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 matches 1-50 of 109)

Label	Polynomial	Discriminant	Galois group	Class group
12.2.96717311574016.3	x^12 + x^8 - 2x^4 - 1	\( -\,2^{24}\cdot 7^{8} \)	$C_4:D_4:C_3$ (as 12T61)	Trivial
12.2.96717311574016.4	x^12 + 4x^8 + 3x^4 - 1	\( -\,2^{24}\cdot 7^{8} \)	$C_4:D_4:C_3$ (as 12T61)	Trivial
12.2.677021181018112.1	x^12 + 4x^10 + 3x^8 - 8x^6 - 21x^4 - 28x^2 - 7	\( -\,2^{24}\cdot 7^{9} \)	$C_4:D_4:C_3$ (as 12T61)	Trivial
12.2.677021181018112.6	x^12 + 2x^10 - 8x^8 + 6x^6 - 7x^4 + 14x^2 - 7	\( -\,2^{24}\cdot 7^{9} \)	$C_4:D_4:C_3$ (as 12T61)	Trivial
12.2.722204136308736.12	x^12 - 3x^8 - 6x^4 - 1	\( -\,2^{24}\cdot 3^{16} \)	$C_4:D_4:C_3$ (as 12T61)	Trivial
12.2.722204136308736.13	x^12 - 3x^4 - 1	\( -\,2^{24}\cdot 3^{16} \)	$C_4:D_4:C_3$ (as 12T61)	Trivial
12.2.773738492592128.4	x^12 - 4x^10 + 4x^8 - 4x^6 + 20x^4 - 16x^2 - 8	\( -\,2^{27}\cdot 7^{8} \)	$C_4:D_4:C_3$ (as 12T61)	Trivial
12.2.773738492592128.5	x^12 + 6x^10 + 16x^8 + 24x^6 + 12x^4 - 8x^2 - 8	\( -\,2^{27}\cdot 7^{8} \)	$C_4:D_4:C_3$ (as 12T61)	Trivial
12.2.2166612408926208.5	x^12 - 9x^8 - 16x^6 + 3x^4 - 3	\( -\,2^{24}\cdot 3^{17} \)	$C_4:D_4:C_3$ (as 12T61)	Trivial
12.2.2166612408926208.8	x^12 + 6x^10 + 15x^8 + 20x^6 + 12x^4 - 3	\( -\,2^{24}\cdot 3^{17} \)	$C_4:D_4:C_3$ (as 12T61)	Trivial
12.2.5416169448144896.4	x^12 + 2x^10 - 8x^8 - 8x^6 + 28x^4 - 56	\( -\,2^{27}\cdot 7^{9} \)	$C_4:D_4:C_3$ (as 12T61)	Trivial
12.2.5416169448144896.6	x^12 - 10x^10 + 38x^8 - 64x^6 + 28x^4 + 56x^2 - 56	\( -\,2^{27}\cdot 7^{9} \)	$C_4:D_4:C_3$ (as 12T61)	Trivial
12.2.5777633090469888.6	x^12 - 6x^10 + 24x^8 - 56x^6 + 60x^4 - 24x^2 - 8	\( -\,2^{27}\cdot 3^{16} \)	$C_4:D_4:C_3$ (as 12T61)	Trivial
12.2.5777633090469888.8	x^12 - 6x^8 + 16x^6 + 24x^2 - 8	\( -\,2^{27}\cdot 3^{16} \)	$C_4:D_4:C_3$ (as 12T61)	Trivial
12.2.13685690504052736.16	x^12 - 3x^8 - 10x^4 - 1	\( -\,2^{24}\cdot 13^{8} \)	$C_4:D_4:C_3$ (as 12T61)	Trivial
12.2.13685690504052736.17	x^12 - x^8 - 4x^4 - 1	\( -\,2^{24}\cdot 13^{8} \)	$C_4:D_4:C_3$ (as 12T61)	Trivial
12.2.13973766757433344.4	x^12 + 7x^8 - 56x^4 - 16	\( -\,2^{14}\cdot 31^{8} \)	$C_4:D_4:C_3$ (as 12T61)	$[4]$
12.2.13973766757433344.7	x^12 - 5x^11 + 6x^10 - 3x^9 + 15x^8 - 44x^6 + 15x^4 - 3x^3 + 6x^2 - 5x + 1	\( -\,2^{14}\cdot 31^{8} \)	$C_4:D_4:C_3$ (as 12T61)	$[4]$
12.2.17332899271409664.6	x^12 - 6x^8 - 4x^6 + 24x^4 - 24	\( -\,2^{27}\cdot 3^{17} \)	$C_4:D_4:C_3$ (as 12T61)	Trivial
12.2.17332899271409664.8	x^12 - 6x^10 + 6x^8 + 32x^6 - 84x^4 + 72x^2 - 24	\( -\,2^{27}\cdot 3^{17} \)	$C_4:D_4:C_3$ (as 12T61)	Trivial
12.2.109485524032421888.7	x^12 - 6x^10 + 32x^8 - 88x^6 + 92x^4 - 24x^2 - 8	\( -\,2^{27}\cdot 13^{8} \)	$C_4:D_4:C_3$ (as 12T61)	Trivial
12.2.109485524032421888.11	x^12 - 2x^10 - 8x^8 + 16x^6 - 4x^4 + 32x^2 - 8	\( -\,2^{27}\cdot 13^{8} \)	$C_4:D_4:C_3$ (as 12T61)	Trivial
12.2.177913976552685568.3	x^12 + 12x^10 + 48x^8 + 64x^6 - 91x^4 - 364x^2 - 325	\( -\,2^{24}\cdot 13^{9} \)	$C_4:D_4:C_3$ (as 12T61)	Trivial
12.2.177913976552685568.9	x^12 - 12x^10 + 61x^8 - 168x^6 + 247x^4 - 156x^2 - 13	\( -\,2^{24}\cdot 13^{9} \)	$C_4:D_4:C_3$ (as 12T61)	Trivial
12.2.223580268118933504.15	x^12 + 4x^8 - 5x^4 - 16	\( -\,2^{18}\cdot 31^{8} \)	$C_4:D_4:C_3$ (as 12T61)	$[4]$
12.2.223580268118933504.28	x^12 - 15x^8 - 49x^4 - 1	\( -\,2^{18}\cdot 31^{8} \)	$C_4:D_4:C_3$ (as 12T61)	$[4]$
12.2.284936905588473856.17	x^12 - 3x^8 - 16x^4 - 1	\( -\,2^{24}\cdot 19^{8} \)	$C_4:D_4:C_3$ (as 12T61)	Trivial
12.2.284936905588473856.18	x^12 - 2x^8 - 5x^4 - 1	\( -\,2^{24}\cdot 19^{8} \)	$C_4:D_4:C_3$ (as 12T61)	Trivial (GRH)
12.2.894321072475734016.8	x^12 - 8x^10 - 15x^8 - 2x^6 + 192x^4 - 160x^2 - 256	\( -\,2^{20}\cdot 31^{8} \)	$C_4:D_4:C_3$ (as 12T61)	$[2]$ (GRH)
12.2.894321072475734016.47	x^12 - 27x^8 - 160x^4 - 16	\( -\,2^{20}\cdot 31^{8} \)	$C_4:D_4:C_3$ (as 12T61)	$[2]$
12.2.894321072475734016.48	x^12 - 11x^8 - 32x^4 - 16	\( -\,2^{20}\cdot 31^{8} \)	$C_4:D_4:C_3$ (as 12T61)	$[2]$ (GRH)
12.2.894321072475734016.62	x^12 - 4x^11 - x^10 - 8x^9 + 127x^8 - 300x^7 + 397x^6 - 648x^5 + 1006x^4 - 812x^3 + 266x^2 - 24x + 4	\( -\,2^{20}\cdot 31^{8} \)	$C_4:D_4:C_3$ (as 12T61)	$[2]$
12.2.1423311812421484544.21	x^12 + 10x^10 + 42x^8 + 64x^6 - 52x^4 - 312x^2 - 104	\( -\,2^{27}\cdot 13^{9} \)	$C_4:D_4:C_3$ (as 12T61)	Trivial (GRH)
12.2.1423311812421484544.28	x^12 + 4x^10 - 12x^8 + 12x^6 + 52x^4 - 104	\( -\,2^{27}\cdot 13^{9} \)	$C_4:D_4:C_3$ (as 12T61)	Trivial
12.2.2279495244707790848.32	x^12 - 16x^10 + 92x^8 - 220x^6 + 196x^4 - 64x^2 - 8	\( -\,2^{27}\cdot 19^{8} \)	$C_4:D_4:C_3$ (as 12T61)	Trivial
12.2.2279495244707790848.39	x^12 + 2x^10 - 14x^8 + 8x^6 + 80x^4 + 56x^2 - 8	\( -\,2^{27}\cdot 19^{8} \)	$C_4:D_4:C_3$ (as 12T61)	Trivial
12.2.5413801206181003264.6	x^12 - 12x^10 + 48x^8 - 64x^6 - 304x^4 + 1216x^2 - 1216	\( -\,2^{24}\cdot 19^{9} \)	$C_4:D_4:C_3$ (as 12T61)	Trivial
12.2.5413801206181003264.17	x^12 - 2x^10 - 81x^8 - 400x^6 - 912x^4 - 988x^2 - 19	\( -\,2^{24}\cdot 19^{9} \)	$C_4:D_4:C_3$ (as 12T61)	Trivial
12.6.7839262992886707907.1	x^12 - 4x^11 - 12x^10 + 36x^9 + 106x^8 - 216x^7 - 258x^6 + 1064x^5 - 23x^4 - 2976x^3 - 210x^2 + 3668x - 203	\( -\,7^{9}\cdot 181^{5} \)	$C_4:D_4:C_3$ (as 12T61)	$[4]$
12.6.7839262992886707907.4	x^12 - 5x^11 + 2x^10 + 34x^9 - 54x^8 - 52x^7 - 127x^6 + 232x^5 + 888x^4 - 3015x^3 - 3137x^2 + 2621x + 1289	\( -\,7^{9}\cdot 181^{5} \)	$C_4:D_4:C_3$ (as 12T61)	$[4]$
12.4.12772361626857247797.1	x^12 - 3x^11 - 9x^10 + 5x^9 + 33x^8 + 45x^7 - 51x^6 + 270x^5 + 540x^4 - 1989x^3 - 2187x^2 + 648x + 81	\( 3^{16}\cdot 197^{5} \)	$C_4:D_4:C_3$ (as 12T61)	$[4]$
12.4.12772361626857247797.2	x^12 - 3x^11 + 12x^10 + 12x^9 - 36x^8 - 396x^7 + 289x^6 + 954x^5 + 1362x^4 - 3719x^3 - 2805x^2 + 5085x + 213	\( 3^{16}\cdot 197^{5} \)	$C_4:D_4:C_3$ (as 12T61)	$[4]$
12.2.28618274319223488512.1	x^12 - 2x^11 - 5x^10 - 8x^9 + 48x^8 - 12x^6 + 96x^5 - 240x^4 - 648x^3 - 1540x^2 + 6080x - 5336	\( -\,2^{25}\cdot 31^{8} \)	$C_4:D_4:C_3$ (as 12T61)	$[2]$ (GRH)
12.2.28618274319223488512.15	x^12 + 2x^10 + 30x^8 - 384x^6 - 664x^4 - 1088x^2 - 128	\( -\,2^{25}\cdot 31^{8} \)	$C_4:D_4:C_3$ (as 12T61)	$[2]$ (GRH)
12.2.28618274319223488512.46	x^12 + 4x^10 + 27x^8 - 282x^6 - 146x^4 - 96x^2 - 8	\( -\,2^{25}\cdot 31^{8} \)	$C_4:D_4:C_3$ (as 12T61)	$[2]$ (GRH)
12.2.28618274319223488512.66	x^12 + 6x^10 + 22x^8 + 48x^6 + 63x^4 + 46x^2 - 2	\( -\,2^{25}\cdot 31^{8} \)	$C_4:D_4:C_3$ (as 12T61)	$[2]$
12.2.43310409649448026112.21	x^12 + 4x^10 + 18x^8 + 84x^6 - 152x^4 - 912x^2 - 152	\( -\,2^{27}\cdot 19^{9} \)	$C_4:D_4:C_3$ (as 12T61)	Trivial (GRH)
12.2.43310409649448026112.35	x^12 + 6x^10 - 64x^8 + 160x^6 - 228x^4 + 304x^2 - 152	\( -\,2^{27}\cdot 19^{9} \)	$C_4:D_4:C_3$ (as 12T61)	Trivial (GRH)
12.2.55447906493495508992.6	x^12 + 32x^10 + 362x^8 + 2348x^6 + 9424x^4 + 15872x^2 - 15872	\( -\,2^{21}\cdot 31^{9} \)	$C_4:D_4:C_3$ (as 12T61)	$[2]$ (GRH)
12.2.55447906493495508992.7	x^12 - 11x^10 - 32x^8 + 1162x^6 - 7936x^4 + 21824x^2 - 15872	\( -\,2^{21}\cdot 31^{9} \)	$C_4:D_4:C_3$ (as 12T61)	$[2, 2]$