Global number field search results

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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
16.2.145380128593826227.1	x^16 - x^15 - 2x^14 + 2x^13 - 2x^12 + 7x^11 + 5x^10 - 24x^9 + x^8 + 35x^7 - 15x^6 - 42x^5 + 36x^4 + 23x^3 - 28x^2 + 6x - 1	\( -\,283^{7} \)	16T1691	Trivial
16.2.5381489931190917922816.2	x^16 + 2x^14 - 4x^10 - x^8 + 12x^6 - 14x^4 + 6x^2 - 1	\( -\,2^{36}\cdot 23^{8} \)	16T1691	Trivial (GRH)
16.0.1273594451169343707078953.1	x^16 - x^15 + 3x^14 - 18x^13 - 9x^12 - 37x^11 + 113x^10 + 91x^9 + 365x^8 + 238x^7 + 801x^6 + 231x^5 + 793x^4 - 314x^3 + 562x^2 - 545x + 164	\( 2777^{7} \)	16T1691	$[9]$ (GRH)
16.0.1273594451169343707078953.2	x^16 - 4x^15 + 10x^14 - 13x^13 + 22x^12 - 32x^11 + 67x^10 - 96x^9 + 131x^8 + 300x^7 - 567x^6 + 700x^5 - 736x^4 - 531x^3 + 1619x^2 - 2285x + 1838	\( 2777^{7} \)	16T1691	$[9]$ (GRH)
16.0.22613464583653166220836864.1	x^16 - 2x^15 + 10x^14 - 20x^13 + 34x^12 - 156x^11 - 20x^10 + 488x^9 + 1144x^8 + 2296x^7 - 280x^6 - 32x^5 + 384x^4 + 2136x^3 + 2824x^2 - 4144x + 1960	\( 2^{24}\cdot 389^{7} \)	16T1691	$[2]$ (GRH)
16.8.22613464583653166220836864.1	x^16 - 2x^15 - 20x^14 + 26x^13 + 168x^12 - 88x^11 - 954x^10 + 354x^9 + 3140x^8 - 3928x^7 + 1446x^6 + 7320x^5 - 22258x^4 + 12224x^3 + 13240x^2 - 10076x - 658	\( 2^{24}\cdot 389^{7} \)	16T1691	Trivial (GRH)
16.0.22613464583653166220836864.2	x^16 - 8x^15 + 38x^14 - 122x^13 + 294x^12 - 554x^11 + 972x^10 - 1434x^9 + 2414x^8 - 2720x^7 + 3986x^6 - 2768x^5 + 3578x^4 - 584x^3 + 1368x^2 + 648x + 82	\( 2^{24}\cdot 389^{7} \)	16T1691	$[2]$ (GRH)
16.4.22613464583653166220836864.2	x^16 - 6x^15 + 18x^14 - 48x^13 + 78x^12 + 104x^11 - 1044x^10 + 3168x^9 - 4684x^8 + 568x^7 + 13104x^6 - 32800x^5 + 44784x^4 - 38232x^3 + 19992x^2 - 3392x - 1816	\( 2^{24}\cdot 389^{7} \)	16T1691	$[2]$ (GRH)
16.4.22613464583653166220836864.3	x^16 - 6x^15 + 8x^14 + 20x^13 - 110x^12 + 174x^11 + 100x^10 - 512x^9 + 868x^8 + 230x^7 - 1572x^6 - 24x^5 + 498x^4 - 2574x^3 - 1040x^2 + 108x + 395	\( 2^{24}\cdot 389^{7} \)	16T1691	$[2]$ (GRH)
16.4.90453858334612664883347456.1	x^16 - 2x^15 - 22x^13 + 36x^12 - 26x^11 + 128x^10 - 230x^9 + 102x^8 - 278x^7 + 528x^6 - 514x^5 - 796x^4 - 238x^3 + 304x^2 + 350x + 49	\( 2^{26}\cdot 389^{7} \)	16T1691	$[2]$ (GRH)
16.8.90453858334612664883347456.1	x^16 - 2x^15 - 14x^14 + 34x^13 + 34x^12 - 188x^11 + 76x^10 + 116x^9 - 188x^8 + 426x^7 - 652x^6 + 434x^5 + 234x^4 - 524x^3 + 434x^2 - 188x + 25	\( 2^{26}\cdot 389^{7} \)	16T1691	$[2]$ (GRH)
16.4.90453858334612664883347456.2	x^16 - 6x^15 + 32x^14 - 132x^13 + 412x^12 - 900x^11 + 1184x^10 - 1196x^9 + 1596x^8 - 2684x^7 + 2872x^6 - 1392x^5 - 372x^4 + 456x^3 + 8x^2 + 16x + 4	\( 2^{26}\cdot 389^{7} \)	16T1691	$[2]$ (GRH)
16.8.3349520910408744233869290504192.1	x^16 - 4x^15 - 12x^14 - 10x^13 + 429x^12 - 270x^11 + 262x^10 - 6158x^9 - 35517x^8 + 84174x^7 + 219840x^6 - 105174x^5 - 1172115x^4 + 381168x^3 + 1533654x^2 - 411480x - 40257	\( 2^{24}\cdot 3^{16}\cdot 173^{7} \)	16T1691	Trivial (GRH)
16.8.3349520910408744233869290504192.2	x^16 - 8x^14 - 486x^12 + 4144x^10 + 23023x^8 - 16776x^6 - 153194x^4 - 124112x^2 + 1557	\( 2^{24}\cdot 3^{16}\cdot 173^{7} \)	16T1691	Trivial (GRH)
16.0.21367369203669531951904323534848.1	x^16 + 56x^14 + 1142x^12 + 10626x^10 + 46031x^8 + 89398x^6 + 76759x^4 + 26466x^2 + 2777	\( 2^{24}\cdot 2777^{7} \)	16T1691	$[2, 804]$ (GRH)
16.12.21367369203669531951904323534848.1	x^16 - 6x^15 - 26x^14 + 218x^13 + 189x^12 - 4880x^11 + 2x^10 + 78932x^9 + 19066x^8 - 662478x^7 - 272302x^6 + 2586552x^5 + 1183325x^4 - 4338242x^3 - 1977696x^2 + 2413344x + 1300042	\( 2^{24}\cdot 2777^{7} \)	16T1691	$[2]$ (GRH)
16.16.21367369203669531951904323534848.1	x^16 - 56x^14 + 1142x^12 - 10626x^10 + 46031x^8 - 89398x^6 + 76759x^4 - 26466x^2 + 2777	\( 2^{24}\cdot 2777^{7} \)	16T1691	Trivial (GRH)
16.4.21367369203669531951904323534848.1	x^16 + 64x^14 + 998x^12 + 3694x^10 - 12797x^8 - 37650x^6 - 25053x^4 - 190x^2 + 2777	\( 2^{24}\cdot 2777^{7} \)	16T1691	$[2]$ (GRH)
16.8.21367369203669531951904323534848.1	x^16 + 16x^14 - 428x^12 - 1824x^10 + 17966x^8 + 22224x^6 - 62940x^4 + 16576x^2 + 2777	\( 2^{24}\cdot 2777^{7} \)	16T1691	$[2]$ (GRH)
16.0.21367369203669531951904323534848.2	x^16 - 4x^14 - 38x^13 + 163x^12 + 2904x^11 + 11016x^10 - 14346x^9 - 26204x^8 + 328526x^7 - 127400x^6 - 812470x^5 + 2172477x^4 - 1095064x^3 + 1738888x^2 - 846456x + 682568	\( 2^{24}\cdot 2777^{7} \)	16T1691	$[2, 880]$ (GRH)
16.12.21367369203669531951904323534848.2	x^16 - 46x^14 + 163x^12 + 3994x^10 - 29905x^8 + 47118x^6 + 32362x^4 - 31272x^2 + 2777	\( 2^{24}\cdot 2777^{7} \)	16T1691	Trivial (GRH)
16.16.21367369203669531951904323534848.2	x^16 - 92x^14 - 16x^13 + 2647x^12 - 342x^11 - 31052x^10 + 10374x^9 + 157346x^8 - 62988x^7 - 317096x^6 + 91478x^5 + 243709x^4 - 49184x^3 - 59172x^2 + 8816x + 3364	\( 2^{24}\cdot 2777^{7} \)	16T1691	Trivial (GRH)
16.4.21367369203669531951904323534848.2	x^16 - 6x^15 - 14x^14 + 186x^13 - 951x^12 + 4000x^11 - 13558x^10 + 41228x^9 - 90086x^8 + 238146x^7 - 586206x^6 + 599580x^5 - 2327335x^4 + 2146782x^3 - 2500620x^2 + 6390268x - 3549766	\( 2^{24}\cdot 2777^{7} \)	16T1691	$[2]$ (GRH)
16.8.21367369203669531951904323534848.2	x^16 - 16x^14 - 428x^12 + 1824x^10 + 17966x^8 - 22224x^6 - 62940x^4 - 16576x^2 + 2777	\( 2^{24}\cdot 2777^{7} \)	16T1691	Trivial (GRH)