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 17 matches)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.1320330028678597666666010640384.1	x^12 + 1092x^10 + 424242x^8 + 70309512x^6 + 4510403352x^4 + 61163496576x^2 + 222991914600	\( 2^{33}\cdot 3^{6}\cdot 7^{6}\cdot 13^{11} \)	$C_{12}$ (as 12T1)	$[2, 2, 4820212]$ (GRH)
12.0.1669440466451705194787135164416.1	x^12 + 1422x^8 - 924300x^6 - 11027847x^4 + 657177300x^2 + 225275535424	\( 2^{12}\cdot 3^{16}\cdot 79^{10} \)	$C_6\times C_2$ (as 12T2)	$[2, 2, 4, 4, 168, 2520]$ (GRH)
12.0.355491663986814578735616000000000.2	x^12 + 780x^10 + 226980x^8 + 29335800x^6 + 1451174400x^4 + 4672512000x^2 + 3833856000	\( 2^{18}\cdot 3^{18}\cdot 5^{9}\cdot 13^{11} \)	$C_{12}$ (as 12T1)	$[2, 2, 2, 1467420]$ (GRH)
12.0.841568811705324755722156042616832.1	x^12 + 1236x^10 + 391194x^8 + 50258232x^6 + 2784225960x^4 + 60139280736x^2 + 405940144968	\( 2^{33}\cdot 3^{6}\cdot 103^{10} \)	$C_{12}$ (as 12T1)	$[2, 2, 2, 2, 639132]$ (GRH)
12.0.1732127044066296934075975910854656.1	x^12 + 762x^10 + 202311x^8 + 24967184x^6 + 1472174475x^4 + 33659206875x^2 + 252015625	\( 2^{12}\cdot 3^{18}\cdot 127^{10} \)	$C_6\times C_2$ (as 12T2)	$[2, 8, 8, 8, 15960]$ (GRH)
12.0.1829654030234673819254664000000000.2	x^12 + 1095x^10 + 160965x^8 + 9460800x^6 + 262241550x^4 + 3368192625x^2 + 15971752125	\( 2^{12}\cdot 3^{6}\cdot 5^{9}\cdot 73^{11} \)	$C_{12}$ (as 12T1)	$[2, 2, 2, 2, 1372628]$ (GRH)
12.0.2748267123526559548681146214649856.1	x^12 + 798x^10 + 166383x^8 + 11626860x^6 + 174325095x^4 + 743627871x^2 + 1432809	\( 2^{12}\cdot 3^{18}\cdot 7^{10}\cdot 19^{10} \)	$C_6\times C_2$ (as 12T2)	$[6, 6, 327894]$ (GRH)
12.0.2748267123526559548681146214649856.18	x^12 + 64638x^8 - 1550780x^6 + 933713865x^4 + 50119658820x^2 + 624972464704	\( 2^{12}\cdot 3^{18}\cdot 7^{10}\cdot 19^{10} \)	$C_6\times C_2$ (as 12T2)	$[2, 2, 2, 2, 6, 12, 12, 912]$ (GRH)
12.0.2748267123526559548681146214649856.21	x^12 + 64638x^8 - 1550780x^6 + 536348169x^4 + 50119658820x^2 + 1100619202816	\( 2^{12}\cdot 3^{18}\cdot 7^{10}\cdot 19^{10} \)	$C_6\times C_2$ (as 12T2)	$[2, 2, 2, 2, 2, 2, 12, 12, 5928]$ (GRH)
12.0.2748267123526559548681146214649856.23	x^12 + 45486x^8 - 2101932x^6 + 854750169x^4 + 47804239476x^2 + 1417566459456	\( 2^{12}\cdot 3^{18}\cdot 7^{10}\cdot 19^{10} \)	$C_6\times C_2$ (as 12T2)	$[2, 4, 4, 4, 12, 13416]$ (GRH)
12.0.2748267123526559548681146214649856.31	x^12 + 7182x^8 + 4184180x^6 + 167001849x^4 - 15025390380x^2 + 4790180067904	\( 2^{12}\cdot 3^{18}\cdot 7^{10}\cdot 19^{10} \)	$C_6\times C_2$ (as 12T2)	$[2, 2, 2, 2, 4, 4, 12, 6384]$ (GRH)
12.0.3170112398857312997665091547561984.1	x^12 + 1092x^10 + 384930x^8 + 54427464x^6 + 2733815448x^4 + 23518325376x^2 + 449513064	\( 2^{33}\cdot 3^{6}\cdot 7^{10}\cdot 13^{11} \)	$C_{12}$ (as 12T1)	$[2, 2, 2, 814, 4884]$ (GRH)
12.0.3170112398857312997665091547561984.2	x^12 + 1092x^10 + 247338x^8 + 22407840x^6 + 889945056x^4 + 13314502656x^2 + 17178086016	\( 2^{33}\cdot 3^{6}\cdot 7^{10}\cdot 13^{11} \)	$C_{12}$ (as 12T1)	$[2, 2, 2, 2, 709644]$ (GRH)
12.0.11848149020404956572813211180466176.3	x^12 + 80802x^8 + 1466758305x^4 + 42363518976	\( 2^{24}\cdot 3^{18}\cdot 67^{10} \)	$C_6\times C_2$ (as 12T2)	$[2, 2, 2, 4, 4, 16, 16, 336]$ (GRH)
12.0.11848149020404956572813211180466176.5	x^12 + 804x^10 + 242406x^8 + 33685456x^6 + 2115867705x^4 + 48604503852x^2 + 348339581209	\( 2^{24}\cdot 3^{18}\cdot 67^{10} \)	$C_6\times C_2$ (as 12T2)	$[30, 469560]$ (GRH)
12.0.27936189811629258922498551985852416.1	x^12 + 1047x^10 + 298395x^8 + 30228984x^6 + 840352563x^4 + 783107838x^2 + 185472909	\( 2^{12}\cdot 3^{6}\cdot 349^{11} \)	$C_{12}$ (as 12T1)	$[2, 2, 4, 4, 4, 4, 31076]$ (GRH)
12.0.115287720075026486867753102672842752.1	x^12 + 1191x^10 + 403749x^8 + 39960432x^6 + 826306272x^4 + 493931520x^2 + 74089728	\( 2^{12}\cdot 3^{6}\cdot 397^{11} \)	$C_{12}$ (as 12T1)	$[2, 2, 2, 2, 2, 2, 4, 4, 11908]$ (GRH)