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 24 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.8.282912400000000000000.1	x^16 - 6x^15 + 16x^14 - 34x^13 + 58x^12 - 66x^11 + 14x^10 + 8x^9 - 62x^8 + 144x^7 - 24x^6 - 22x^5 + 13x^4 - 42x^3 + 4x^2 + 8x + 1	\( 2^{16}\cdot 5^{14}\cdot 29^{4} \)	16T1496	Trivial
16.8.380686925440000000000.1	x^16 - 4x^15 + 20x^13 - 17x^12 - 46x^11 + 62x^10 + 20x^9 - 86x^8 + 118x^7 - 114x^6 - 66x^5 + 316x^4 - 222x^3 - 70x^2 + 120x - 31	\( 2^{16}\cdot 5^{10}\cdot 29^{6} \)	16T1496	Trivial
16.4.781862084478759765625.1	x^16 - x^14 - x^13 - 11x^12 + 37x^11 + 14x^10 + 141x^9 + 131x^8 + 151x^7 + 201x^6 + 126x^5 + 96x^4 + 96x^3 + 51x^2 + 12x + 1	\( 5^{14}\cdot 71^{6} \)	16T1496	Trivial
16.4.2156696820062500000000.1	x^16 - 3x^15 - x^14 + 22x^13 - 55x^12 + 60x^11 - 45x^10 + 76x^9 - 48x^8 - 166x^7 + 487x^6 - 235x^5 - 663x^4 + 709x^3 - 176x^2 - 83x + 41	\( 2^{8}\cdot 5^{12}\cdot 431^{4} \)	16T1496	Trivial
16.0.2599902210706873778176.1	x^16 - 4x^15 + 10x^14 - 12x^13 + 6x^12 + 8x^11 - 20x^10 + 8x^9 + 7x^8 + 8x^7 - 20x^6 + 8x^5 + 6x^4 - 12x^3 + 10x^2 - 4x + 1	\( 2^{34}\cdot 73^{6} \)	16T1496	Trivial
16.0.3172348973027587890625.1	x^16 + 6x^14 + 11x^12 + 26x^10 - 9x^8 + 45x^6 - 10x^4 + 25	\( 5^{12}\cdot 11^{4}\cdot 31^{6} \)	16T1496	$[2]$
16.0.3241899901987119140625.1	x^16 - 7x^15 + 22x^14 - 38x^13 + 43x^12 - 22x^11 - 35x^10 + 86x^9 - 80x^8 + 7x^7 + 120x^6 - 211x^5 + 203x^4 - 131x^3 + 53x^2 - 11x + 1	\( 3^{8}\cdot 5^{10}\cdot 11^{6}\cdot 13^{4} \)	16T1496	$[2, 2]$
16.8.142493403492656494140625.1	x^16 - x^15 - 8x^14 + 16x^13 - 4x^12 - 30x^11 + 53x^10 + 15x^9 - 83x^8 + 15x^7 + 53x^6 - 30x^5 - 4x^4 + 16x^3 - 8x^2 - x + 1	\( 5^{12}\cdot 7^{4}\cdot 79^{6} \)	16T1496	Trivial (GRH)
16.0.474648244387840000000000.1	x^16 - 8x^15 + 24x^14 - 24x^13 + 2x^12 - 108x^11 + 412x^10 - 440x^9 + 234x^8 - 888x^7 + 1912x^6 - 1640x^5 + 2140x^4 - 3768x^3 + 4280x^2 - 2144x + 844	\( 2^{36}\cdot 5^{10}\cdot 29^{4} \)	16T1496	$[2]$
16.0.871230922174922119140625.1	x^16 - 4x^15 + 29x^14 - 70x^13 + 236x^12 - 217x^11 + 95x^10 + 2822x^9 - 6853x^8 + 20221x^7 - 18995x^6 - 1969x^5 + 75351x^4 - 286710x^3 + 538071x^2 - 463678x + 706541	\( 5^{12}\cdot 59^{4}\cdot 131^{4} \)	16T1496	$[2, 8]$
16.0.922838846045156494140625.1	x^16 - 3x^15 + 17x^14 - 46x^13 + 131x^12 - 142x^11 + 513x^10 + 835x^9 - 655x^8 + 3719x^7 - 4558x^6 - 17144x^5 + 72849x^4 - 221070x^3 + 508254x^2 - 674471x + 1152731	\( 5^{12}\cdot 7841^{4} \)	16T1496	$[16]$
16.8.1063085825545660556640625.1	x^16 - 4x^15 + 3x^12 + 84x^11 - 43x^10 - 165x^9 - 61x^8 + 228x^7 - 129x^6 + 79x^5 + 36x^4 + 138x^3 + 50x^2 - 5x - 1	\( 5^{10}\cdot 691^{6} \)	16T1496	Trivial (GRH)
16.0.2372805251213789306640625.1	x^16 - 4x^15 + 12x^14 - 46x^13 + 23x^12 - 131x^11 + 63x^10 + 659x^9 + 1849x^8 + 5605x^7 + 10205x^6 + 10653x^5 + 21062x^4 + 7970x^3 + 21255x^2 + 7044x + 11281	\( 5^{12}\cdot 9929^{4} \)	16T1496	$[22]$
16.4.2602156134400000000000000.1	x^16 + 6x^14 - 32x^13 + 29x^12 - 144x^11 + 416x^10 - 568x^9 + 1246x^8 - 3072x^7 + 5514x^6 - 7648x^5 + 7856x^4 - 5392x^3 + 2344x^2 - 256x - 379	\( 2^{24}\cdot 5^{14}\cdot 71^{4} \)	16T1496	Trivial (GRH)
16.4.3285974248179316650390625.1	x^16 - 2x^15 - 3x^14 + 13x^13 - 48x^12 - 38x^11 - 23x^10 - 73x^9 - 431x^8 + 1335x^7 - 174x^6 + 5111x^5 + 2683x^4 + 17040x^3 + 9270x^2 + 16689x + 1091	\( 5^{12}\cdot 10771^{4} \)	16T1496	Trivial (GRH)
16.0.4021669330769062744140625.1	x^16 - 2x^15 + 17x^14 - 30x^13 + 120x^12 - 181x^11 + 425x^10 - 678x^9 + 1251x^8 - 2325x^7 + 4840x^6 - 7487x^5 + 16238x^4 - 14272x^3 + 34438x^2 - 28815x + 32141	\( 5^{12}\cdot 11329^{4} \)	16T1496	$[22]$
16.0.11155710553525738792812544.1	x^16 - 4x^15 + 14x^14 - 64x^13 + 199x^12 - 468x^11 + 1104x^10 - 2040x^9 + 3459x^8 - 4492x^7 + 5922x^6 - 5208x^5 + 5171x^4 - 2988x^3 + 1516x^2 - 416x + 146	\( 2^{46}\cdot 631^{4} \)	16T1496	$[2]$
16.0.218866876534085943603515625.1	x^16 - 2x^15 - 9x^14 - 30x^13 + 265x^12 + 78x^11 - 836x^10 - 4217x^9 + 9740x^8 + 9775x^7 - 17024x^6 - 55212x^5 + 57916x^4 + 51870x^3 + 28185x^2 - 35550x + 16155	\( 3^{8}\cdot 5^{14}\cdot 11^{4}\cdot 139^{4} \)	16T1496	$[2, 2, 2]$ (GRH)
16.8.363399780582976484619140625.1	x^16 - 8x^15 + 22x^14 + 39x^13 - 364x^12 + 353x^11 + 1133x^10 - 1565x^9 - 5285x^8 + 18864x^7 + 11557x^6 - 71279x^5 + 24594x^4 - 58165x^3 + 7489x^2 + 288164x - 126149	\( 3^{8}\cdot 5^{12}\cdot 3881^{4} \)	16T1496	$[2]$ (GRH)
16.8.3032754840090903896728515625.1	x^16 - 4x^15 + 13x^14 - 42x^13 - 113x^12 + 726x^11 - 756x^10 - 728x^9 + 1108x^8 + 2649x^7 - 7901x^6 + 3896x^5 + 7426x^4 - 4265x^3 - 3505x^2 + 295x + 295	\( 5^{12}\cdot 59^{6}\cdot 131^{4} \)	16T1496	$[2]$ (GRH)
16.16.10684260544555930240000000000.1	x^16 - 4x^15 - 36x^14 + 156x^13 + 391x^12 - 2002x^11 - 1394x^10 + 11138x^9 - 733x^8 - 27098x^7 + 9856x^6 + 24792x^5 - 4989x^4 - 10046x^3 - 1886x^2 + 284x + 71	\( 2^{16}\cdot 5^{10}\cdot 19^{4}\cdot 71^{6} \)	16T1496	Trivial (GRH)
16.0.45693790427241426095360180224.1	x^16 + 8x^14 - 64x^13 + 196x^12 - 304x^11 + 1088x^10 - 3632x^9 + 6770x^8 - 5984x^7 + 9688x^6 - 32928x^5 + 69116x^4 - 87824x^3 + 159216x^2 - 287120x + 265409	\( 2^{58}\cdot 631^{4} \)	16T1496	$[468]$ (GRH)
16.16.126933971543808993896728515625.1	x^16 - 4x^15 - 54x^14 + 225x^13 + 1027x^12 - 4752x^11 - 7319x^10 + 45684x^9 + 532x^8 - 184970x^7 + 167394x^6 + 174664x^5 - 297890x^4 + 53446x^3 + 103419x^2 - 61303x + 10021	\( 5^{12}\cdot 11^{6}\cdot 4139^{4} \)	16T1496	Trivial (GRH)
16.0.879975068812771568896884765625.1	x^16 - 6x^15 + 95x^14 - 420x^13 + 3516x^12 - 12135x^11 + 67230x^10 - 183922x^9 + 717275x^8 - 1612435x^7 + 4288394x^6 - 8562175x^5 + 14806730x^4 - 25438633x^3 + 37525970x^2 - 24641603x + 61523369	\( 5^{10}\cdot 547889^{4} \)	16T1496	$[15795]$ (GRH)