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 )

Label	Polynomial	Discriminant	Galois group	Class group
6.0.30060272.1	x^6 - x^5 + 17x^4 - 11x^3 + 112x^2 - 88x + 308	\( -\,2^{4}\cdot 11^{2}\cdot 15527 \)	$S_4\times C_2$ (as 6T11)	$[11]$
6.0.31055216.1	x^6 - 3x^5 + 17x^4 - 29x^3 + 62x^2 - 48x + 16	\( -\,2^{4}\cdot 79^{2}\cdot 311 \)	$S_4\times C_2$ (as 6T11)	$[11]$
6.0.31504463.2	x^6 - 3x^5 + x^4 - x^3 - 57x^2 + 207x + 459	\( -\,31^{2}\cdot 32783 \)	$S_4\times C_2$ (as 6T11)	$[11]$
6.0.31594759.1	x^6 - 2x^5 + 19x^4 - 28x^3 + 122x^2 - 106x + 281	\( -\,7^{4}\cdot 13159 \)	$A_4\times C_2$ (as 6T6)	$[11]$
6.0.33559808.1	x^6 - 2x^5 - 4x^4 - 8x^3 + 26x^2 + 72x + 40	\( -\,2^{8}\cdot 337\cdot 389 \)	$C_3^2:D_4$ (as 6T13)	$[11]$
6.0.34082471.1	x^6 - 2x^5 + 17x^4 - 21x^3 + 98x^2 - 53x + 176	\( -\,59^{2}\cdot 9791 \)	$S_4\times C_2$ (as 6T11)	$[11]$
6.0.34148336.1	x^6 - x^5 + 9x^4 - 13x^3 + 30x^2 - 50x + 86	\( -\,2^{4}\cdot 37^{2}\cdot 1559 \)	$S_4\times C_2$ (as 6T11)	$[11]$
6.0.34250608.1	x^6 - x^5 - 3x^4 + x^3 + 28x^2 + 2x + 64	\( -\,2^{4}\cdot 7^{3}\cdot 79^{2} \)	$D_{6}$ (as 6T3)	$[11]$
6.0.35199728.1	x^6 - x^5 + 9x^4 - 5x^3 + 24x^2 - 2x + 50	\( -\,2^{4}\cdot 37^{2}\cdot 1607 \)	$S_4\times C_2$ (as 6T11)	$[11]$
6.0.36081503.3	x^6 - x^5 + 28x^4 - 15x^3 + 290x^2 - 16x + 1049	\( -\,23^{2}\cdot 68207 \)	$S_4\times C_2$ (as 6T11)	$[11]$
6.0.36300719.1	x^6 - x^5 + 19x^4 - 13x^3 + 119x^2 - 49x + 301	\( -\,7^{4}\cdot 13\cdot 1163 \)	$A_4\times C_2$ (as 6T6)	$[12]$
6.0.37242880.1	x^6 - 2x^5 - 5x^4 + 32x^3 - 16x^2 - 76x + 170	\( -\,2^{11}\cdot 5\cdot 3637 \)	$C_3^2:D_4$ (as 6T13)	$[11]$
6.0.38198560.1	x^6 - x^5 + 10x^4 - 3x^3 + 33x^2 + 2x + 46	\( -\,2^{5}\cdot 5\cdot 193\cdot 1237 \)	$S_6$ (as 6T16)	$[11]$
6.0.38317559.1	x^6 - 2x^5 + 22x^4 - 32x^3 + 143x^2 - 130x + 349	\( -\,7^{4}\cdot 15959 \)	$A_4\times C_2$ (as 6T6)	$[11]$
6.0.38353904.1	x^6 - 3x^5 + 11x^4 - 15x^3 + 38x^2 - 18x + 50	\( -\,2^{4}\cdot 17\cdot 37^{2}\cdot 103 \)	$S_4\times C_2$ (as 6T11)	$[12]$
6.0.38404871.2	x^6 - x^5 + 12x^4 + 19x^3 + 36x^2 + 286x + 1127	\( -\,19\cdot 23^{2}\cdot 3821 \)	$S_4\times C_2$ (as 6T11)	$[12]$
6.0.38720927.1	x^6 - 2x^5 + 20x^4 - 20x^3 + 133x^2 - 56x + 301	\( -\,7^{4}\cdot 16127 \)	$A_4\times C_2$ (as 6T6)	$[11]$
6.0.38729583.1	x^6 + 15x^4 - 10x^3 + 72x^2 - 72x + 153	\( -\,3^{8}\cdot 5903 \)	$A_4\times C_2$ (as 6T6)	$[11]$
6.0.39054832.1	x^6 - 3x^5 + 17x^4 - 29x^3 + 66x^2 - 52x + 40	\( -\,2^{4}\cdot 37^{2}\cdot 1783 \)	$S_4\times C_2$ (as 6T11)	$[11]$
6.0.39272896.1	x^6 - x^5 + x^4 - 5x^3 + 2x^2 - 14x + 104	\( -\,2^{6}\cdot 13^{2}\cdot 3631 \)	$S_4\times C_2$ (as 6T11)	$[13]$
6.0.39662119.1	x^6 - 3x^5 + 25x^4 - 45x^3 + 167x^2 - 145x + 293	\( -\,7^{4}\cdot 16519 \)	$A_4\times C_2$ (as 6T6)	$[11]$
6.0.39674367.1	x^6 - 3x^5 + 18x^4 - 27x^3 + 78x^2 - 48x + 152	\( -\,3^{8}\cdot 6047 \)	$A_4\times C_2$ (as 6T6)	$[11]$
6.0.39761375.1	x^6 - x^5 - 12x^4 + 39x^3 - 44x^2 - 268x + 744	\( -\,5^{3}\cdot 31^{2}\cdot 331 \)	$S_4\times C_2$ (as 6T11)	$[12]$
6.0.40361039.1	x^6 - 3x^5 - 9x^4 + 23x^3 - 48x^2 + 36x + 648	\( -\,31^{2}\cdot 41999 \)	$S_4\times C_2$ (as 6T11)	$[11]$
6.0.40430231.1	x^6 - 2x^5 - 11x^4 - 15x^3 + 14x^2 + 272x + 632	\( -\,31^{2}\cdot 42071 \)	$S_4\times C_2$ (as 6T11)	$[13]$
6.0.41434343.1	x^6 - 2x^5 - 11x^4 + 27x^3 + 22x^2 - 173x + 272	\( -\,59^{2}\cdot 11903 \)	$S_4\times C_2$ (as 6T11)	$[11]$
6.0.41468111.1	x^6 - 3x^5 + 27x^4 - 49x^3 + 249x^2 - 225x + 729	\( -\,31^{2}\cdot 43151 \)	$S_4\times C_2$ (as 6T11)	$[13]$
6.0.41680439.1	x^6 - x^5 - 7x^4 - 21x^3 - 121x^2 + 263x + 1243	\( -\,23^{2}\cdot 78791 \)	$S_4\times C_2$ (as 6T11)	$[13]$
6.0.42332167.1	x^6 - 2x^5 + 12x^4 - 44x^3 + 117x^2 - 356x + 1393	\( -\,23^{2}\cdot 43\cdot 1861 \)	$S_4\times C_2$ (as 6T11)	$[12]$
6.0.42398359.1	x^6 - 2x^5 + 20x^4 - 31x^3 + 200x^2 - 63x + 811	\( -\,31^{2}\cdot 44119 \)	$S_4\times C_2$ (as 6T11)	$[11]$
6.0.43453503.1	x^6 - 3x^5 + 18x^4 - 27x^3 + 96x^2 - 84x + 152	\( -\,3^{8}\cdot 37\cdot 179 \)	$A_4\times C_2$ (as 6T6)	$[12]$
6.0.43619904.1	x^6 - 2x^5 - 14x^4 + 24x^3 + 48x^2 - 54x + 81	\( -\,2^{6}\cdot 3^{3}\cdot 25243 \)	$C_3^2:D_4$ (as 6T13)	$[11]$
6.0.44771447.1	x^6 - 3x^5 + 25x^4 - 45x^3 + 174x^2 - 152x + 328	\( -\,7^{4}\cdot 29\cdot 643 \)	$A_4\times C_2$ (as 6T6)	$[12]$
6.0.45194023.1	x^6 - x^5 + 22x^4 - x^3 + 148x^2 + 20x + 344	\( -\,7^{5}\cdot 2689 \)	$A_4\times C_2$ (as 6T6)	$[12]$
6.0.45578183.1	x^6 - x^5 + 23x^4 - 11x^3 + 145x^2 - x + 377	\( -\,7^{4}\cdot 41\cdot 463 \)	$A_4\times C_2$ (as 6T6)	$[14]$
6.0.46116007.1	x^6 - x^5 + 24x^4 - 35x^3 + 180x^2 - 156x + 379	\( -\,7^{4}\cdot 19207 \)	$A_4\times C_2$ (as 6T6)	$[11]$
6.0.47220976.2	x^6 - x^5 + 15x^4 - 11x^3 + 122x^2 - 120x + 406	\( -\,2^{4}\cdot 11^{2}\cdot 24391 \)	$S_4\times C_2$ (as 6T11)	$[11]$
6.0.47595023.1	x^6 - 3x^5 + 27x^4 - 49x^3 + 195x^2 - 171x + 351	\( -\,7^{4}\cdot 43\cdot 461 \)	$A_4\times C_2$ (as 6T6)	$[12]$
6.0.48451639.1	x^6 - 2x^5 - 2x^4 + 19x^3 - 66x^2 + 319x + 1403	\( -\,23^{2}\cdot 91591 \)	$S_4\times C_2$ (as 6T11)	$[13]$
6.0.48574631.1	x^6 - x^5 + 21x^4 - 5x^3 + 147x^2 + 19x + 377	\( -\,7^{4}\cdot 20231 \)	$A_4\times C_2$ (as 6T6)	$[11]$
6.0.49594599.1	x^6 - 3x^5 + 21x^4 - 29x^3 + 111x^2 - 9x + 159	\( -\,3^{8}\cdot 7559 \)	$A_4\times C_2$ (as 6T6)	$[13]$
6.0.50094448.1	x^6 - 3x^5 + 15x^4 - 25x^3 + 56x^2 - 44x + 46	\( -\,2^{4}\cdot 37^{2}\cdot 2287 \)	$S_4\times C_2$ (as 6T11)	$[13]$
6.0.50188103.2	x^6 - 2x^5 + 24x^4 - 16x^3 + 165x^2 - 16x + 377	\( -\,7^{4}\cdot 20903 \)	$A_4\times C_2$ (as 6T6)	$[11]$
6.0.50817856.2	x^6 + 34x^4 + 389x^2 + 1501	\( -\,2^{6}\cdot 19\cdot 23^{2}\cdot 79 \)	$S_4\times C_2$ (as 6T11)	$[2, 6]$
6.0.51247971.1	x^6 + 15x^4 - 10x^3 + 81x^2 - 45x + 171	\( -\,3^{8}\cdot 73\cdot 107 \)	$A_4\times C_2$ (as 6T6)	$[12]$
6.0.51522831.1	x^6 - 2x^5 + 12x^4 - 15x^3 + 74x^2 - 64x + 160	\( -\,3^{3}\cdot 83^{2}\cdot 277 \)	$S_4\times C_2$ (as 6T11)	$[12]$
6.0.52032071.1	x^6 - 3x^5 + 25x^4 - 45x^3 + 181x^2 - 159x + 377	\( -\,7^{4}\cdot 13\cdot 1667 \)	$A_4\times C_2$ (as 6T6)	$[12]$
6.0.52197232.1	x^6 - 3x^5 + 13x^4 - 13x^3 + 40x^2 - 20x + 68	\( -\,2^{4}\cdot 37^{2}\cdot 2383 \)	$S_4\times C_2$ (as 6T11)	$[13]$
6.0.52287583.1	x^6 - 2x^5 - x^4 - 17x^3 + 10x^2 + 59x + 62	\( -\,107^{2}\cdot 4567 \)	$S_4\times C_2$ (as 6T11)	$[11]$
6.0.52624112.1	x^6 - x^5 + 8x^4 - 6x^3 + 32x^2 - 16x + 64	\( -\,2^{4}\cdot 17\cdot 31\cdot 79^{2} \)	$S_4\times C_2$ (as 6T11)	$[14]$

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