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 8 matches)

Label	Polynomial	Discriminant	Galois group	Class group
14.6.10260628712958602189.1	x^14 - 7x^13 + 30x^12 - 89x^11 + 184x^10 - 271x^9 + 254x^8 - 83x^7 - 96x^6 + 119x^5 - 37x^4 - 17x^3 + 13x^2 - x - 1	\( 29^{13} \)	$C_2\times F_8$ (as 14T9)	$[2]$
14.8.773792930870360792667.1	x^14 - 3x^13 - 18x^12 + 28x^11 + 114x^10 - 104x^9 - 289x^8 + 119x^7 + 365x^6 + 104x^5 - 343x^4 - 175x^3 + 158x^2 + 61x - 17	\( -\,3^{7}\cdot 29^{12} \)	$C_2\times F_8$ (as 14T9)	Trivial
14.6.1738292029888469398433.2	x^14 - 5x^13 - 3x^12 + 4x^11 + 13x^10 + 43x^9 + 57x^8 + 69x^7 + 57x^6 + 43x^5 + 13x^4 + 4x^3 - 3x^2 - 5x + 1	\( 17^{3}\cdot 29^{12} \)	$C_2\times F_8$ (as 14T9)	Trivial
14.0.5796901408038404767744.3	x^14 + 16x^12 + 89x^10 + 212x^8 + 236x^6 + 119x^4 + 23x^2 + 1	\( -\,2^{14}\cdot 29^{12} \)	$C_2\times F_8$ (as 14T9)	$[2, 2, 8]$
14.8.5796901408038404767744.3	x^14 - 13x^12 + 31x^10 + 9x^8 - 54x^6 + 3x^4 + 23x^2 + 1	\( -\,2^{14}\cdot 29^{12} \)	$C_2\times F_8$ (as 14T9)	Trivial
14.0.168110140833113738264576.2	x^14 + 29x^12 + 348x^10 + 2233x^8 + 8236x^6 + 17342x^4 + 19111x^2 + 8381	\( -\,2^{14}\cdot 29^{13} \)	$C_2\times F_8$ (as 14T9)	$[2, 2, 2, 12]$ (GRH)
14.14.168110140833113738264576.1	x^14 - 29x^12 + 348x^10 - 2233x^8 + 8236x^6 - 17342x^4 + 19111x^2 - 8381	\( 2^{14}\cdot 29^{13} \)	$C_2\times F_8$ (as 14T9)	$[2]$
14.14.742003380228915810271232.2	x^14 - 32x^12 + 356x^10 - 1696x^8 + 3776x^6 - 3808x^4 + 1472x^2 - 128	\( 2^{21}\cdot 29^{12} \)	$C_2\times F_8$ (as 14T9)	Trivial (GRH)