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 43 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.0.538142295685559947264.1	x^18 - x^16 - x^12 + 3x^10 + 19x^8 + 33x^6 + 10x^4 + 2x^2 + 1	\( -\,2^{12}\cdot 23^{6}\cdot 31^{6} \)	18T461	Trivial
18.0.538142295685559947264.2	x^18 + 9x^16 + 38x^14 + 95x^12 + 151x^10 + 155x^8 + 103x^6 + 46x^4 + 14x^2 + 1	\( -\,2^{12}\cdot 23^{6}\cdot 31^{6} \)	18T461	Trivial
18.2.6641883018437135958016.1	x^18 - 5x^16 + 12x^14 - 21x^12 + 24x^10 - x^8 + 19x^6 - 148x^4 + 196x^2 - 76	\( 2^{22}\cdot 11^{6}\cdot 19^{7} \)	18T461	Trivial
18.2.12377272800767878787072.1	x^18 - 3x^17 + 2x^16 + 6x^15 - 13x^14 + 19x^13 + 21x^12 - 38x^11 + 11x^10 + 17x^9 - 76x^8 + 28x^7 + 52x^6 - 12x^5 + 35x^4 + 44x^3 - 133x^2 - 5x + 67	\( 2^{12}\cdot 23^{7}\cdot 31^{6} \)	18T461	Trivial
18.4.34841614129512494137344.1	x^18 - 9x^17 + 36x^16 - 81x^15 + 114x^14 - 129x^13 + 177x^12 - 240x^11 + 198x^10 - 74x^9 + 36x^8 - 60x^7 + 24x^6 + 12x^5 + 12x^4 - 24x^3 + 12x - 4	\( -\,2^{20}\cdot 3^{24}\cdot 7^{6} \)	18T461	Trivial
18.2.104524842388537482412032.1	x^18 + 6x^16 - 6x^15 + 18x^14 - 24x^13 + 15x^12 - 54x^11 - 12x^10 + 46x^9 - 66x^8 + 180x^7 - 141x^6 + 222x^5 - 132x^4 + 36x^3 + 6x^2 + 1	\( 2^{20}\cdot 3^{25}\cdot 7^{6} \)	18T461	Trivial
18.0.557465826072199906197504.1	x^18 + 6x^16 + 12x^14 + 15x^12 + 30x^10 + 36x^8 + 3x^6 + 6x^4 + 6x^2 + 1	\( -\,2^{24}\cdot 3^{24}\cdot 7^{6} \)	18T461	Trivial
18.4.557465826072199906197504.2	x^18 - 6x^16 + 12x^14 + 3x^12 - 42x^10 + 24x^8 + 51x^6 - 18x^4 - 42x^2 + 1	\( -\,2^{24}\cdot 3^{24}\cdot 7^{6} \)	18T461	Trivial
18.6.1672397478216599718592512.1	x^18 - 12x^16 + 54x^14 - 99x^12 + 18x^10 + 162x^8 - 135x^6 - 108x^4 + 162x^2 - 27	\( 2^{24}\cdot 3^{25}\cdot 7^{6} \)	18T461	Trivial
18.2.1672397478216599718592512.2	x^18 + 9x^16 + 39x^14 + 111x^12 + 204x^10 + 240x^8 + 216x^6 + 144x^4 - 48	\( 2^{24}\cdot 3^{25}\cdot 7^{6} \)	18T461	Trivial
18.0.3283504922879511109042176.1	x^18 + x^16 + x^14 + 7x^12 + 10x^10 + 3x^8 - 3x^6 + 3x^4 + 5x^2 + 1	\( -\,2^{18}\cdot 3^{6}\cdot 107^{8} \)	18T461	Trivial
18.6.5489609792939182635429888.1	x^18 - 10x^16 + 34x^14 - 76x^12 + 171x^10 - 312x^8 + 472x^6 - 463x^4 + 321x^2 - 107	\( 2^{12}\cdot 3^{6}\cdot 107^{9} \)	18T461	Trivial
18.6.88654632917746799944138752.3	x^18 - 5x^16 + 4x^14 - 4x^12 + 15x^10 - 57x^8 + 99x^6 - 99x^4 + 81x^2 - 27	\( 2^{18}\cdot 3^{9}\cdot 107^{8} \)	18T461	Trivial (GRH)
18.6.88654632917746799944138752.4	x^18 + x^16 + 6x^14 - 52x^12 + 45x^10 - 45x^8 + 90x^6 + 9x^4 - 27x^2 - 27	\( 2^{18}\cdot 3^{9}\cdot 107^{8} \)	18T461	Trivial (GRH)
18.0.2294529340113174813908926464.1	x^18 + 24x^16 + 174x^14 + 237x^12 - 1638x^10 - 3318x^8 + 2205x^6 + 8820x^4 + 6174x^2 + 1029	\( -\,2^{26}\cdot 3^{25}\cdot 7^{9} \)	18T461	$[2, 2]$
18.0.2393675088779163598491746304.2	x^18 - 3x^16 - 3x^14 + 90x^12 + 135x^10 + 405x^8 + 1404x^6 + 486x^4 - 243x^2 + 729	\( -\,2^{18}\cdot 3^{12}\cdot 107^{8} \)	18T461	$[2, 2]$
18.12.2855870434202241384378793984.1	x^18 - 8x^16 - 23x^14 + 168x^12 + 139x^10 - 1040x^8 - 133x^6 + 1920x^4 - 352x^2 + 16	\( -\,2^{20}\cdot 37^{6}\cdot 101^{6} \)	18T461	Trivial (GRH)
18.4.2855870434202241384378793984.1	x^18 + 12x^16 + 12x^14 - 304x^12 - 1008x^10 + 496x^8 + 5744x^6 + 7616x^4 + 3328x^2 + 256	\( -\,2^{20}\cdot 37^{6}\cdot 101^{6} \)	18T461	Trivial
18.12.2855870434202241384378793984.2	x^18 - 3x^16 - 44x^14 + 129x^12 + 316x^10 - 1051x^8 + 19x^6 + 1320x^4 - 704x^2 + 16	\( -\,2^{20}\cdot 37^{6}\cdot 101^{6} \)	18T461	Trivial (GRH)
18.8.2855870434202241384378793984.3	x^18 - 6x^17 + 3x^16 + 54x^15 - 142x^14 + 42x^13 + 265x^12 - 144x^11 - 118x^10 - 1310x^9 + 3011x^8 - 1396x^7 - 2119x^6 + 3380x^5 - 1500x^4 - 570x^3 + 972x^2 - 472x + 86	\( -\,2^{20}\cdot 37^{6}\cdot 101^{6} \)	18T461	Trivial (GRH)
18.8.2855870434202241384378793984.4	x^18 - 2x^16 - 85x^14 + 244x^12 + 887x^10 - 610x^8 - 1555x^6 + 288x^4 + 224x^2 + 16	\( -\,2^{20}\cdot 37^{6}\cdot 101^{6} \)	18T461	Trivial (GRH)
18.4.11423481736808965537515175936.1	x^18 + 9x^16 - 4x^14 - 163x^12 - 164x^10 + 437x^8 + 859x^6 + 508x^4 + 104x^2 + 4	\( -\,2^{22}\cdot 37^{6}\cdot 101^{6} \)	18T461	$[2]$
18.10.35675388820222120719231418368.1	x^18 - 3x^17 - 12x^16 + 63x^15 - 25x^14 - 438x^13 + 915x^12 + 967x^11 - 5033x^10 + 2588x^9 + 11369x^8 - 20207x^7 + 2289x^6 + 28810x^5 - 33483x^4 + 8201x^3 + 11392x^2 - 9421x + 1963	\( 2^{16}\cdot 3^{9}\cdot 37^{6}\cdot 47^{6} \)	18T461	Trivial (GRH)
18.12.105667206065482931222015377408.1	x^18 - 19x^16 - 12x^15 + 185x^14 - 112x^13 - 777x^12 + 2120x^11 - 2026x^10 - 532x^9 + 4972x^8 - 10436x^7 + 10324x^6 - 2836x^5 - 1952x^4 + 1208x^3 - 80x^2 - 40x + 4	\( -\,2^{20}\cdot 37^{7}\cdot 101^{6} \)	18T461	Trivial (GRH)
18.8.105667206065482931222015377408.1	x^18 - 7x^16 - 60x^14 + 56x^12 + 822x^10 + 1018x^8 - 1132x^6 - 2512x^4 - 975x^2 + 37	\( -\,2^{20}\cdot 37^{7}\cdot 101^{6} \)	18T461	Trivial (GRH)
18.12.105667206065482931222015377408.2	x^18 - 14x^16 + 18x^14 + 407x^12 - 1636x^10 + 1376x^8 + 1059x^6 - 1274x^4 + 18x^2 + 37	\( -\,2^{20}\cdot 37^{7}\cdot 101^{6} \)	18T461	Trivial (GRH)
18.8.105667206065482931222015377408.2	x^18 - 6x^17 + 12x^16 - 26x^15 + 78x^14 - 128x^13 + 4x^12 + 108x^11 + 444x^10 - 132x^9 - 1620x^8 + 72x^7 + 2188x^6 - 8x^5 - 1392x^4 + 528x^3 + 416x^2 - 448x - 128	\( -\,2^{20}\cdot 37^{7}\cdot 101^{6} \)	18T461	Trivial (GRH)
18.12.122625582310394722227216973824.1	x^18 - 3x^16 - 72x^14 + 497x^12 - 1044x^10 + 549x^8 + 139x^6 - 144x^4 + 12x^2 + 4	\( -\,2^{20}\cdot 3^{18}\cdot 7^{6}\cdot 37^{6} \)	18T461	Trivial (GRH)
18.12.122625582310394722227216973824.2	x^18 - 15x^16 - 9x^14 + 639x^12 - 840x^10 - 3924x^8 + 3840x^6 - 960x^4 + 16	\( -\,2^{20}\cdot 3^{18}\cdot 7^{6}\cdot 37^{6} \)	18T461	Trivial (GRH)
18.14.570806221123553931507702693888.1	x^18 - 5x^17 - 10x^16 + 117x^15 - 248x^14 - 363x^13 + 2851x^12 - 4622x^11 - 2370x^10 + 16122x^9 - 14032x^8 - 9476x^7 + 20184x^6 - 7080x^5 - 2316x^4 + 1288x^3 + 8x^2 - 52x + 4	\( 2^{20}\cdot 3^{9}\cdot 37^{6}\cdot 47^{6} \)	18T461	Trivial (GRH)
18.10.570806221123553931507702693888.2	x^18 - 6x^17 - 4x^16 + 98x^15 - 252x^14 + 140x^13 + 735x^12 - 2234x^11 + 2014x^10 + 2382x^9 - 6748x^8 + 4266x^7 + 2149x^6 - 4700x^5 + 2260x^4 + 648x^3 - 674x^2 - 114x + 1	\( 2^{20}\cdot 3^{9}\cdot 37^{6}\cdot 47^{6} \)	18T461	Trivial (GRH)
18.14.570806221123553931507702693888.2	x^18 - 23x^16 + 148x^14 + 200x^12 - 6170x^10 + 27594x^8 - 53948x^6 + 47904x^4 - 15615x^2 - 27	\( 2^{20}\cdot 3^{9}\cdot 37^{6}\cdot 47^{6} \)	18T461	Trivial (GRH)
18.6.570806221123553931507702693888.2	x^18 + 16x^16 + 45x^14 - 328x^12 - 1221x^10 + 1920x^8 + 3879x^6 - 648x^4 - 2160x^2 - 432	\( 2^{20}\cdot 3^{9}\cdot 37^{6}\cdot 47^{6} \)	18T461	Trivial (GRH)
18.6.570806221123553931507702693888.3	x^18 - 6x^17 + 25x^16 - 82x^15 + 194x^14 - 314x^13 - 291x^12 + 2174x^11 - 3114x^10 + 2064x^9 - 4153x^8 + 10464x^7 + 7361x^6 - 29038x^5 + 46162x^4 - 31784x^3 + 12108x^2 - 788x - 524	\( 2^{20}\cdot 3^{9}\cdot 37^{6}\cdot 47^{6} \)	18T461	Trivial (GRH)
18.6.9132899537976862904123243102208.2	x^18 + 8x^16 - 70x^14 - 799x^12 - 1938x^10 + 138x^8 + 2961x^6 + 828x^4 - 270x^2 - 27	\( 2^{24}\cdot 3^{9}\cdot 37^{6}\cdot 47^{6} \)	18T461	Trivial (GRH)
18.6.9132899537976862904123243102208.3	x^18 + 5x^16 - 82x^14 - 487x^12 + 1206x^10 + 9921x^8 + 3915x^6 - 30924x^4 - 7776x^2 - 432	\( 2^{24}\cdot 3^{9}\cdot 37^{6}\cdot 47^{6} \)	18T461	Trivial (GRH)
18.10.36531598151907451616492972408832.1	x^18 - 31x^16 + 278x^14 - 37x^12 - 8844x^10 + 23091x^8 + 16875x^6 - 1260x^4 - 1404x^2 - 108	\( 2^{26}\cdot 3^{9}\cdot 37^{6}\cdot 47^{6} \)	18T461	Trivial (GRH)
18.10.36531598151907451616492972408832.2	x^18 + 13x^16 - 18x^14 - 331x^12 + 582x^10 + 1725x^8 - 4473x^6 + 1548x^4 + 1728x^2 - 432	\( 2^{26}\cdot 3^{9}\cdot 37^{6}\cdot 47^{6} \)	18T461	Trivial (GRH)
18.0.144658405103646132842939051671552.1	x^18 + 6x^16 - 26x^15 - 71x^14 - 288x^13 - 492x^12 - 1080x^11 + 1611x^10 + 13200x^9 + 79570x^8 + 262722x^7 + 709455x^6 + 1484828x^5 + 2377900x^4 + 2887300x^3 + 2846716x^2 + 1984240x + 853324	\( -\,2^{20}\cdot 37^{9}\cdot 101^{6} \)	18T461	$[2, 2, 152]$ (GRH)
18.0.250219943963063581133732413702144.1	x^18 + 56x^16 + 1174x^14 + 11479x^12 + 53662x^10 + 118116x^8 + 128427x^6 + 68376x^4 + 16428x^2 + 1369	\( -\,2^{26}\cdot 37^{8}\cdot 101^{6} \)	18T461	$[2, 2, 326]$ (GRH)
18.18.12368576588601948950695443500515796713472.1	x^18 - 256x^16 + 27504x^14 - 1617752x^12 + 56785664x^10 - 1210694656x^8 + 15164892608x^6 - 100967291904x^4 + 285575267328x^2 - 270683161088	\( 2^{33}\cdot 37^{6}\cdot 101^{6}\cdot 22993^{2} \)	18T461	Trivial (GRH)
18.18.626505509942454520199576299631626650927497216.1	x^18 - 628x^16 + 129096x^14 - 13334542x^12 + 800495088x^10 - 29538867680x^8 + 675706834748x^6 - 9269088389392x^4 + 69227150021088x^2 - 214233033727976	\( 2^{33}\cdot 37^{9}\cdot 101^{6}\cdot 22993^{2} \)	18T461	$[2, 2]$ (GRH)
18.6.51624177137754227336536682168566437749832086648167693412837925000000000000.1	x^18 - 6x^17 - 79635x^16 + 726016x^15 - 21346492116x^14 + 262385243232x^13 - 222640923218036x^12 + 5287125117175824x^11 + 36115874586042869742x^10 - 315574620417688738476x^9 + 1064246929788629129834742x^8 - 10094756489315953842318336x^7 + 5555830520763339794029338844x^6 - 66983200453112231194458550608x^5 - 95464018377851901223533667416996x^4 + 244705662148773213221767445905616x^3 - 887010722785755909642099142950505815x^2 + 1957760134295180518228084208239496514x - 371023633673372769266300083152445623019	\( 2^{12}\cdot 3^{24}\cdot 5^{14}\cdot 13^{6}\cdot 1061117^{7} \)	18T461	n/a