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 4 matches)

Label	Polynomial	Discriminant	Galois group	Class group
12.4.36442794820015380778081.1	x^12 - 3x^11 - 5x^10 + 11x^9 + 40x^8 + 139x^7 - 1505x^6 + 9090x^5 - 24504x^4 + 5576x^3 + 95056x^2 - 153440x + 59712	\( 661^{8} \)	$M_{11}$ (as 12T272)	Trivial (GRH)
12.4.1476225000000000000000000.1	x^12 - x^11 - 16x^10 + 15x^9 + 145x^8 - 8x^7 - 392x^6 + 88x^5 + 415x^4 - 255x^3 - 64x^2 + 89x - 41	\( 2^{18}\cdot 3^{10}\cdot 5^{20} \)	$M_{11}$ (as 12T272)	$[2]$ (GRH)
12.12.273644380620093450686292199131386889530712784896.1	x^12 - 5526x^10 - 11000x^9 + 11072751x^8 + 48056976x^7 - 9806288196x^6 - 66045530544x^5 + 3652512071076x^4 + 32827558924192x^3 - 401077519158720x^2 - 3666673786739256x + 5270752514492878	\( 2^{32}\cdot 3^{12}\cdot 337^{4}\cdot 310501^{4} \)	$M_{11}$ (as 12T272)	$[2]$ (GRH)
12.12.392917207432060604272953142193224798570962446217446400000000.1	x^12 - x^11 - 100067x^10 + 4532198x^9 + 2259444770x^8 - 152359965054x^7 - 16041513207467x^6 + 1461301745883639x^5 + 14413851909825665x^4 - 3552570264974645508x^3 + 69523530327654696348x^2 + 31953284631467426916x - 861259903428927255084	\( 2^{16}\cdot 3^{4}\cdot 5^{8}\cdot 11^{12}\cdot 13^{4}\cdot 17^{4}\cdot 347^{10} \)	$M_{11}$ (as 12T272)	$[2]$ (GRH)