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
16.0.65161500126431909.1	x^16 - 3x^14 - 4x^13 + 3x^12 + 13x^11 + 16x^10 + 4x^9 - 14x^8 - 20x^7 - 10x^6 + 5x^5 + 15x^4 + 14x^3 + 7x^2 + 3x + 1	\( 17^{4}\cdot 149\cdot 269^{4} \)	16T1944	Trivial
16.0.96648936429137261.1	x^16 - 2x^15 - 2x^14 + 6x^13 - 3x^11 + x^10 - 4x^9 + x^8 + 4x^7 + x^6 + 3x^5 - 6x^3 - 2x^2 + 2x + 1	\( 13\cdot 17^{5}\cdot 269^{4} \)	16T1944	Trivial
16.2.1343547471949962304.1	x^16 + 5x^14 + 6x^12 + 2x^10 + x^8 - 16x^6 + x^4 + 17x^2 - 9	\( -\,2^{6}\cdot 12037^{4} \)	16T1944	Trivial
16.2.1826384844681980007.1	x^16 - x^15 - 3x^14 - 2x^13 + 2x^12 + 16x^11 + 7x^10 - 5x^9 - 27x^8 - 5x^7 + 7x^6 + 16x^5 + 2x^4 - 2x^3 - 3x^2 - x + 1	\( -\,3\cdot 29\cdot 12037^{4} \)	16T1944	Trivial
16.6.2162271712669470583.1	x^16 - 2x^15 - 2x^14 + 2x^13 + 9x^12 + 9x^11 - 21x^10 - 33x^9 + 9x^8 + 39x^7 + 15x^6 - 12x^5 - 10x^4 - 6x^3 - x^2 + 3x + 1	\( -\,103\cdot 12037^{4} \)	16T1944	Trivial
16.6.2330215146663215871.1	x^16 - x^15 - x^14 + 7x^13 - 3x^12 - 5x^11 - 5x^10 - 11x^9 + 17x^8 - 6x^7 - 17x^6 + 25x^5 + 2x^4 - 19x^3 + 4x^2 + 8x + 1	\( -\,3\cdot 37\cdot 12037^{4} \)	16T1944	Trivial
16.4.3127946458133505989.1	x^16 - 7x^15 + 24x^14 - 58x^13 + 115x^12 - 200x^11 + 322x^10 - 471x^9 + 565x^8 - 502x^7 + 287x^6 - 64x^5 - 35x^4 + 29x^3 - x^2 - 5x + 1	\( 149\cdot 12037^{4} \)	16T1944	Trivial
16.4.3799720194108487141.1	x^16 - 4x^15 + x^14 + 25x^13 - 55x^12 + x^11 + 166x^10 - 247x^9 + 32x^8 + 291x^7 - 338x^6 + 100x^5 + 118x^4 - 153x^3 + 77x^2 - 13x - 1	\( 181\cdot 12037^{4} \)	16T1944	Trivial
16.8.115385034158949540033.1	x^16 - 10x^14 - 3x^13 + 48x^12 + 11x^11 - 127x^10 + 31x^9 + 149x^8 - 121x^7 - 41x^6 + 87x^5 - 44x^4 + 18x^2 - 9x + 1	\( 3^{4}\cdot 4273^{5} \)	16T1944	Trivial
16.0.9346187766874912742673.1	x^16 - 5x^15 + 10x^14 - 7x^13 + 3x^12 + 17x^11 - 35x^10 + 79x^9 - 84x^8 + 82x^7 + 38x^6 - 147x^5 + 281x^4 - 187x^3 + 143x^2 - 27x + 16	\( 3^{8}\cdot 4273^{5} \)	16T1944	$[2]$
16.8.22376666708006423560192.1	x^16 - 8x^15 + 18x^14 + 14x^13 - 97x^12 + 36x^11 + 217x^10 - 128x^9 - 319x^8 + 152x^7 + 341x^6 - 68x^5 - 230x^4 - 20x^3 + 73x^2 + 18x - 7	\( 2^{16}\cdot 947^{4}\cdot 424537 \)	16T1944	Trivial
16.8.26130580103505867675852.1	x^16 - 3x^15 - 3x^14 + 18x^13 - 22x^12 + 5x^11 + 26x^10 - 57x^9 + 72x^8 - 57x^7 + 26x^6 + 5x^5 - 22x^4 + 18x^3 - 3x^2 - 3x + 1	\( 2^{2}\cdot 3\cdot 17^{4}\cdot 97^{4}\cdot 131^{4} \)	16T1944	Trivial (GRH)
16.8.26130580103505867675852.2	x^16 - 6x^15 + 9x^14 + x^13 - 18x^12 + 48x^11 - 43x^10 + 47x^9 + 27x^8 - 4x^7 - 25x^6 - 148x^5 + 119x^4 + 72x^3 - 75x^2 + 4x + 4	\( 2^{2}\cdot 3\cdot 17^{4}\cdot 97^{4}\cdot 131^{4} \)	16T1944	Trivial
16.0.75537189434878320443392.1	x^16 + 10x^14 + 37x^12 + 58x^10 + 21x^8 - 36x^6 - 25x^4 + 10x^2 + 7	\( 2^{32}\cdot 7\cdot 1259^{4} \)	16T1944	$[4]$
16.10.87101933678352892252840.1	x^16 - 2x^15 - 11x^14 + 17x^13 + 29x^12 - 43x^11 - 7x^10 + 35x^9 - 18x^8 + 35x^7 - 7x^6 - 43x^5 + 29x^4 + 17x^3 - 11x^2 - 2x + 1	\( -\,2^{3}\cdot 5\cdot 17^{4}\cdot 97^{4}\cdot 131^{4} \)	16T1944	Trivial
16.6.87101933678352892252840.1	x^16 - 6x^15 + 4x^14 + 39x^13 - 95x^12 + 73x^11 - 11x^10 + 4x^9 - 54x^8 + 95x^7 + 114x^6 - 22x^5 - 3x^4 - 313x^3 - 443x^2 - 280x - 36	\( -\,2^{3}\cdot 5\cdot 17^{4}\cdot 97^{4}\cdot 131^{4} \)	16T1944	$[2]$
16.10.87101933678352892252840.2	x^16 - x^15 - 7x^14 - 14x^13 + 33x^12 + 50x^11 + 111x^10 - 89x^9 - 278x^8 - 282x^7 - 86x^6 + 273x^5 + 222x^4 - 17x^3 - 53x^2 - 14x - 1	\( -\,2^{3}\cdot 5\cdot 17^{4}\cdot 97^{4}\cdot 131^{4} \)	16T1944	Trivial
16.6.87101933678352892252840.2	x^16 - 6x^15 + 100x^13 - 376x^12 + 556x^11 + 115x^10 - 1891x^9 + 3306x^8 - 2261x^7 - 1068x^6 + 3931x^5 - 4280x^4 + 2793x^3 - 1199x^2 + 320x - 40	\( -\,2^{3}\cdot 5\cdot 17^{4}\cdot 97^{4}\cdot 131^{4} \)	16T1944	$[2]$
16.12.124120255491652871460297.1	x^16 - 5x^15 - 4x^14 + 45x^13 - 9x^12 - 135x^11 - 15x^10 + 222x^9 + 300x^8 - 338x^7 - 675x^6 + 434x^5 + 527x^4 - 251x^3 - 106x^2 + 15x - 8	\( 3\cdot 17^{4}\cdot 19\cdot 97^{4}\cdot 131^{4} \)	16T1944	Trivial
16.4.124120255491652871460297.1	x^16 - 8x^14 - 27x^13 + 3x^12 + 113x^11 + 244x^10 + 342x^9 + 199x^8 + 14x^7 + 56x^6 + 102x^5 + 207x^4 + 74x^3 - 211x^2 - 129x - 6	\( 3\cdot 17^{4}\cdot 19\cdot 97^{4}\cdot 131^{4} \)	16T1944	$[2]$
16.4.165493673988870495280396.1	x^16 - 6x^15 + 11x^14 - 11x^13 + 21x^12 - 31x^11 + 33x^10 - 37x^9 + 40x^8 - 37x^7 + 33x^6 - 31x^5 + 21x^4 - 11x^3 + 11x^2 - 6x + 1	\( 2^{2}\cdot 17^{4}\cdot 19\cdot 97^{4}\cdot 131^{4} \)	16T1944	Trivial
16.2.267838446060935143677483.1	x^16 - 7x^15 + 25x^14 - 28x^13 - 110x^12 + 648x^11 - 1621x^10 + 2390x^9 - 1337x^8 - 2440x^7 + 8238x^6 - 11873x^5 + 11601x^4 - 7806x^3 + 3700x^2 - 966x + 225	\( -\,3\cdot 17^{4}\cdot 41\cdot 97^{4}\cdot 131^{4} \)	16T1944	$[2]$
16.2.285258832796605722128051.1	x^16 - 2x^15 - 3x^14 - 8x^13 - 8x^12 - 14x^11 - 11x^10 - 15x^9 - 11x^8 - 15x^7 - 11x^6 - 14x^5 - 8x^4 - 8x^3 - 3x^2 - 2x + 1	\( -\,17^{4}\cdot 97^{4}\cdot 131^{5} \)	16T1944	$[2]$
16.12.385426056526711548218817.1	x^16 - 6x^15 + 20x^14 - 48x^13 + 63x^12 - 39x^11 - 288x^10 + 1021x^9 - 795x^8 - 593x^7 + 944x^6 - 149x^5 - 225x^4 + 90x^3 + 7x^2 - 8x + 1	\( 3\cdot 17^{4}\cdot 59\cdot 97^{4}\cdot 131^{4} \)	16T1944	Trivial
16.14.3612726245193459267796992.1	x^16 - 24x^14 + 152x^12 - 248x^10 - 488x^8 + 1664x^6 - 1488x^4 + 480x^2 - 48	\( -\,2^{30}\cdot 3^{9}\cdot 643^{4} \)	16T1944	Trivial (GRH)
16.14.35676952034653344666763264.1	x^16 - 16x^14 + 86x^12 - 162x^10 - 19x^8 + 353x^6 - 351x^4 + 129x^2 - 16	\( -\,2^{14}\cdot 17^{4}\cdot 97^{4}\cdot 131^{4} \)	16T1944	Trivial (GRH)
16.0.3460664347361374432676036608.1	x^16 + 37x^14 + 470x^12 + 2616x^10 + 6625x^8 + 7739x^6 + 4268x^4 + 1067x^2 + 97	\( 2^{14}\cdot 17^{4}\cdot 97^{5}\cdot 131^{4} \)	16T1944	$[2, 480]$ (GRH)
16.16.3460664347361374432676036608.1	x^16 - 27x^14 + 277x^12 - 1381x^10 + 3563x^8 - 4785x^6 + 3201x^4 - 970x^2 + 97	\( 2^{14}\cdot 17^{4}\cdot 97^{5}\cdot 131^{4} \)	16T1944	Trivial (GRH)
16.0.3460664347361374432676036608.2	x^16 + 36x^14 + 487x^12 + 3298x^10 + 12452x^8 + 27261x^6 + 34241x^4 + 22795x^2 + 6208	\( 2^{14}\cdot 17^{4}\cdot 97^{5}\cdot 131^{4} \)	16T1944	$[2, 88]$ (GRH)
16.16.3460664347361374432676036608.2	x^16 - 34x^14 + 466x^12 - 3337x^10 + 13402x^8 - 29739x^6 + 32689x^4 - 12901x^2 + 873	\( 2^{14}\cdot 17^{4}\cdot 97^{5}\cdot 131^{4} \)	16T1944	Trivial (GRH)