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
16.0.13852994719059873.1	x^16 + x^14 - 3x^13 - 7x^12 - 9x^11 - 5x^10 + 18x^9 + 49x^8 + 87x^7 + 113x^6 + 105x^5 + 77x^4 + 45x^3 + 20x^2 + 6x + 1	\( 3^{12}\cdot 13^{4}\cdot 97^{3} \)	16T1432	Trivial
16.0.28903161821248377.1	x^16 - 7x^15 + 23x^14 - 52x^13 + 98x^12 - 161x^11 + 228x^10 - 280x^9 + 301x^8 - 284x^7 + 238x^6 - 173x^5 + 106x^4 - 52x^3 + 19x^2 - 5x + 1	\( 3^{8}\cdot 13^{6}\cdot 97^{3} \)	16T1432	Trivial
16.4.68076302383738701.1	x^16 - x^15 - 2x^14 + 2x^13 - 7x^12 + 5x^11 + 29x^10 - 19x^9 - 50x^8 + 28x^7 + 49x^6 - 22x^5 - 28x^4 + 9x^3 + 9x^2 - x - 1	\( 3^{4}\cdot 13^{8}\cdot 101^{3} \)	16T1432	Trivial
16.4.243112369495703125.1	x^16 - x^15 - 3x^14 + x^13 + x^12 - 3x^10 + 2x^9 - 4x^8 + 11x^7 + 13x^6 - 25x^5 - 4x^4 + 13x^3 - 2x^2 - 2x + 1	\( 5^{8}\cdot 11^{4}\cdot 349^{3} \)	16T1432	Trivial
16.0.6891748502900000000.1	x^16 - 3x^14 + 8x^12 - 12x^10 + x^8 + 25x^6 + 13x^4 - 58x^2 + 29	\( 2^{8}\cdot 5^{8}\cdot 29^{3}\cdot 41^{4} \)	16T1432	Trivial
16.0.6891748502900000000.2	x^16 - 3x^15 + 2x^14 + x^13 - 4x^11 + 2x^10 + 20x^9 - 31x^8 - 30x^7 + 148x^6 - 222x^5 + 190x^4 - 103x^3 + 38x^2 - 9x + 1	\( 2^{8}\cdot 5^{8}\cdot 29^{3}\cdot 41^{4} \)	16T1432	Trivial
16.8.8310412719464453125.1	x^16 - x^15 - 7x^14 + 14x^13 + 15x^12 - 48x^11 + 3x^10 + 73x^9 - 28x^8 - 110x^7 + 88x^6 + 99x^5 - 187x^4 + 105x^3 - 12x^2 - 7x + 1	\( 5^{8}\cdot 11^{6}\cdot 229^{3} \)	16T1432	Trivial
16.0.40917952102400000000.1	x^16 - 4x^15 + 6x^14 + 10x^12 - 112x^11 + 258x^10 - 132x^9 - 401x^8 + 760x^7 - 214x^6 - 980x^5 + 1742x^4 - 1520x^3 + 788x^2 - 232x + 31	\( 2^{32}\cdot 5^{8}\cdot 29^{3} \)	16T1432	Trivial
16.8.40917952102400000000.1	x^16 - 4x^15 + 6x^14 - 12x^13 + 4x^12 - 12x^11 + 40x^10 + 24x^9 + 103x^8 - 276x^7 - 20x^6 + 168x^5 - 2x^4 - 4x^3 - 14x^2 - 4x + 1	\( 2^{32}\cdot 5^{8}\cdot 29^{3} \)	16T1432	Trivial
16.12.230208256960351953125.1	x^16 - 7x^15 + 12x^14 + 11x^13 - 39x^12 + 14x^11 + 12x^10 - 6x^9 + 36x^8 - 57x^7 - 26x^6 + 73x^5 + 8x^4 - 33x^3 - 4x^2 + 5x + 1	\( 5^{8}\cdot 29^{4}\cdot 941^{3} \)	16T1432	Trivial
16.0.654687233638400000000.1	x^16 - 22x^12 + 52x^10 + 447x^8 + 468x^6 - 150x^4 + 116x^2 + 29	\( 2^{36}\cdot 5^{8}\cdot 29^{3} \)	16T1432	Trivial
16.4.143880160600219970703125.1	x^16 - 3x^15 + 7x^14 - 19x^13 + 36x^12 + 77x^11 - 320x^10 + 823x^9 - 1341x^8 + 2059x^7 - 265x^6 + 1114x^5 + 1656x^4 - 1912x^3 + 663x^2 + 294x - 229	\( 5^{12}\cdot 29^{4}\cdot 941^{3} \)	16T1432	Trivial
16.4.193605144103655992578125.1	x^16 - 5x^15 + 19x^14 - 42x^13 + 78x^12 - 173x^11 + 209x^10 - 665x^9 + 870x^8 - 1804x^7 + 2586x^6 - 3343x^5 + 4565x^4 - 3379x^3 + 2751x^2 - 1158x - 149	\( 5^{8}\cdot 29^{6}\cdot 941^{3} \)	16T1432	$[2]$
16.0.15086928328153625600000000.1	x^16 + 23x^14 + 216x^12 + 1089x^10 + 3243x^8 + 5873x^6 + 6349x^4 + 3764x^2 + 941	\( 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 941^{3} \)	16T1432	$[130]$ (GRH)
16.12.15086928328153625600000000.1	x^16 - 15x^14 + 2x^12 + 598x^10 - 2116x^8 + 1858x^6 + 1529x^4 - 2823x^2 + 941	\( 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 941^{3} \)	16T1432	Trivial (GRH)
16.16.15086928328153625600000000.1	x^16 - 23x^14 + 216x^12 - 1089x^10 + 3243x^8 - 5873x^6 + 6349x^4 - 3764x^2 + 941	\( 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 941^{3} \)	16T1432	Trivial (GRH)
16.8.15086928328153625600000000.1	x^16 - 9x^14 - 16x^12 + 237x^10 - 72x^8 - 1179x^6 + 76x^4 + 1882x^2 + 941	\( 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 941^{3} \)	16T1432	Trivial (GRH)
16.8.15086928328153625600000000.2	x^16 - 6x^14 - 36x^12 + 218x^10 + 163x^8 - 1491x^6 - 304x^4 + 2823x^2 + 941	\( 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 941^{3} \)	16T1432	Trivial (GRH)
16.8.15086928328153625600000000.3	x^16 + 9x^14 - 16x^12 - 237x^10 - 72x^8 + 1179x^6 + 76x^4 - 1882x^2 + 941	\( 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 941^{3} \)	16T1432	$[2]$ (GRH)
16.8.15086928328153625600000000.4	x^16 + 6x^14 - 36x^12 - 218x^10 + 163x^8 + 1491x^6 - 304x^4 - 2823x^2 + 941	\( 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 941^{3} \)	16T1432	$[2]$ (GRH)
16.0.24695998799082214400000000.1	x^16 + 24x^14 + 234x^12 + 1217x^10 + 3710x^8 + 6827x^6 + 7451x^4 + 4436x^2 + 1109	\( 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 1109^{3} \)	16T1432	$[146]$ (GRH)
16.16.24695998799082214400000000.1	x^16 - 24x^14 + 234x^12 - 1217x^10 + 3710x^8 - 6827x^6 + 7451x^4 - 4436x^2 + 1109	\( 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 1109^{3} \)	16T1432	Trivial (GRH)