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 7 matches)

Label	Polynomial	Discriminant	Galois group	Class group
14.2.20325604337285010030592.1	x^14 - 2x^13 + 13x^12 - 52x^11 + 104x^10 - 364x^9 + 806x^8 - 1300x^7 + 2990x^6 - 4212x^5 + 4680x^4 - 7020x^3 + 5265x^2 - 1802x + 445	\( 2^{26}\cdot 13^{13} \)	$\PGL(2,13)$ (as 14T39)	Trivial (GRH)
14.2.24805806724123444820437.1	x^14 - 52x^7 + 91x^6 + 273x^5 - 364x^4 - 1456x^3 - 455x^2 + 1568x + 1495	\( 7^{12}\cdot 13^{11} \)	$\PGL(2,13)$ (as 14T39)	Trivial (GRH)
14.2.73944117820374267578125.1	x^14 - x^13 - 26x^11 + 39x^10 + 104x^9 - 299x^8 - 195x^7 + 676x^6 + 481x^5 - 156x^4 - 39x^3 + 65x^2 - 14x + 1	\( 5^{12}\cdot 13^{13} \)	$\PGL(2,13)$ (as 14T39)	$[6]$ (GRH)
14.2.2637172728176533939372032.1	x^14 - 2x^13 - 78x^10 + 585x^6 + 234x^5 - 1404x^2 - 648x - 108	\( 2^{14}\cdot 3^{12}\cdot 13^{13} \)	$\PGL(2,13)$ (as 14T39)	Trivial (GRH)
14.0.5203354710344962567831552.1	x^14 - 6x^13 + 39x^12 - 156x^11 + 624x^10 - 1924x^9 + 5538x^8 - 12896x^7 + 26416x^6 - 43888x^5 + 60736x^4 - 66144x^3 + 54496x^2 - 31328x + 9296	\( -\,2^{34}\cdot 13^{13} \)	$\PGL(2,13)$ (as 14T39)	Trivial (GRH)
14.2.18929694162015812500000000.1	x^14 - 2x^13 - 130x^10 + 1625x^6 + 650x^5 - 6500x^2 - 3000x - 500	\( 2^{8}\cdot 5^{12}\cdot 13^{13} \)	$\PGL(2,13)$ (as 14T39)	Trivial (GRH)
14.0.270332558098599894702382383104.1	x^14 - 6x^13 + 26x^12 - 78x^11 + 78x^10 + 78x^9 - 702x^8 + 1872x^7 - 130x^6 - 1950x^5 + 11050x^4 - 29406x^3 + 7267x^2 + 16218x + 4014	\( -\,2^{18}\cdot 13^{13}\cdot 23^{7} \)	$\PGL(2,13)$ (as 14T39)	$[2]$ (GRH)