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 32 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.29865750236756037.1	x^16 - x^15 - 2x^14 + 8x^12 - 2x^11 - 16x^10 + 11x^9 + 19x^8 - 30x^7 + 19x^6 - 25x^5 + 48x^4 - 50x^3 + 28x^2 - 8x + 1	\( 3^{8}\cdot 16573^{3} \)	16T1872	Trivial
16.0.2419125769177238997.1	x^16 - 3x^15 + 3x^14 + 8x^13 - 19x^12 + 3x^11 + 54x^10 - 99x^9 + 42x^8 + 56x^7 - 102x^6 + 24x^5 + 51x^4 - 38x^3 + 9x^2 + 40x + 13	\( 3^{12}\cdot 16573^{3} \)	16T1872	Trivial
16.4.7376062834448828125.1	x^16 - 5x^15 + 10x^14 - 3x^13 - 24x^12 + 47x^11 - 33x^10 + 3x^9 + 17x^8 - 48x^7 + 61x^6 - 42x^5 + 34x^4 - 18x^3 + 4x^2 - 4x - 1	\( 5^{8}\cdot 31^{3}\cdot 859^{3} \)	16T1872	Trivial
16.4.8195775610914453125.1	x^16 - 4x^15 + 9x^14 - 17x^13 + 18x^12 - 18x^11 + 13x^10 - 11x^9 + 11x^8 + x^7 - 3x^6 - 17x^5 - 2x^4 + 22x^3 + 17x^2 + 6x - 1	\( 5^{8}\cdot 27581^{3} \)	16T1872	Trivial
16.6.672488745723457421875.1	x^16 - 3x^15 + x^14 + x^12 + 20x^11 - 49x^10 - 24x^9 + 159x^8 - 242x^7 + 370x^6 - 324x^5 + 207x^4 - 49x^3 - 245x^2 + 217x - 41	\( -\,5^{8}\cdot 119851^{3} \)	16T1872	Trivial
16.0.771319558913600000000.1	x^16 - 3x^15 + 8x^14 - 29x^13 + 79x^12 - 162x^11 + 383x^10 - 767x^9 + 1258x^8 - 2211x^7 + 3339x^6 - 4082x^5 + 5253x^4 - 4915x^3 + 3400x^2 - 4125x + 2929	\( 2^{12}\cdot 5^{8}\cdot 7841^{3} \)	16T1872	Trivial
16.0.771319558913600000000.2	x^16 - 4x^15 + 6x^14 + 10x^13 - 50x^12 + 76x^11 + 101x^10 - 368x^9 + 408x^8 + 806x^7 - 2017x^6 + 1662x^5 + 2484x^4 - 5604x^3 + 5589x^2 - 1480x + 400	\( 2^{12}\cdot 5^{8}\cdot 7841^{3} \)	16T1872	Trivial
16.6.420305466077160888671875.1	x^16 - 6x^15 + 7x^14 + 28x^13 - 88x^12 + 85x^11 - 302x^10 + 1961x^9 - 6740x^8 + 14919x^7 - 22562x^6 + 21295x^5 - 6488x^4 - 12943x^3 + 27877x^2 - 24424x + 3781	\( -\,5^{12}\cdot 119851^{3} \)	16T1872	Trivial (GRH)
16.8.463175124098862339453125.1	x^16 - 5x^15 - 6x^14 + 73x^13 - 168x^12 + 261x^11 - 398x^10 + 382x^9 + 17x^8 - 370x^7 + 472x^6 - 871x^5 + 759x^4 + 100x^3 - 140x^2 - 65x - 41	\( 5^{8}\cdot 439^{3}\cdot 2411^{3} \)	16T1872	Trivial (GRH)
16.0.24471271802225000000000000.3	x^16 - 2x^15 + 31x^14 - 78x^13 + 481x^12 - 1036x^11 + 4189x^10 - 6854x^9 + 20667x^8 - 22064x^7 + 57849x^6 - 36406x^5 + 101581x^4 - 33138x^3 + 94071x^2 - 22942x + 26951	\( 2^{12}\cdot 5^{14}\cdot 9929^{3} \)	16T1872	$[2]$ (GRH)
16.4.24471271802225000000000000.3	x^16 - 7x^15 + 16x^14 - 3x^13 - 224x^12 + 1429x^11 - 4751x^10 + 12576x^9 - 28293x^8 + 48021x^7 - 68431x^6 + 77634x^5 - 52679x^4 + 8287x^3 + 43171x^2 - 69872x + 32716	\( 2^{12}\cdot 5^{14}\cdot 9929^{3} \)	16T1872	Trivial (GRH)
16.8.24471271802225000000000000.3	x^16 - 2x^15 - 4x^14 - 53x^13 + 141x^12 + 264x^11 - 516x^10 - 104x^9 - 1898x^8 + 9536x^7 - 8771x^6 - 20976x^5 + 52901x^4 - 62703x^3 + 43171x^2 - 9777x - 1529	\( 2^{12}\cdot 5^{14}\cdot 9929^{3} \)	16T1872	Trivial (GRH)
16.0.24471271802225000000000000.4	x^16 - 5x^15 + 41x^14 - 155x^13 + 672x^12 - 1955x^11 + 5678x^10 - 13220x^9 + 26010x^8 - 49895x^7 + 78422x^6 - 116005x^5 + 141942x^4 - 138940x^3 + 129214x^2 - 72795x + 51851	\( 2^{12}\cdot 5^{14}\cdot 9929^{3} \)	16T1872	$[6]$ (GRH)
16.4.24471271802225000000000000.4	x^16 - 5x^15 + 31x^14 - 85x^13 + 227x^12 - 70x^11 - 1152x^10 + 5525x^9 - 14215x^8 + 25905x^7 - 30383x^6 + 32000x^5 - 29888x^4 - 6895x^3 + 10364x^2 + 10070x + 2621	\( 2^{12}\cdot 5^{14}\cdot 9929^{3} \)	16T1872	Trivial (GRH)
16.8.24471271802225000000000000.4	x^16 - 2x^15 - 29x^14 - 13x^13 + 346x^12 + 489x^11 - 2001x^10 - 4129x^9 + 6632x^8 + 17956x^7 - 9696x^6 - 31191x^5 - 1604x^4 - 24178x^3 - 47594x^2 + 4483x + 13981	\( 2^{12}\cdot 5^{14}\cdot 9929^{3} \)	16T1872	Trivial (GRH)
16.10.44072222439732505600000000.1	x^16 - 32x^14 + 364x^12 - 1453x^10 - 3210x^8 + 46201x^6 - 146854x^4 + 196885x^2 - 119851	\( -\,2^{16}\cdot 5^{8}\cdot 119851^{3} \)	16T1872	Trivial (GRH)
16.2.44072222439732505600000000.1	x^16 - 277x^12 - 2665x^10 - 9245x^8 - 14890x^6 - 33514x^4 - 105370x^2 - 119851	\( -\,2^{16}\cdot 5^{8}\cdot 119851^{3} \)	16T1872	Trivial (GRH)
16.10.44072222439732505600000000.2	x^16 - 2x^14 - 144x^12 + 244x^10 + 6835x^8 - 11929x^6 - 117076x^4 + 322533x^2 - 119851	\( -\,2^{16}\cdot 5^{8}\cdot 119851^{3} \)	16T1872	Trivial (GRH)
16.2.44072222439732505600000000.2	x^16 + 16x^14 - 35x^12 - 1514x^10 - 5703x^8 + 3011x^6 - 1667x^4 - 143899x^2 - 119851	\( -\,2^{16}\cdot 5^{8}\cdot 119851^{3} \)	16T1872	Trivial (GRH)
16.6.44072222439732505600000000.3	x^16 + 2x^14 - 118x^12 - 76x^10 + 3836x^8 - 2412x^6 - 13507x^4 + 13576x^2 - 119851	\( -\,2^{16}\cdot 5^{8}\cdot 119851^{3} \)	16T1872	$[3]$ (GRH)
16.6.44072222439732505600000000.4	x^16 + 8x^14 - 169x^12 - 1473x^10 - 1358x^8 + 30276x^6 + 27721x^4 - 108806x^2 - 119851	\( -\,2^{16}\cdot 5^{8}\cdot 119851^{3} \)	16T1872	Trivial (GRH)
16.12.30354644932943042278400000000.1	x^16 - 21x^14 - 313x^12 + 5040x^10 + 6573x^8 - 338136x^6 + 1674055x^4 - 2872357x^2 + 1058429	\( 2^{16}\cdot 5^{8}\cdot 439^{3}\cdot 2411^{3} \)	16T1872	Trivial (GRH)
16.16.30354644932943042278400000000.1	x^16 - 69x^14 + 1938x^12 - 28372x^10 + 230216x^8 - 1020006x^6 + 2316187x^4 - 2532253x^2 + 1058429	\( 2^{16}\cdot 5^{8}\cdot 439^{3}\cdot 2411^{3} \)	16T1872	Trivial (GRH)
16.4.30354644932943042278400000000.1	x^16 + 65x^14 + 1443x^12 + 13180x^10 + 39415x^8 - 81405x^6 - 545739x^4 - 253680x^2 + 1058429	\( 2^{16}\cdot 5^{8}\cdot 439^{3}\cdot 2411^{3} \)	16T1872	$[2]$ (GRH)
16.8.30354644932943042278400000000.1	x^16 + 27x^14 - 258x^12 - 5716x^10 + 44746x^8 + 89343x^6 - 628402x^4 - 810879x^2 + 1058429	\( 2^{16}\cdot 5^{8}\cdot 439^{3}\cdot 2411^{3} \)	16T1872	Trivial (GRH)
16.12.30354644932943042278400000000.2	x^16 - 32x^14 + 87x^12 + 5659x^10 - 44795x^8 - 182216x^6 + 2322248x^4 - 3601580x^2 + 1058429	\( 2^{16}\cdot 5^{8}\cdot 439^{3}\cdot 2411^{3} \)	16T1872	Trivial (GRH)
16.4.30354644932943042278400000000.2	x^16 + 27x^14 - 251x^12 - 13759x^10 - 143955x^8 - 584042x^6 - 764135x^4 + 441954x^2 + 1058429	\( 2^{16}\cdot 5^{8}\cdot 439^{3}\cdot 2411^{3} \)	16T1872	$[6]$ (GRH)
16.8.30354644932943042278400000000.2	x^16 - 27x^14 - 258x^12 + 5716x^10 + 44746x^8 - 89343x^6 - 628402x^4 + 810879x^2 + 1058429	\( 2^{16}\cdot 5^{8}\cdot 439^{3}\cdot 2411^{3} \)	16T1872	Trivial (GRH)
16.8.30354644932943042278400000000.3	x^16 + 10x^14 - 316x^12 - 1296x^10 + 28265x^8 + 21273x^6 - 659599x^4 + 670612x^2 + 1058429	\( 2^{16}\cdot 5^{8}\cdot 439^{3}\cdot 2411^{3} \)	16T1872	$[2]$ (GRH)
16.0.115446638528641004057600000000.1	x^16 + 85x^14 + 2709x^12 + 41896x^10 + 344677x^8 + 1544032x^6 + 3659235x^4 + 4140999x^2 + 1652141	\( 2^{16}\cdot 5^{8}\cdot 1652141^{3} \)	16T1872	$[2, 5530]$ (GRH)
16.16.115446638528641004057600000000.1	x^16 - 67x^14 + 1783x^12 - 24503x^10 + 190864x^8 - 867148x^6 + 2249431x^4 - 3045621x^2 + 1652141	\( 2^{16}\cdot 5^{8}\cdot 1652141^{3} \)	16T1872	Trivial (GRH)
16.0.115446638528641004057600000000.2	x^16 + 67x^14 + 1783x^12 + 24503x^10 + 190864x^8 + 867148x^6 + 2249431x^4 + 3045621x^2 + 1652141	\( 2^{16}\cdot 5^{8}\cdot 1652141^{3} \)	16T1872	$[2, 3144]$ (GRH)