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
18.2.4570752111750967984128.1	x^18 + 9x^16 + 35x^14 + 74x^12 + 78x^10 + 3x^8 - 117x^6 - 171x^4 - 108x^2 - 27	\( 2^{24}\cdot 3^{9}\cdot 7^{12} \)	18T176	Trivial
18.4.10834375376002294480896.1	x^18 - 3x^14 - x^12 + 3x^10 + 2x^8 + 4x^6 - x^4 - 5x^2 + 1	\( -\,2^{30}\cdot 3^{6}\cdot 7^{12} \)	18T176	Trivial
18.4.19408409961765342806016.1	x^18 - 3x^16 - 3x^14 + 7x^12 + 9x^10 + 3x^8 - 10x^6 + 3x^2 + 1	\( -\,2^{36}\cdot 3^{24} \)	18T176	Trivial
18.2.155267279694122742448128.1	x^18 - 9x^14 + 12x^12 + 18x^10 - 36x^8 + 3x^6 + 18x^4 - 8	\( 2^{39}\cdot 3^{24} \)	18T176	Trivial
18.8.80421398252924334225227776.3	x^18 - x^16 - 33x^14 + 72x^12 + 141x^10 - 276x^8 - 195x^6 - 12x^4 + 9x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 53^{6} \)	18T176	Trivial (GRH)
18.12.80421398252924334225227776.4	x^18 - 9x^16 + 10x^14 + 99x^12 - 266x^10 + 61x^8 + 244x^6 - 97x^4 - 17x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 53^{6} \)	18T176	Trivial (GRH)
18.8.80421398252924334225227776.4	x^18 + 2x^16 - 14x^14 - 38x^12 + 29x^10 + 164x^8 + 142x^6 + 11x^4 - 17x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 53^{6} \)	18T176	Trivial (GRH)
18.10.279992823820843547402730217.3	x^18 - x^17 - 23x^16 + 19x^15 + 190x^14 - 96x^13 - 726x^12 - 63x^11 + 1363x^10 + 1596x^9 - 995x^8 - 4056x^7 - 1266x^6 + 4947x^5 + 2707x^4 - 2873x^3 - 2012x^2 + 618x + 83	\( 7^{12}\cdot 53^{6}\cdot 97^{3} \)	18T176	Trivial (GRH)
18.0.4171602042088091202978054144.1	x^18 + 2x^16 - 2x^15 - 17x^14 - 48x^13 + 339x^12 + 1178x^11 - 551x^10 - 10134x^9 - 15270x^8 + 27200x^7 + 126940x^6 + 223408x^5 + 420755x^4 + 1130120x^3 + 2252001x^2 + 2436132x + 1085323	\( -\,2^{24}\cdot 3^{9}\cdot 7^{12}\cdot 97^{3} \)	18T176	$[2, 2]$ (GRH)
18.6.4171602042088091202978054144.1	x^18 - 2x^16 - 10x^15 - 125x^14 + 156x^13 - 411x^12 + 1220x^11 + 3067x^10 + 3930x^9 - 7418x^8 + 16954x^7 + 22576x^6 - 73138x^5 - 309185x^4 - 567980x^3 - 625015x^2 - 410972x - 99917	\( 2^{24}\cdot 3^{9}\cdot 7^{12}\cdot 97^{3} \)	18T176	Trivial (GRH)
18.0.9888241877542142110762795008.1	x^18 + 7x^16 - 48x^14 - 426x^12 + 922x^10 + 24636x^8 + 193428x^6 + 878238x^4 + 1815937x^2 + 912673	\( -\,2^{30}\cdot 3^{6}\cdot 7^{12}\cdot 97^{3} \)	18T176	$[2]$ (GRH)
18.6.9888241877542142110762795008.1	x^18 - 7x^16 - 48x^14 + 426x^12 + 922x^10 - 24636x^8 + 193428x^6 - 878238x^4 + 1815937x^2 - 912673	\( 2^{30}\cdot 3^{6}\cdot 7^{12}\cdot 97^{3} \)	18T176	Trivial (GRH)
18.10.23969878594169966578599985152.1	x^18 - 9x^16 + 6x^14 + 111x^12 - 126x^10 - 423x^8 + 120x^6 + 279x^4 + 63x^2 - 3	\( 2^{18}\cdot 3^{31}\cdot 23^{6} \)	18T176	Trivial (GRH)
18.12.27584539600753046639253127168.1	x^18 - 7x^16 - 70x^14 + 504x^12 + 931x^10 - 8722x^8 + 6860x^6 + 6517x^4 - 3430x^2 + 343	\( -\,2^{18}\cdot 7^{15}\cdot 53^{6} \)	18T176	Trivial (GRH)
18.6.27584539600753046639253127168.1	x^18 + 7x^16 - 70x^14 - 504x^12 + 931x^10 + 8722x^8 + 6860x^6 - 6517x^4 - 3430x^2 - 343	\( 2^{18}\cdot 7^{15}\cdot 53^{6} \)	18T176	$[2]$ (GRH)
18.6.112579505930176715137054670848.1	x^18 + 13x^16 - 2x^14 - 468x^12 - 693x^10 + 3129x^8 + 2030x^6 + 217x^4 - 49x^2 - 7	\( 2^{18}\cdot 7^{15}\cdot 67^{6} \)	18T176	Trivial (GRH)
18.6.1904231969930704953529379769840621.1	x^18 - 4x^17 - 4x^16 + 31x^15 - 12x^14 + 14x^13 - 43x^12 - 274x^11 + 956x^10 - 7434x^9 + 3728x^8 + 30688x^7 - 36963x^6 + 18796x^5 - 7212x^4 + 75884x^3 + 13362x^2 - 210290x + 118777	\( 3^{9}\cdot 7^{12}\cdot 107^{6}\cdot 167^{3} \)	18T176	Trivial (GRH)
18.18.4469642099029414895974730306243001.1	x^18 - 6x^17 - 53x^16 + 387x^15 + 821x^14 - 9422x^13 + 930x^12 + 106986x^11 - 135808x^10 - 547108x^9 + 1226686x^8 + 785608x^7 - 3884238x^6 + 1863610x^5 + 3012697x^4 - 3172986x^3 + 685681x^2 + 79619x - 22133	\( 3^{3}\cdot 7^{13}\cdot 181^{3}\cdot 257^{6} \)	18T176	$[2]$ (GRH)
18.12.34316371298286047031542175649181696.1	x^18 - 2x^17 + 5x^16 - 40x^15 - 266x^14 + 255x^13 - 300x^12 + 9132x^11 + 17814x^10 + 9355x^9 - 184219x^8 - 600376x^7 + 1205481x^6 + 2196473x^5 - 3497873x^4 - 2434847x^3 + 3889164x^2 + 444781x - 1012607	\( -\,2^{12}\cdot 7^{12}\cdot 37^{9}\cdot 167^{3} \)	18T176	Trivial (GRH)
18.0.74422866183848971206656000000000000.1	x^18 + 113x^16 + 4986x^14 + 109769x^12 + 1290015x^10 + 8207609x^8 + 29008613x^6 + 56338590x^4 + 55167918x^2 + 20511149	\( -\,2^{30}\cdot 5^{12}\cdot 7^{12}\cdot 29^{5} \)	18T176	$[2, 2, 6, 1536]$ (GRH)
18.18.244109409460733537552375387021430784.1	x^18 - 6x^17 - 190x^16 + 1044x^15 + 14860x^14 - 72108x^13 - 621949x^12 + 2539072x^11 + 15046066x^10 - 48293558x^9 - 211154628x^8 + 478686318x^7 + 1635451266x^6 - 2126342036x^5 - 6161937706x^4 + 2788171094x^3 + 7204566626x^2 - 907486600x - 219172337	\( 2^{12}\cdot 7^{12}\cdot 53^{6}\cdot 181^{5} \)	18T176	Trivial (GRH)
18.0.595382929470791769653248000000000000.1	x^18 - 2x^17 + 69x^16 - 270x^15 + 2116x^14 - 11216x^13 + 52049x^12 - 220932x^11 + 978299x^10 - 2750554x^9 + 9953429x^8 - 22885542x^7 + 57594463x^6 - 121071826x^5 + 205773548x^4 - 351569070x^3 + 444155462x^2 - 445836796x + 437249189	\( -\,2^{33}\cdot 5^{12}\cdot 7^{12}\cdot 29^{5} \)	18T176	$[2, 2, 2, 12364]$ (GRH)
18.6.715444690703398259054531116568150016.1	x^18 + 54x^16 - 468x^14 - 34284x^12 + 75357x^10 + 2253780x^8 + 5534130x^6 + 2407509x^4 - 3518667x^2 - 2476099	\( 2^{18}\cdot 3^{32}\cdot 19^{5}\cdot 29^{6} \)	18T176	$[4]$ (GRH)
18.12.1738227155372083140288705823158000447488.1	x^18 - 6x^17 - 165x^16 + 1089x^15 + 8769x^14 - 70026x^13 - 122314x^12 + 1794941x^11 - 2497471x^10 - 9914269x^9 + 47970630x^8 - 175203836x^7 + 419590832x^6 - 119867456x^5 - 3145932384x^4 + 22714675904x^3 - 68178001536x^2 + 33272275968x + 101785794048	\( -\,2^{12}\cdot 7^{12}\cdot 37^{12}\cdot 167^{3} \)	18T176	$[2]$ (GRH)