} \)	16T1870	Trivial (GRH)
16.8.32995303182626734400000000.3	x^16 - x^15 - 22x^14 + 10x^13 + 219x^12 + 44x^11 - 1303x^10 - 585x^9 + 3615x^8 + 1107x^7 - 3252x^6 + 1011x^5 + 808x^4 - 905x^3 - 247x^2 + 228x + 41	\( 2^{12}\cdot 5^{8}\cdot 11^{4}\cdot 269^{5} \)	16T1870	Trivial (GRH)
16.12.164976515913133672000000000.1	x^16 - 2x^15 + x^14 + 52x^13 - 169x^12 + 4x^11 + 1084x^10 - 3386x^9 + 1148x^8 + 13712x^7 - 21038x^6 - 4780x^5 + 29495x^4 - 19004x^3 + 2359x^2 + 588x - 101	\( 2^{12}\cdot 5^{9}\cdot 11^{4}\cdot 269^{5} \)	16T1870	Trivial (GRH)
16.4.164976515913133672000000000.1	x^16 - x^15 + 3x^14 + 8x^13 + 6x^12 + 36x^11 - 121x^10 + 361x^9 - 284x^8 - 407x^7 + 1763x^6 - 424x^5 + 932x^4 + 3508x^3 + 259x^2 + 1175x + 1681	\( 2^{12}\cdot 5^{9}\cdot 11^{4}\cdot 269^{5} \)	16T1870	$[2]$ (GRH)
16.8.164976515913133672000000000.1	x^16 - x^15 - 11x^14 + 28x^13 - 27x^12 + 9x^11 + 4x^10 + 73x^9 - 23x^8 - 1542x^7 + 3979x^6 + 541x^5 - 10401x^4 + 6356x^3 + 5806x^2 - 5584x + 956	\( 2^{12}\cdot 5^{9}\cdot 11^{4}\cdot 269^{5} \)	16T1870	Trivial (GRH)
16.12.164976515913133672000000000.2	x^16 - 2x^15 - 14x^14 + 27x^13 + 2x^12 - 102x^11 + 819x^10 + 45x^9 - 4482x^8 + 1131x^7 + 9602x^6 - 7075x^5 - 16118x^4 + 6423x^3 + 13479x^2 + 989x - 1849	\( 2^{12}\cdot 5^{9}\cdot 11^{4}\cdot 269^{5} \)	16T1870	Trivial (GRH)
16.8.164976515913133672000000000.2	x^16 - 2x^15 - 18x^14 - 5x^13 + 189x^12 + 312x^11 - 1301x^10 - 1838x^9 + 4981x^8 + 3957x^7 - 9615x^6 - 2371x^5 + 7987x^4 - 2244x^3 - 634x^2 + 456x + 36	\( 2^{12}\cdot 5^{9}\cdot 11^{4}\cdot 269^{5} \)	16T1870	Trivial (GRH)
16.12.527924850922027750400000000.1	x^16 - 18x^14 + 104x^12 - 168x^10 - 339x^8 + 1212x^6 - 672x^4 - 538x^2 + 269	\( 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 269^{5} \)	16T1870	Trivial (GRH)
16.16.527924850922027750400000000.1	x^16 - 26x^14 + 256x^12 - 1244x^10 + 3261x^8 - 4776x^6 + 3872x^4 - 1614x^2 + 269	\( 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 269^{5} \)	16T1870	Trivial (GRH)
16.4.527924850922027750400000000.1	x^16 - 2x^15 + 2x^14 - 14x^13 - 44x^12 - 2x^11 + 122x^10 + 332x^9 + 708x^8 - 3096x^7 + 648x^6 - 5152x^5 + 10956x^4 + 4544x^3 - 6080x^2 - 4304	\( 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 269^{5} \)	16T1870	$[2, 2]$ (GRH)
16.8.527924850922027750400000000.1	x^16 + 14x^14 - 67x^12 - 588x^10 + 628x^8 + 4540x^6 - 3104x^4 - 8608x^2 + 4304	\( 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 269^{5} \)	16T1870	$[2]$ (GRH)
16.12.527924850922027750400000000.2	x^16 - 21x^14 - 18x^13 + 160x^12 + 254x^11 - 543x^10 - 1110x^9 + 1024x^8 + 1812x^7 - 1365x^6 - 506x^5 + 1045x^4 - 1162x^3 - 62x^2 + 524x - 44	\( 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 269^{5} \)	16T1870	Trivial (GRH)
16.4.527924850922027750400000000.2	x^16 + 18x^14 + 104x^12 + 168x^10 - 339x^8 - 1212x^6 - 672x^4 + 538x^2 + 269	\( 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 269^{5} \)	16T1870	$[2]$ (GRH)
16.4.2639624254610138752000000000.1	x^16 - x^15 - 13x^14 + 23x^13 + x^12 + 38x^11 + 180x^10 - 215x^9 - 556x^8 - 1320x^7 - 86x^6 + 1971x^5 + 1519x^4 + 265x^3 - 3815x^2 - 2324x - 1949	\( 2^{16}\cdot 5^{9}\cdot 11^{4}\cdot 269^{5} \)	16T1870	$[2]$ (GRH)
16.0.8446797614752444006400000000.1	x^16 + 33x^14 + 427x^12 + 2816x^10 + 10448x^8 + 22460x^6 + 27344x^4 + 17216x^2 + 4304	\( 2^{20}\cdot 5^{8}\cdot 11^{4}\cdot 269^{5} \)	16T1870	$[2, 88]$ (GRH)
16.16.8446797614752444006400000000.1	x^16 - 38x^14 + 530x^12 - 3422x^10 + 11109x^8 - 17836x^6 + 12536x^4 - 3228x^2 + 269	\( 2^{20}\cdot 5^{8}\cdot 11^{4}\cdot 269^{5} \)	16T1870	Trivial (GRH)