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 20 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.74504940890829813.1	x^16 - 6x^15 + 14x^14 - 9x^13 - 24x^12 + 60x^11 - 47x^10 - 22x^9 + 103x^8 - 163x^7 + 192x^6 - 172x^5 + 107x^4 - 43x^3 + 14x^2 - 5x + 1	\( 3^{8}\cdot 7^{3}\cdot 13^{6}\cdot 19^{3} \)	16T1477	Trivial
16.2.195238297600000000.1	x^16 - 4x^15 + 6x^14 - 6x^13 + 10x^12 - 26x^11 + 52x^10 - 54x^9 - 12x^8 + 82x^7 - 54x^6 - 24x^5 + 49x^4 - 32x^3 + 16x^2 - 6x + 1	\( -\,2^{24}\cdot 5^{8}\cdot 31^{3} \)	16T1477	Trivial
16.2.3123812761600000000.1	x^16 - 2x^12 - 5x^8 + 26x^4 - 31	\( -\,2^{28}\cdot 5^{8}\cdot 31^{3} \)	16T1477	Trivial
16.4.8310412719464453125.1	x^16 - 2x^15 - x^14 + 6x^13 - 2x^12 - 5x^10 + 5x^9 - 11x^8 + 17x^7 + 4x^6 - 11x^5 - 43x^4 - 20x^3 - 3x^2 + 5x + 1	\( 5^{8}\cdot 11^{6}\cdot 229^{3} \)	16T1477	Trivial
16.0.12591335010550238397.1	x^16 - x^15 - 4x^14 - 2x^13 + 16x^12 - 4x^11 + 18x^10 - 37x^9 - 41x^8 + 11x^7 + 56x^6 + 61x^5 + 7x^4 - 28x^3 - 8x^2 + 3x + 1	\( 3^{8}\cdot 7^{3}\cdot 13^{8}\cdot 19^{3} \)	16T1477	$[2]$
16.0.1005559939055198828125.1	x^16 - 3x^15 + 8x^14 - 17x^13 + 35x^12 - 73x^11 + 158x^10 - 201x^9 + 119x^8 - 3x^7 + 52x^6 - 81x^5 + 20x^4 + 34x^3 + 17x^2 + 4x + 1	\( 5^{8}\cdot 11^{8}\cdot 229^{3} \)	16T1477	$[2]$
16.4.5194007949665283203125.1	x^16 - 4x^15 + 2x^14 + 3x^13 - 17x^12 + 83x^11 - 78x^10 + 4x^9 + 125x^8 - 237x^7 - 957x^6 + 2298x^5 - 2524x^4 + 1173x^3 + 1878x^2 - 1230x + 571	\( 5^{12}\cdot 11^{6}\cdot 229^{3} \)	16T1477	Trivial
16.8.47478162926559980078125.1	x^16 - x^15 - 14x^14 + 18x^13 + 46x^12 - 32x^11 - 89x^10 - 84x^9 + 153x^8 + 163x^7 + 167x^6 + 68x^5 - 407x^4 - 455x^3 - 254x^2 - 92x + 1	\( 5^{8}\cdot 19^{3}\cdot 29^{6}\cdot 31^{3} \)	16T1477	Trivial (GRH)
16.4.193605144103655992578125.2	x^16 - 4x^15 + 19x^14 - 40x^13 + 92x^12 - 74x^11 - 100x^10 + 499x^9 - 1065x^8 + 601x^7 - 330x^6 - 111x^5 + 1682x^4 - 410x^3 - 1171x^2 + 799x + 271	\( 5^{8}\cdot 29^{6}\cdot 941^{3} \)	16T1477	$[4]$
16.0.628474961909499267578125.1	x^16 - x^15 - 13x^14 + 8x^13 + 37x^12 + 10x^11 + 103x^10 - 134x^9 - 520x^8 + 779x^7 + 123x^6 - 4000x^5 + 4652x^4 - 568x^3 + 1172x^2 + 14581x + 7951	\( 5^{12}\cdot 11^{8}\cdot 229^{3} \)	16T1477	$[2, 2]$
16.16.17139616816488152808203125.1	x^16 - 4x^15 - 38x^14 + 148x^13 + 526x^12 - 2026x^11 - 3067x^10 + 12556x^9 + 5604x^8 - 33409x^7 + 6724x^6 + 25387x^5 - 13100x^4 - 2749x^3 + 3029x^2 - 644x + 41	\( 5^{8}\cdot 19^{5}\cdot 29^{6}\cdot 31^{3} \)	16T1477	Trivial (GRH)
16.4.17139616816488152808203125.1	x^16 - 3x^15 + 10x^14 - 33x^13 + 52x^12 - 23x^11 - 307x^10 + 1565x^9 - 5274x^8 + 14121x^7 - 31412x^6 + 56450x^5 - 88705x^4 + 112080x^3 - 115415x^2 + 85873x - 21059	\( 5^{8}\cdot 19^{5}\cdot 29^{6}\cdot 31^{3} \)	16T1477	$[2, 2]$
16.12.29673851829099987548828125.1	x^16 - 3x^15 - 21x^14 + 86x^13 - 35x^12 - 176x^11 + 709x^10 - 3025x^9 + 8152x^8 - 14111x^7 - 309x^6 + 55818x^5 - 67883x^4 - 23715x^3 + 61506x^2 - 2204x - 14669	\( 5^{12}\cdot 19^{3}\cdot 29^{6}\cdot 31^{3} \)	16T1477	Trivial (GRH)
16.8.29673851829099987548828125.1	x^16 - 2x^15 + x^14 + 10x^13 - 74x^12 - 56x^11 + 95x^10 + 1154x^9 + 97x^8 - 4897x^7 - 295x^6 + 6817x^5 + 15576x^4 - 13760x^3 - 32751x^2 + 11694x + 13691	\( 5^{12}\cdot 19^{3}\cdot 29^{6}\cdot 31^{3} \)	16T1477	Trivial (GRH)
16.16.45626514572424140855078125.1	x^16 - 5x^15 - 37x^14 + 148x^13 + 617x^12 - 1580x^11 - 5603x^10 + 6722x^9 + 26852x^8 - 5404x^7 - 58752x^6 - 26447x^5 + 36579x^4 + 30433x^3 + 2337x^2 - 1771x + 121	\( 5^{8}\cdot 19^{3}\cdot 29^{6}\cdot 31^{5} \)	16T1477	Trivial (GRH)
16.12.121003215064784995361328125.1	x^16 - x^15 - 37x^14 + 24x^13 + 442x^12 - 140x^11 - 1518x^10 - 378x^9 - 4525x^8 + 8032x^7 + 31797x^6 - 55905x^5 - 70683x^4 + 157319x^3 + 136913x^2 - 82011x - 57769	\( 5^{12}\cdot 29^{6}\cdot 941^{3} \)	16T1477	Trivial (GRH)
16.8.3111528885555034854400000000.1	x^16 + 10x^14 - 131x^12 - 1149x^10 + 6015x^8 + 36962x^6 - 109489x^4 - 290377x^2 + 495349	\( 2^{16}\cdot 5^{8}\cdot 19^{3}\cdot 29^{6}\cdot 31^{3} \)	16T1477	Trivial (GRH)
16.8.3111528885555034854400000000.2	x^16 - 33x^14 - 525x^12 + 6009x^10 + 22553x^8 - 106926x^6 - 218307x^4 + 512430x^2 + 495349	\( 2^{16}\cdot 5^{8}\cdot 19^{3}\cdot 29^{6}\cdot 31^{3} \)	16T1477	Trivial (GRH)
16.0.12688106723977199129600000000.1	x^16 + 81x^14 + 2406x^12 + 34724x^10 + 267248x^8 + 1121762x^6 + 2480479x^4 + 2537877x^2 + 791381	\( 2^{16}\cdot 5^{8}\cdot 29^{6}\cdot 941^{3} \)	16T1477	$[2, 2056]$ (GRH)
16.0.20769334990028142310400000000.1	x^16 + 55x^14 + 1238x^12 + 14935x^10 + 105960x^8 + 454835x^6 + 1158836x^4 + 1608050x^2 + 932669	\( 2^{16}\cdot 5^{8}\cdot 29^{6}\cdot 1109^{3} \)	16T1477	$[2, 2442]$ (GRH)