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
12.4.53983295298479387097.1	x^12 - 3x^11 - 8x^10 + 39x^9 - 113x^8 + 325x^7 - 608x^6 - 236x^5 + 2566x^4 - 3435x^3 - 1799x^2 + 5226x - 2027	\( 3^{6}\cdot 257^{7} \)	$C_2^2.A_4:C_4$ (as 12T98)	Trivial
12.4.53983295298479387097.2	x^12 - 3x^11 - 16x^10 - 19x^9 - 121x^8 - 281x^7 - 52x^6 - 442x^5 - 1002x^4 + 349x^3 + 1141x^2 + 1180x - 167	\( 3^{6}\cdot 257^{7} \)	$C_2^2.A_4:C_4$ (as 12T98)	Trivial
12.0.97210242184192000000.1	x^12 + 20x^10 - 2x^9 + 175x^8 - 6x^7 + 862x^6 - 4x^5 + 2375x^4 + 194x^3 + 4536x^2 + 1254x + 5189	\( 2^{16}\cdot 5^{6}\cdot 37^{7} \)	$C_2^2.A_4:C_4$ (as 12T98)	$[6, 6]$
12.8.97210242184192000000.1	x^12 - 2x^11 - 16x^10 - 28x^9 - 99x^8 - 28x^7 + 558x^6 + 1214x^5 + 339x^4 - 2154x^3 - 1800x^2 + 90x + 163	\( 2^{16}\cdot 5^{6}\cdot 37^{7} \)	$C_2^2.A_4:C_4$ (as 12T98)	Trivial
12.8.97210242184192000000.2	x^12 - 4x^11 - 28x^10 + 60x^9 + 174x^8 - 74x^7 + 488x^6 + 534x^5 - 1364x^4 + 332x^3 + 414x^2 - 1584x + 702	\( 2^{16}\cdot 5^{6}\cdot 37^{7} \)	$C_2^2.A_4:C_4$ (as 12T98)	Trivial
12.0.117303817966709400832.1	x^12 - 6x^11 + 52x^10 - 205x^9 + 845x^8 - 2216x^7 + 5217x^6 - 8690x^5 + 11889x^4 - 11503x^3 + 7833x^2 - 3217x + 551	\( 2^{8}\cdot 13^{6}\cdot 37^{7} \)	$C_2^2.A_4:C_4$ (as 12T98)	$[6, 6]$
12.12.388840968736768000000.1	x^12 - 2x^11 - 42x^10 - 12x^9 + 518x^8 + 754x^7 - 1896x^6 - 4808x^5 - 928x^4 + 4356x^3 + 2018x^2 - 956x - 226	\( 2^{18}\cdot 5^{6}\cdot 37^{7} \)	$C_2^2.A_4:C_4$ (as 12T98)	Trivial (GRH)
12.12.407729307634125242368.1	x^12 - 36x^10 + 317x^8 - 1036x^6 + 1295x^4 - 444x^2 + 37	\( 2^{32}\cdot 37^{7} \)	$C_2^2.A_4:C_4$ (as 12T98)	Trivial (GRH)