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 22 matches)

Label	Polynomial	Discriminant	Galois group	Class group
9.3.1618930577917087333772795971776.2	x^9 - 3x^8 - 1221x^7 - 33360x^6 - 468492x^5 - 4028151x^4 - 21971391x^3 - 74216559x^2 - 141693072x - 116934011	\( -\,2^{6}\cdot 3^{15}\cdot 19^{3}\cdot 307^{7} \)	$S_3\times C_3$ (as 9T4)	$[3, 3, 42, 34398]$ (GRH)
9.3.3873496509817600597571142141632.1	x^9 - x^8 - 1045x^7 + 29560x^6 - 417628x^5 + 3585287x^4 - 19479671x^3 + 65515343x^2 - 124577908x + 102451091	\( -\,2^{6}\cdot 7^{7}\cdot 53^{3}\cdot 337^{7} \)	$S_3\times C_3$ (as 9T4)	$[6, 6, 283896]$ (GRH)
9.3.10070215181463105265791477576384.2	x^9 - 3x^8 - 1365x^7 - 10410x^6 + 646854x^5 + 11394435x^4 - 48531561x^3 - 2802169227x^2 - 26368099602x - 83468320741	\( -\,2^{6}\cdot 3^{15}\cdot 7^{7}\cdot 13^{3}\cdot 67^{7} \)	$S_3\times C_3$ (as 9T4)	$[3, 6, 6, 113868]$ (GRH)
9.3.27238792507107657316781252581568.1	x^9 - 4x^8 - 1313x^7 + 44491x^6 - 733595x^5 + 7301738x^4 - 45971710x^3 + 179531183x^2 - 397550999x + 381879679	\( -\,2^{6}\cdot 13^{7}\cdot 59^{3}\cdot 229^{7} \)	$S_3\times C_3$ (as 9T4)	$[3, 3, 2581830]$ (GRH)
9.3.49804565956681921138455674074816.1	x^9 - 2x^8 - 1417x^7 + 47083x^6 - 773167x^5 + 7694710x^4 - 48508270x^3 + 189764407x^2 - 420948217x + 405005803	\( -\,2^{6}\cdot 7^{7}\cdot 61^{3}\cdot 457^{7} \)	$S_3\times C_3$ (as 9T4)	$[3, 6, 1635606]$ (GRH)
9.3.50962325800568799445377418567872.1	x^9 - 3x^8 - 1845x^7 + 70446x^6 - 1318464x^5 + 14917527x^4 - 106922079x^3 + 476252001x^2 - 1205266068x + 1325705823	\( -\,2^{6}\cdot 3^{15}\cdot 23^{3}\cdot 463^{7} \)	$S_3\times C_3$ (as 9T4)	$[3, 11362932]$ (GRH)
9.3.66819788036888077076517052849664.1	x^9 - x^8 - 1469x^7 + 48382x^6 - 793070x^5 + 7893095x^4 - 49792969x^3 + 194960777x^2 - 432853214x + 416791129	\( -\,2^{9}\cdot 31^{3}\cdot 3313^{7} \)	$S_3\times C_3$ (as 9T4)	$[2, 2, 2, 6, 320454]$ (GRH)
9.3.86077156701845432324698961861043.1	x^9 - 3x^6 - 524904x^3 - 1	\( -\,3^{13}\cdot 19441^{6} \)	$S_3\times C_3$ (as 9T4)	$[3, 3, 252, 8316]$ (GRH)
9.3.98617155609873521667261976176128.1	x^9 - 2x^8 - 5111x^7 - 98827x^6 + 1155889x^5 - 18079154x^4 + 108296402x^3 - 612717833x^2 + 1613120173x - 3927745279	\( -\,2^{9}\cdot 15259^{7} \)	$S_3\times C_3$ (as 9T4)	$[2, 2, 2, 2, 752618]$ (GRH)
9.3.99822360672900157944131675077347.1	x^9 - 3x^6 - 538026x^3 - 1	\( -\,3^{13}\cdot 19927^{6} \)	$S_3\times C_3$ (as 9T4)	$[3, 6, 18, 58590]$ (GRH)
9.3.156709892840072826878199345848000.1	x^9 - 2x^8 - 1625x^7 - 52291x^6 - 853247x^5 - 8495846x^4 - 53712742x^3 - 210868919x^2 - 469393757x - 453036163	\( -\,2^{6}\cdot 5^{3}\cdot 13^{3}\cdot 19^{7}\cdot 193^{7} \)	$S_3\times C_3$ (as 9T4)	$[2, 2, 6, 1449426]$ (GRH)
9.3.270379224077520942015142156644544.1	x^9 - 4x^8 - 1729x^7 - 54907x^6 - 893755x^5 - 8904010x^4 - 56380654x^3 - 221740207x^2 - 494442079x - 477940399	\( -\,2^{6}\cdot 7^{7}\cdot 13^{7}\cdot 43^{7}\cdot 67^{3} \)	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 57, 35568]$ (GRH)
9.3.681178347371552581469632290964672.1	x^9 - 4x^8 - 9033x^7 - 359861x^6 - 2910119x^5 - 41373100x^4 - 151418854x^3 - 1012666779x^2 - 1671033865x - 6584680237	\( -\,2^{6}\cdot 27067^{7} \)	$S_3\times C_3$ (as 9T4)	$[2, 12114970]$ (GRH)
9.3.765763711957563428907417238099136.1	x^9 - x^8 - 1965x^7 + 73862x^6 - 1377684x^5 + 15584739x^4 - 111818439x^3 + 498777897x^2 - 1264170258x + 1392458831	\( -\,2^{6}\cdot 43^{7}\cdot 71^{3}\cdot 103^{7} \)	$S_3\times C_3$ (as 9T4)	$[2, 2, 42, 558516]$ (GRH)
9.3.1092248715644997058477173893624000.1	x^9 - 2x^8 - 4905x^7 - 71331x^6 + 1753533x^5 - 26039686x^4 + 196483798x^3 - 1074133819x^2 + 3296384083x - 6648336463	\( -\,2^{6}\cdot 5^{3}\cdot 73^{7}\cdot 199^{7} \)	$S_3\times C_3$ (as 9T4)	$[18, 234, 14274]$ (GRH)
9.3.1259466642471540279228280776978112.1	x^9 - x^8 - 2085x^7 - 77286x^6 - 1437264x^5 - 16258695x^4 - 116782119x^3 - 521681457x^2 - 1324203408x - 1460616767	\( -\,2^{6}\cdot 37^{7}\cdot 73^{3}\cdot 127^{7} \)	$S_3\times C_3$ (as 9T4)	$[3, 18, 1524510]$ (GRH)
9.3.1606599934405705783673028426265088.1	x^9 - 2x^8 - 2145x^7 - 79001x^6 - 1467189x^5 - 16598202x^4 - 119289204x^3 - 533274861x^2 - 1354643343x - 1495222583	\( -\,2^{9}\cdot 7^{7}\cdot 37^{3}\cdot 691^{7} \)	$S_3\times C_3$ (as 9T4)	$[3, 3, 1160481]$ (GRH)
9.1.5259726386972322735254120238966336.1	x^9 - 3x^8 + 66x^7 + 26333x^6 - 51534x^5 - 505365x^4 + 234481891x^3 - 222820542x^2 - 9591070860x + 691037609738	\( 2^{6}\cdot 3^{9}\cdot 7^{7}\cdot 13^{7}\cdot 97^{7} \)	$S_3^2$ (as 9T8)	$[3, 3, 3, 6, 18, 72, 72]$ (GRH)
9.3.10536470579780185613945471604157952.1	x^9 - 2x^8 - 3575x^7 + 7821x^6 + 1971289x^5 - 46669722x^4 + 524651850x^3 - 3436972865x^2 + 12798407621x - 22633585879	\( -\,2^{9}\cdot 13^{3}\cdot 9907^{7} \)	$S_3\times C_3$ (as 9T4)	$[2, 8, 2303672]$ (GRH)
9.3.12761527872381199036171781456729664.2	x^9 - 3x^8 - 11778x^7 - 343563x^6 + 6802959x^5 - 118025175x^4 + 976314459x^3 - 6434869944x^2 + 22446840324x - 58194334529	\( -\,2^{6}\cdot 3^{15}\cdot 3907^{7} \)	$S_3\times C_3$ (as 9T4)	$[3, 6, 84, 27468]$ (GRH)
9.3.17971044653397089488481063155542528.1	x^9 - 18057x^7 - 475501x^6 + 146478384x^5 - 1403751180x^4 - 46876525748x^3 + 22126109197140x^2 - 1477617177418200x - 55954234334768328	\( -\,2^{9}\cdot 3^{13}\cdot 13^{6}\cdot 463^{7} \)	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 3, 3, 311766]$ (GRH)
9.3.28137346150667129747744198503104000.1	x^9 - 7833x^7 - 154049x^6 + 20679120x^5 + 817921860x^4 - 10296478500x^3 - 1098270413100x^2 - 21904052373000x - 146020198499000	\( -\,2^{9}\cdot 3^{12}\cdot 5^{3}\cdot 7^{7}\cdot 373^{7} \)	$S_3\times C_3$ (as 9T4)	$[3, 3, 21, 267414]$ (GRH)