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
18.4.496528931236524572736.1	x^18 + x^16 - x^15 - x^14 - 7x^13 - 11x^12 - 12x^11 - 49x^10 - 52x^9 - 87x^8 - 127x^7 - 112x^6 - 125x^5 - 99x^4 - 62x^3 - 37x^2 - 14x - 2	\( -\,2^{6}\cdot 3^{6}\cdot 7^{6}\cdot 67^{6} \)	18T228	Trivial
18.4.2661084740845748882007.1	x^18 - 5x^15 + 3x^12 + 7x^9 - 13x^6 - 8x^3 - 1	\( -\,3^{6}\cdot 7^{9}\cdot 67^{6} \)	18T228	Trivial
18.2.13406281143386163463872.1	x^18 - 4x^17 + 9x^16 - 9x^15 - 2x^14 + 46x^13 - 107x^12 + 146x^11 - 77x^10 - 11x^9 + 4x^8 + 91x^7 - 109x^6 + 82x^5 - 32x^4 + 6x^3 - 2x^2 + x + 1	\( 2^{6}\cdot 3^{9}\cdot 7^{6}\cdot 67^{6} \)	18T228	Trivial
18.0.15034518472210440781824.1	x^18 - x^12 + 1	\( -\,2^{18}\cdot 3^{18}\cdot 23^{6} \)	18T228	Trivial
18.2.71849288002835219814189.1	x^18 - 2x^17 - 7x^16 + 13x^15 + 23x^14 - 59x^13 + 7x^12 + 64x^11 - 58x^10 - 6x^9 + 69x^8 - 49x^7 - 20x^6 - 12x^5 - 2x^4 + 6x^3 + 2x^2 - 3x + 1	\( 3^{9}\cdot 7^{9}\cdot 67^{6} \)	18T228	Trivial
18.0.90134835385419696439296.1	x^18 + x^6 + 1	\( -\,2^{18}\cdot 3^{18}\cdot 31^{6} \)	18T228	Trivial
18.2.121271000268800000000000.1	x^18 - 8x^17 + 30x^16 - 70x^15 + 107x^14 - 106x^13 + 80x^12 - 40x^11 + 31x^10 + 88x^9 - 298x^8 + 598x^7 - 711x^6 + 570x^5 - 348x^4 + 216x^3 - 124x^2 + 48x - 8	\( 2^{24}\cdot 5^{11}\cdot 23^{6} \)	18T228	Trivial
18.2.121271000268800000000000.2	x^18 + x^16 - 10x^15 + 11x^14 - 50x^13 + 12x^12 + 10x^11 + 184x^10 - 262x^9 + 331x^8 - 304x^7 - 53x^6 + 120x^5 - 121x^4 + 22x^3 + 20x^2 - 6x + 11	\( 2^{24}\cdot 5^{11}\cdot 23^{6} \)	18T228	Trivial
18.0.962209182221468210036736.1	x^18 + 18x^16 + 135x^14 + 536x^12 + 1167x^10 + 1242x^8 + 297x^6 - 324x^4 + 64	\( -\,2^{24}\cdot 3^{18}\cdot 23^{6} \)	18T228	Trivial (GRH)
18.6.4460220854277417832808448.1	x^18 - 12x^16 + 27x^14 - 13x^12 + 63x^10 - 102x^8 + 216x^6 - 261x^4 + 135x^2 - 27	\( 2^{24}\cdot 3^{11}\cdot 107^{6} \)	18T228	Trivial (GRH)
18.0.5768629464666860572114944.1	x^18 + 18x^16 + 135x^14 + 540x^12 + 1215x^10 + 1458x^8 + 745x^6 + 96x^4 + 144x^2 + 64	\( -\,2^{24}\cdot 3^{18}\cdot 31^{6} \)	18T228	Trivial (GRH)
18.6.10899803098504187420700672.1	x^18 - 3x^17 - 10x^16 + 37x^15 + 36x^14 - 193x^13 - 18x^12 + 455x^11 - 94x^10 - 445x^9 - 141x^8 + 404x^7 + 500x^6 - 480x^5 - 287x^4 + 101x^3 + 147x^2 + 50x + 4	\( 2^{12}\cdot 3^{6}\cdot 7^{9}\cdot 67^{6} \)	18T228	Trivial (GRH)
18.0.13380662562832253498425344.1	x^18 + 7x^16 - 8x^15 + 37x^14 + 16x^13 + 96x^12 + 58x^11 + 72x^10 + 346x^9 + 303x^8 + 172x^7 + 457x^6 + 418x^5 + 103x^4 + 36x^3 + 82x^2 + 48x + 9	\( -\,2^{24}\cdot 3^{12}\cdot 107^{6} \)	18T228	$[2, 2]$
18.6.53321094333449969673424896.1	x^18 - 18x^16 - 4x^15 + 126x^14 + 54x^13 - 493x^12 - 432x^11 + 762x^10 + 876x^9 - 846x^8 - 1302x^7 + 941x^6 + 1710x^5 - 840x^4 - 1216x^3 + 432x^2 + 288x - 64	\( 2^{12}\cdot 3^{18}\cdot 23^{6}\cdot 61^{3} \)	18T228	Trivial (GRH)
18.6.125869072545329914529206272.1	x^18 - 9x^16 - 22x^15 + 6x^14 + 135x^13 - 57x^12 - 447x^11 + 846x^10 + 2772x^9 + 75x^8 - 6834x^7 - 7971x^6 - 129x^5 + 4695x^4 + 1211x^3 - 1977x^2 - 1305x - 227	\( 2^{12}\cdot 3^{19}\cdot 31^{9} \)	18T228	Trivial (GRH)
18.0.294294683659613060358918144.1	x^18 - 3x^17 + 11x^16 - 11x^15 + 24x^14 - 12x^13 + 121x^12 - 95x^11 + 727x^10 + 25x^9 + 1172x^8 + 1386x^7 + 3079x^6 + 893x^5 + 4781x^4 + 825x^3 + 1247x^2 - 1319x + 982	\( -\,2^{12}\cdot 3^{9}\cdot 7^{9}\cdot 67^{6} \)	18T228	$[2, 8]$
18.6.6078695067822268102823903232000.1	x^18 - 36x^16 - 20x^15 + 378x^14 + 84x^13 - 2344x^12 + 11868x^10 + 1744x^9 - 42804x^8 - 12504x^7 + 103556x^6 + 19440x^5 - 114528x^4 + 22144x^3 + 4608x^2 + 1536x - 1024	\( 2^{26}\cdot 3^{24}\cdot 5^{3}\cdot 37^{6} \)	18T228	Trivial (GRH)
18.12.12449167498900005074583353819136.1	x^18 + 12x^16 - 216x^14 - 940x^12 + 17100x^10 - 62712x^8 + 82948x^6 - 24768x^4 - 11520x^2 + 1024	\( -\,2^{34}\cdot 3^{24}\cdot 37^{6} \)	18T228	Trivial (GRH)
18.12.21007970154393758563359409569792.1	x^18 - 18x^16 + 63x^14 + 372x^12 - 2349x^10 + 1242x^8 + 9009x^6 - 6588x^4 - 6480x^2 + 1728	\( -\,2^{30}\cdot 3^{27}\cdot 37^{6} \)	18T228	Trivial (GRH)
18.6.97259121085156289645182451712000.1	x^18 - 18x^16 + 180x^14 - 24x^13 - 2376x^12 - 864x^11 + 20544x^10 + 13824x^9 - 140112x^8 - 274656x^7 + 40720x^6 + 561600x^5 + 600960x^4 + 238592x^3 + 9216x^2 - 24576x - 8192	\( 2^{30}\cdot 3^{24}\cdot 5^{3}\cdot 37^{6} \)	18T228	$[6]$ (GRH)
18.0.591675863121548288056467444989952.1	x^18 + 18x^16 - 44x^15 + 234x^14 - 204x^13 + 614x^12 - 2664x^11 + 24636x^10 - 67840x^9 + 228168x^8 - 423168x^7 + 827536x^6 - 1017216x^5 + 1105152x^4 - 712448x^3 + 258048x^2 - 49152x + 8192	\( -\,2^{26}\cdot 3^{24}\cdot 23^{3}\cdot 37^{6} \)	18T228	$[2, 522]$ (GRH)
18.0.2208317976138187855160934400000000.1	x^18 + 36x^16 + 419x^14 + 2155x^12 + 5331x^10 + 6514x^8 + 3808x^6 + 959x^4 + 71x^2 + 1	\( -\,2^{24}\cdot 5^{8}\cdot 7^{8}\cdot 197^{6} \)	18T228	$[3, 180]$ (GRH)
18.18.18976421633167013985250838518431744.1	x^18 - 72x^16 - 52x^15 + 1629x^14 + 1956x^13 - 14650x^12 - 23580x^11 + 47697x^10 + 105944x^9 - 12816x^8 - 128964x^7 - 45215x^6 + 51840x^5 + 30552x^4 - 4304x^3 - 4608x^2 - 192x + 128	\( 2^{30}\cdot 3^{24}\cdot 29^{3}\cdot 37^{6} \)	18T228	Trivial (GRH)
18.18.151469020959116361742455665917427712.1	x^18 - 72x^16 - 60x^15 + 1755x^14 + 2796x^13 - 16488x^12 - 36936x^11 + 48171x^10 + 155800x^9 - 8352x^8 - 224988x^7 - 90831x^6 + 79308x^5 + 39264x^4 - 9200x^3 - 4320x^2 + 384x + 128	\( 2^{34}\cdot 3^{24}\cdot 23^{3}\cdot 37^{6} \)	18T228	Trivial (GRH)