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 28 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.0.894396879913401450496.1	x^18 + 9x^16 + 34x^14 + 73x^12 + 103x^10 + 105x^8 + 77x^6 + 34x^4 + 6x^2 + 1	\( -\,2^{30}\cdot 97^{6} \)	18T370	Trivial
18.0.894396879913401450496.2	x^18 - 2x^16 - x^14 + 5x^12 - x^10 - 12x^8 + 14x^6 - x^4 - 3x^2 + 1	\( -\,2^{30}\cdot 97^{6} \)	18T370	Trivial
18.4.1410638724627903913536.1	x^18 - 3x^16 + 6x^14 + 3x^12 + 30x^10 + 39x^8 - 6x^6 - 21x^4 - 3x^2 + 1	\( -\,2^{6}\cdot 3^{20}\cdot 43^{6} \)	18T370	Trivial
18.2.4231916173883711740608.1	x^18 - 3x^16 - 9x^14 + 21x^12 + 18x^10 + 9x^8 - 9x^6 - 15x^4 - 9x^2 - 3	\( 2^{6}\cdot 3^{21}\cdot 43^{6} \)	18T370	Trivial
18.2.8302304247987471323328.1	x^18 - 5x^17 + 11x^16 - 11x^15 + 15x^13 - 16x^12 - 11x^11 + 21x^10 - 9x^9 - 22x^8 - 8x^7 - 10x^6 - 2x^5 + 19x^4 + 16x^3 + 4x^2 + x + 1	\( 2^{6}\cdot 3^{9}\cdot 433^{6} \)	18T370	Trivial
18.4.19679535995229561655296.1	x^18 - 3x^16 + 2x^14 + 3x^12 - 6x^10 - 5x^8 - 10x^6 + 13x^4 - 9x^2 + 1	\( -\,2^{12}\cdot 3^{6}\cdot 433^{6} \)	18T370	Trivial
18.2.499935225246570775390625.1	x^18 - 4x^17 + 3x^16 + 8x^15 - 15x^14 + 8x^13 + 26x^12 + 10x^11 + 31x^10 + 48x^9 + 74x^8 + 96x^7 + 75x^6 + 76x^5 + 88x^4 + 63x^3 + 28x^2 + 8x + 1	\( 5^{9}\cdot 13^{9}\cdot 17^{6} \)	18T370	$[2]$
18.6.531347471871198164692992.1	x^18 - 2x^16 - 14x^14 + 20x^12 + 33x^10 - 132x^8 + 306x^6 - 297x^4 + 135x^2 - 27	\( 2^{12}\cdot 3^{9}\cdot 433^{6} \)	18T370	Trivial (GRH)
18.2.694883159214474119078125.1	x^18 - 4x^17 + 8x^16 - 16x^15 + 23x^14 - 46x^13 + 72x^12 - 102x^11 + 153x^10 - 190x^9 + 316x^8 - 346x^7 + 373x^6 - 371x^5 + 332x^4 - 409x^3 + 351x^2 - 137x + 19	\( 5^{6}\cdot 61^{3}\cdot 241^{6} \)	18T370	Trivial (GRH)
18.0.1259490303694691945938944.1	x^18 + 4x^16 + 8x^14 + 15x^12 + 12x^10 - 4x^8 - x^6 + 4x^2 + 1	\( -\,2^{18}\cdot 3^{6}\cdot 433^{6} \)	18T370	Trivial
18.0.1259490303694691945938944.2	x^18 + 10x^16 + 43x^14 + 105x^12 + 158x^10 + 145x^8 + 73x^6 + 13x^4 - 2x^2 + 1	\( -\,2^{18}\cdot 3^{6}\cdot 433^{6} \)	18T370	Trivial
18.0.1259490303694691945938944.3	x^18 + 4x^16 + 6x^14 + 13x^12 + 17x^10 + 7x^8 - 3x^6 - 2x^4 + 3x^2 + 1	\( -\,2^{18}\cdot 3^{6}\cdot 433^{6} \)	18T370	Trivial
18.6.5586993939121968703901696.1	x^18 - 6x^17 + 4x^16 + 42x^15 - 107x^14 + 2x^13 + 374x^12 - 566x^11 - 60x^10 + 1090x^9 - 1272x^8 + 198x^7 + 987x^6 - 1222x^5 + 690x^4 - 196x^3 + 32x^2 + 16x - 8	\( 2^{12}\cdot 89^{3}\cdot 353^{6} \)	18T370	Trivial (GRH)
18.0.5777976216075894429843456.1	x^18 - 9x^14 + 24x^10 - 3x^8 - 18x^6 + 12x^4 + 9x^2 + 1	\( -\,2^{18}\cdot 3^{20}\cdot 43^{6} \)	18T370	Trivial
18.6.17333928648227683289530368.1	x^18 - 6x^16 + 27x^14 - 72x^12 + 117x^10 - 75x^8 - 12x^6 - 6x^4 + 18x^2 - 3	\( 2^{18}\cdot 3^{21}\cdot 43^{6} \)	18T370	Trivial
18.6.17333928648227683289530368.2	x^18 - 15x^14 - 6x^12 + 132x^10 - 249x^8 + 219x^6 - 105x^4 + 27x^2 - 3	\( 2^{18}\cdot 3^{21}\cdot 43^{6} \)	18T370	Trivial
18.8.34400814135672603325575168.1	x^18 - 5x^17 + 5x^16 + 12x^15 - 29x^14 + 28x^13 - 35x^12 + 12x^11 + 86x^10 - 122x^9 + 67x^8 - 77x^7 + 54x^6 + 47x^5 - 38x^4 - 16x^3 + 10x^2 + 2x - 1	\( -\,2^{12}\cdot 3^{3}\cdot 19^{6}\cdot 137^{6} \)	18T370	Trivial (GRH)
18.8.81542670543816541216178176.1	x^18 - 3x^16 - 34x^14 + 24x^12 + 209x^10 - 15x^8 - 303x^6 - 67x^4 + 3x^2 + 1	\( -\,2^{18}\cdot 19^{6}\cdot 137^{6} \)	18T370	Trivial
18.10.159263028405891682062848000.1	x^18 - 6x^16 - 12x^15 + x^14 + 49x^13 + 79x^12 + x^11 - 174x^10 - 229x^9 - 4x^8 + 296x^7 + 270x^6 - 44x^5 - 206x^4 - 63x^3 + 40x^2 + x - 1	\( 2^{12}\cdot 5^{3}\cdot 19^{6}\cdot 137^{6} \)	18T370	Trivial (GRH)
18.12.1493196207631454487439212544.1	x^18 - 12x^16 - 2x^15 + 34x^14 + 44x^13 + 105x^12 - 324x^11 - 799x^10 + 1052x^9 + 1851x^8 - 1670x^7 - 2161x^6 + 1330x^5 + 1380x^4 - 512x^3 - 453x^2 + 76x + 59	\( -\,2^{24}\cdot 2113^{6} \)	18T370	Trivial (GRH)
18.12.1549310740332514283107385344.1	x^18 - 3x^17 - 8x^16 + 35x^15 + 12x^14 - 168x^13 + 31x^12 + 576x^11 - 408x^10 - 920x^9 + 960x^8 + 656x^7 - 936x^6 - 208x^5 + 436x^4 + 24x^3 - 96x^2 + 8	\( -\,2^{18}\cdot 19^{7}\cdot 137^{6} \)	18T370	Trivial (GRH)
18.10.72909971075754613644492800000.1	x^18 - 5x^17 - 10x^16 + 97x^15 - 115x^14 - 423x^13 + 1333x^12 + 274x^11 - 5107x^10 + 757x^9 + 10252x^8 + 3756x^7 - 9586x^6 - 14473x^5 - 3360x^4 + 7660x^3 + 5133x^2 + 760x + 31	\( 2^{18}\cdot 5^{5}\cdot 2113^{6} \)	18T370	Trivial (GRH)
18.6.114626140126458373387325800448.1	x^18 - x^17 - 14x^16 + 13x^15 + 75x^14 - 63x^13 - 186x^12 + 133x^11 + 220x^10 - 144x^9 - 152x^8 + 250x^7 - 59x^6 - 261x^5 + 336x^4 - 97x^3 + 210x^2 - 284x - 104	\( 2^{18}\cdot 17^{3}\cdot 2113^{6} \)	18T370	Trivial (GRH)
18.0.333998778547472552821465808896.1	x^18 + 24x^16 + 228x^14 + 1129x^12 + 3177x^10 + 5133x^8 + 4523x^6 + 1874x^4 + 231x^2 + 1	\( -\,2^{30}\cdot 19^{6}\cdot 137^{6} \)	18T370	$[2, 64]$ (GRH)
18.6.3679878271031164268664465640625.1	x^18 - 4x^17 - 8x^16 + 49x^15 + 36x^14 - 320x^13 - 174x^12 + 1594x^11 + 671x^10 - 6184x^9 - 921x^8 + 16202x^7 - 2813x^6 - 25817x^5 + 12686x^4 + 21392x^3 - 17867x^2 + 2383x + 523	\( 5^{6}\cdot 41^{3}\cdot 3881^{6} \)	18T370	Trivial (GRH)
18.0.8041717026786576033268170489856.1	x^18 + 23x^16 + 186x^14 + 702x^12 + 1357x^10 + 1399x^8 + 768x^6 + 215x^4 + 27x^2 + 1	\( -\,2^{18}\cdot 13^{6}\cdot 1361^{6} \)	18T370	$[4, 88]$ (GRH)
18.18.154058768883069498630813286400000.1	x^18 - 8x^17 - 22x^16 + 311x^15 - 177x^14 - 4042x^13 + 6893x^12 + 21877x^11 - 57757x^10 - 38438x^9 + 201810x^8 - 60402x^7 - 280959x^6 + 236262x^5 + 86871x^4 - 148589x^3 + 19788x^2 + 22313x - 5737	\( 2^{18}\cdot 5^{5}\cdot 2113^{7} \)	18T370	Trivial (GRH)
18.18.273643466419358056354703134640625.1	x^18 - 3x^17 - 57x^16 + 183x^15 + 1038x^14 - 3634x^13 - 7620x^12 + 31281x^11 + 21054x^10 - 125283x^9 - 5951x^8 + 231621x^7 - 44061x^6 - 191169x^5 + 47367x^4 + 59805x^3 - 11475x^2 - 5022x + 972	\( 3^{9}\cdot 5^{6}\cdot 31^{6}\cdot 139^{7} \)	18T370	Trivial (GRH)