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
16.4.11292016640000000000.1	x^16 - 6x^14 - 2x^13 + 2x^12 + 12x^11 + 35x^10 - 10x^9 - 30x^8 - 12x^7 - 42x^6 + 34x^5 + 20x^4 - 24x^3 + 5x^2 + 2x - 1	\( 2^{24}\cdot 5^{10}\cdot 41^{3} \)	16T1398	Trivial
16.2.80779509760000000000.1	x^16 - 6x^15 + 19x^14 - 36x^13 + 49x^12 - 32x^11 - 43x^10 + 172x^9 - 312x^8 + 352x^7 - 257x^6 + 144x^5 - 79x^4 + 62x^3 - 56x^2 + 24x - 1	\( -\,2^{24}\cdot 5^{10}\cdot 79^{3} \)	16T1398	Trivial
16.4.282300416000000000000.1	x^16 - 2x^15 - x^14 + 12x^13 - 26x^12 + 28x^11 - 4x^10 - 6x^9 + 19x^8 - 44x^7 - 49x^6 + 90x^5 - 133x^4 + 54x^3 - 20x^2 - 20x + 1	\( 2^{24}\cdot 5^{12}\cdot 41^{3} \)	16T1398	Trivial
16.6.2019487744000000000000.1	x^16 - 4x^15 + 8x^14 - 8x^13 - 2x^12 + 20x^11 - 26x^10 - 44x^9 + 248x^8 - 452x^7 + 306x^6 + 276x^5 - 797x^4 + 776x^3 - 388x^2 + 96x - 9	\( -\,2^{24}\cdot 5^{12}\cdot 79^{3} \)	16T1398	Trivial (GRH)
16.2.20679554498560000000000.1	x^16 - 8x^15 + 26x^14 - 36x^13 - 13x^12 + 64x^11 + 136x^10 - 436x^9 + 126x^8 + 352x^7 + 152x^6 - 732x^5 + 479x^4 - 176x^3 + 34x^2 - 4x - 1	\( -\,2^{32}\cdot 5^{10}\cdot 79^{3} \)	16T1398	$[2]$ (GRH)
16.8.72206103511040000000000.3	x^16 - 2x^15 - 13x^14 + 22x^13 + 61x^12 - 30x^11 - 274x^10 - 164x^9 + 1091x^8 + 178x^7 - 1576x^6 - 200x^5 + 586x^4 + 656x^3 + 38x^2 - 224x - 79	\( 2^{24}\cdot 5^{10}\cdot 761^{3} \)	16T1398	Trivial (GRH)
16.6.112589990684262400000000.1	x^16 + 12x^14 + 48x^12 + 64x^10 - 34x^8 - 120x^6 - 16x^4 + 48x^2 - 4	\( -\,2^{58}\cdot 5^{8} \)	16T1398	Trivial (GRH)
16.0.1805152587776000000000000.3	x^16 - 6x^15 + 37x^14 - 136x^13 + 433x^12 - 1136x^11 + 2691x^10 - 5628x^9 + 10358x^8 - 16196x^7 + 21159x^6 - 23100x^5 + 20703x^4 - 14682x^3 + 7828x^2 - 2956x + 631	\( 2^{24}\cdot 5^{12}\cdot 761^{3} \)	16T1398	$[8]$ (GRH)
16.8.18484762498826240000000000.1	x^16 - 22x^14 - 24x^13 + 29x^12 + 320x^11 + 1324x^10 - 948x^9 - 6843x^8 + 1704x^7 + 15362x^6 - 2372x^5 - 20563x^4 + 5744x^3 + 12878x^2 - 9768x + 2169	\( 2^{32}\cdot 5^{10}\cdot 761^{3} \)	16T1398	Trivial (GRH)
16.12.18484762498826240000000000.3	x^16 - 22x^14 - 12x^13 + 157x^12 + 184x^11 - 378x^10 - 996x^9 - 163x^8 + 2232x^7 + 1788x^6 - 1684x^5 - 2661x^4 + 24x^3 + 1528x^2 + 232x - 239	\( 2^{32}\cdot 5^{10}\cdot 761^{3} \)	16T1398	Trivial (GRH)
16.4.18484762498826240000000000.3	x^16 + 14x^14 - 12x^13 + 67x^12 - 112x^11 + 70x^10 - 552x^9 - 296x^8 - 936x^7 - 566x^6 + 152x^5 + 1874x^4 + 4952x^3 + 4972x^2 + 1804x + 79	\( 2^{32}\cdot 5^{10}\cdot 761^{3} \)	16T1398	Trivial (GRH)
16.12.18484762498826240000000000.4	x^16 - 12x^14 - 12x^13 - 8x^12 + 120x^11 + 356x^10 - 232x^9 - 632x^8 - 1104x^7 - 226x^6 + 3832x^5 + 561x^4 - 3352x^3 + 210x^2 + 668x - 89	\( 2^{32}\cdot 5^{10}\cdot 761^{3} \)	16T1398	Trivial (GRH)
16.4.18484762498826240000000000.4	x^16 - 12x^13 - 8x^12 + 8x^11 - 116x^10 - 100x^9 - 98x^8 + 400x^7 + 1482x^6 + 840x^5 + 1963x^4 + 7464x^3 + 12292x^2 + 12084x + 5409	\( 2^{32}\cdot 5^{10}\cdot 761^{3} \)	16T1398	$[2]$ (GRH)
16.0.462119062470656000000000000.1	x^16 + 34x^14 + 487x^12 + 3862x^10 + 19025x^8 + 62768x^6 + 140512x^4 + 194816x^2 + 194816	\( 2^{32}\cdot 5^{12}\cdot 761^{3} \)	16T1398	$[2, 8]$ (GRH)
16.0.2830725463103588061237215232.3	x^16 + 24x^14 + 236x^12 + 1240x^10 + 3813x^8 + 7060x^6 + 7734x^4 + 4612x^2 + 1153	\( 2^{48}\cdot 3^{8}\cdot 1153^{3} \)	16T1398	$[2, 2, 134]$ (GRH)
16.16.2830725463103588061237215232.3	x^16 - 24x^14 + 236x^12 - 1240x^10 + 3813x^8 - 7060x^6 + 7734x^4 - 4612x^2 + 1153	\( 2^{48}\cdot 3^{8}\cdot 1153^{3} \)	16T1398	Trivial (GRH)
16.0.4732099199699517440000000000.1	x^16 + 62x^14 + 1543x^12 + 20412x^10 + 157716x^8 + 727930x^6 + 1948310x^4 + 2739600x^2 + 1541025	\( 2^{40}\cdot 5^{10}\cdot 761^{3} \)	16T1398	$[2, 708]$ (GRH)
16.16.4732099199699517440000000000.1	x^16 - 62x^14 + 1543x^12 - 20412x^10 + 157716x^8 - 727930x^6 + 1948310x^4 - 2739600x^2 + 1541025	\( 2^{40}\cdot 5^{10}\cdot 761^{3} \)	16T1398	Trivial (GRH)
16.8.4732099199699517440000000000.7	x^16 + 8x^14 - 322x^12 - 642x^10 + 12596x^8 + 11740x^6 - 90585x^4 - 114150x^2 + 19025	\( 2^{40}\cdot 5^{10}\cdot 761^{3} \)	16T1398	Trivial (GRH)
16.8.4732099199699517440000000000.8	x^16 + 4x^14 - 608x^12 + 6556x^10 - 19234x^8 - 14500x^6 + 72160x^4 + 76100x^2 + 19025	\( 2^{40}\cdot 5^{10}\cdot 761^{3} \)	16T1398	Trivial (GRH)
16.8.4732099199699517440000000000.9	x^16 - 8x^14 - 322x^12 + 642x^10 + 12596x^8 - 11740x^6 - 90585x^4 + 114150x^2 + 19025	\( 2^{40}\cdot 5^{10}\cdot 761^{3} \)	16T1398	$[2]$ (GRH)
16.8.4732099199699517440000000000.10	x^16 - 4x^14 - 608x^12 - 6556x^10 - 19234x^8 + 14500x^6 + 72160x^4 - 76100x^2 + 19025	\( 2^{40}\cdot 5^{10}\cdot 761^{3} \)	16T1398	Trivial (GRH)