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
16.4.36693661450240000000000.1	x^16 - 8x^13 - 6x^12 + 8x^11 - 4x^10 + 12x^9 - 91x^8 + 416x^7 - 776x^6 + 948x^5 - 644x^4 - 152x^3 + 356x^2 - 132x + 31	\( 2^{28}\cdot 5^{10}\cdot 241^{3} \)	16T1360	Trivial (GRH)
16.4.36693661450240000000000.2	x^16 - 2x^15 - 7x^14 + 2x^13 - 5x^12 + 24x^11 + 22x^10 - 60x^9 - 12x^8 - 2x^6 + 52x^5 - 15x^4 + 14x^3 + 67x^2 + 54x + 31	\( 2^{28}\cdot 5^{10}\cdot 241^{3} \)	16T1360	Trivial (GRH)
16.10.423544570986942386889818112.1	x^16 - 44x^14 + 702x^12 - 4876x^10 + 12653x^8 + 12032x^6 - 116748x^4 + 194392x^2 - 103823	\( -\,2^{48}\cdot 3^{8}\cdot 47^{5} \)	16T1360	Trivial (GRH)
16.2.423544570986942386889818112.1	x^16 - 12x^14 - 190x^12 + 1384x^10 + 16413x^8 - 188x^6 - 235188x^4 - 309260x^2 - 103823	\( -\,2^{48}\cdot 3^{8}\cdot 47^{5} \)	16T1360	$[2, 2]$ (GRH)
16.6.423544570986942386889818112.1	x^16 + 8x^14 - 74x^12 - 572x^10 + 1677x^8 + 13160x^6 - 6956x^4 - 97196x^2 - 103823	\( -\,2^{48}\cdot 3^{8}\cdot 47^{5} \)	16T1360	$[2]$ (GRH)
16.10.423544570986942386889818112.2	x^16 - 44x^14 + 750x^12 - 6364x^10 + 28493x^8 - 62416x^6 + 34404x^4 + 88360x^2 - 103823	\( -\,2^{48}\cdot 3^{8}\cdot 47^{5} \)	16T1360	$[2]$ (GRH)
16.2.423544570986942386889818112.2	x^16 + 28x^14 + 106x^12 - 2224x^10 - 21486x^8 - 78020x^6 - 156698x^4 - 194392x^2 - 103823	\( -\,2^{48}\cdot 3^{8}\cdot 47^{5} \)	16T1360	$[2, 2]$ (GRH)
16.6.423544570986942386889818112.2	x^16 + 16x^14 - 132x^12 - 892x^10 + 1061x^8 + 15416x^6 + 73602x^4 + 35344x^2 - 103823	\( -\,2^{48}\cdot 3^{8}\cdot 47^{5} \)	16T1360	Trivial (GRH)
16.0.20963552577967882240000000000.1	x^16 + 70x^12 + 600x^10 + 1725x^8 + 6000x^6 + 68750x^4 + 300000x^2 + 484375	\( 2^{56}\cdot 5^{10}\cdot 31^{3} \)	16T1360	$[4]$ (GRH)
16.0.20963552577967882240000000000.2	x^16 + 6x^12 - 40x^10 + 119x^8 - 160x^6 + 890x^4 - 1400x^2 + 775	\( 2^{56}\cdot 5^{10}\cdot 31^{3} \)	16T1360	$[4]$ (GRH)
16.8.41816070871416995840000000000.1	x^16 - 6x^15 - x^14 + 84x^13 - 574x^12 + 1582x^11 + 1760x^10 - 12170x^9 + 33347x^8 - 57334x^7 - 66718x^6 + 332270x^5 - 559210x^4 + 302348x^3 - 410547x^2 - 2864814x - 1114489	\( 2^{24}\cdot 5^{10}\cdot 761^{5} \)	16T1360	Trivial (GRH)
16.8.41816070871416995840000000000.2	x^16 - 6x^15 + 27x^14 - 120x^13 - 280x^12 + 3082x^11 - 14962x^10 + 56100x^9 - 51313x^8 - 250320x^7 + 1447360x^6 - 3321280x^5 - 3705440x^4 + 19282960x^3 - 1259768x^2 - 25661216x + 967184	\( 2^{24}\cdot 5^{10}\cdot 761^{5} \)	16T1360	Trivial (GRH)
16.12.10704914143082750935040000000000.1	x^16 - 8x^15 + 8x^14 + 44x^13 - 434x^12 + 1944x^11 - 5638x^10 + 53604x^9 + 131044x^8 - 1676940x^7 - 847870x^6 + 13170272x^5 + 6980273x^4 - 37161060x^3 - 28910620x^2 + 22581108x + 18421911	\( 2^{32}\cdot 5^{10}\cdot 761^{5} \)	16T1360	Trivial (GRH)
16.4.10704914143082750935040000000000.1	x^16 - 8x^15 + 32x^14 - 36x^13 - 1408x^12 + 8548x^11 - 44354x^10 + 114852x^9 - 205841x^8 - 208908x^7 + 2305578x^6 - 7603764x^5 + 19279562x^4 - 27521876x^3 + 53236782x^2 - 34630408x + 69429119	\( 2^{32}\cdot 5^{10}\cdot 761^{5} \)	16T1360	$[2, 2]$ (GRH)
16.12.10704914143082750935040000000000.2	x^16 - 4x^15 - 44x^14 + 144x^13 - 773x^12 + 660x^11 + 57384x^10 - 56564x^9 - 510761x^8 + 993092x^7 - 9940324x^6 - 29825900x^5 + 170611937x^4 + 450315088x^3 - 514469646x^2 - 2050188192x - 1309532249	\( 2^{32}\cdot 5^{10}\cdot 761^{5} \)	16T1360	Trivial (GRH)
16.4.10704914143082750935040000000000.2	x^16 + 90x^14 - 56x^13 + 1609x^12 - 1976x^11 - 56396x^10 + 177724x^9 - 2155256x^8 + 6678928x^7 - 25810424x^6 + 33988936x^5 - 37254054x^4 - 70355216x^3 + 125361914x^2 - 166669624x + 72311951	\( 2^{32}\cdot 5^{10}\cdot 761^{5} \)	16T1360	$[2, 2]$ (GRH)
16.0.2740458020629184239370240000000000.1	x^16 + 206x^14 + 16665x^12 + 700728x^10 + 16860739x^8 + 237751620x^6 + 1901560165x^4 + 7673353250x^2 + 11017777025	\( 2^{40}\cdot 5^{10}\cdot 761^{5} \)	16T1360	$[2, 2, 2, 142756]$ (GRH)
16.16.2740458020629184239370240000000000.1	x^16 - 296x^14 + 32730x^12 - 1789768x^10 + 52634519x^8 - 825989400x^6 + 6211122190x^4 - 16215388000x^2 + 11017777025	\( 2^{40}\cdot 5^{10}\cdot 761^{5} \)	16T1360	Trivial (GRH)
16.8.2740458020629184239370240000000000.1	x^16 + 170x^14 + 5879x^12 - 215060x^10 - 8613381x^8 + 97742840x^6 + 183275435x^4 - 4372363550x^2 + 11017777025	\( 2^{40}\cdot 5^{10}\cdot 761^{5} \)	16T1360	$[2]$ (GRH)
16.0.2740458020629184239370240000000000.2	x^16 + 282x^14 + 31085x^12 + 1718124x^10 + 50358639x^8 + 754622820x^6 + 5074169165x^4 + 13117090650x^2 + 11017777025	\( 2^{40}\cdot 5^{10}\cdot 761^{5} \)	16T1360	$[2, 2, 6, 31908]$ (GRH)
16.16.2740458020629184239370240000000000.2	x^16 - 226x^14 + 20015x^12 - 909288x^10 + 23102024x^8 - 332792910x^6 + 2590542930x^4 - 9439672300x^2 + 11017777025	\( 2^{40}\cdot 5^{10}\cdot 761^{5} \)	16T1360	Trivial (GRH)
16.8.2740458020629184239370240000000000.2	x^16 + 68x^14 - 2110x^12 - 173674x^10 - 668896x^8 + 65004620x^6 + 299670385x^4 - 6862583850x^2 + 11017777025	\( 2^{40}\cdot 5^{10}\cdot 761^{5} \)	16T1360	$[2]$ (GRH)
16.8.2740458020629184239370240000000000.3	x^16 + 30x^14 - 8549x^12 - 501580x^10 - 3800056x^8 + 127201150x^6 + 328287790x^4 - 5617473700x^2 + 11017777025	\( 2^{40}\cdot 5^{10}\cdot 761^{5} \)	16T1360	$[2]$ (GRH)
16.8.2740458020629184239370240000000000.4	x^16 - 50x^14 - 8929x^12 + 381600x^10 + 11965279x^8 - 116935260x^6 - 3599138085x^4 - 14912365750x^2 + 11017777025	\( 2^{40}\cdot 5^{10}\cdot 761^{5} \)	16T1360	$[2]$ (GRH)