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 16 matches)

Label	Polynomial	Discriminant	Galois group	Class group
14.0.16973485041483.1	x^14 - 2x^13 + 2x^12 - 6x^11 + 8x^10 - 4x^9 + 9x^8 - 11x^7 + 6x^6 - 6x^5 + 5x^4 - 4x^3 + 2x^2 + 1	\( -\,3^{7}\cdot 37^{2}\cdot 2381^{2} \)	$S_7\times C_2$ (as 14T49)	Trivial
14.0.28466647927227.1	x^14 - x^13 + 2x^12 + 3x^11 - x^10 + 4x^9 + 3x^8 + 2x^7 + 2x^4 - 2x^3 - x^2 + 1	\( -\,3^{7}\cdot 114089^{2} \)	$S_7\times C_2$ (as 14T49)	Trivial
14.0.51902598731283.1	x^14 - 2x^13 + 3x^12 - 6x^11 + 6x^10 - 4x^9 + 3x^8 + x^7 - x^5 + 3x^4 + 3x^2 + x + 1	\( -\,3^{11}\cdot 17117^{2} \)	$S_7\times C_2$ (as 14T49)	Trivial
14.0.74532401109963.1	x^14 - x^13 + 2x^12 - x^11 + 2x^10 - 2x^9 + 2x^8 - 2x^7 - 3x^5 - x^3 + 2x^2 + x + 1	\( -\,3^{7}\cdot 184607^{2} \)	$S_7\times C_2$ (as 14T49)	Trivial
14.0.172575877556547.1	x^14 - x^13 - x^12 + 2x^10 + x^9 - x^8 - x^7 - x^6 + x^5 + 2x^4 - x^2 - x + 1	\( -\,3^{7}\cdot 280909^{2} \)	$S_7\times C_2$ (as 14T49)	Trivial
14.0.263657868936003.1	x^14 + x^12 - 2x^11 - x^10 + 3x^7 - x^4 - 2x^3 + x^2 + 1	\( -\,3^{7}\cdot 103^{2}\cdot 3371^{2} \)	$S_7\times C_2$ (as 14T49)	Trivial
14.2.321952970703125.1	x^14 - 3x^13 + 2x^12 + 3x^11 - 7x^10 + 11x^9 - 25x^8 + 33x^7 - 4x^6 - 56x^5 + 93x^4 - 78x^3 + 38x^2 - 10x + 1	\( 5^{9}\cdot 37^{2}\cdot 347^{2} \)	$S_7\times C_2$ (as 14T49)	Trivial
14.2.386441371953125.1	x^14 - x^13 - 2x^12 + 4x^11 - 2x^10 - 3x^9 + x^8 + 6x^6 - 11x^5 + 5x^4 - 12x^3 + 24x^2 - 20x + 5	\( 5^{7}\cdot 53^{2}\cdot 1327^{2} \)	$S_7\times C_2$ (as 14T49)	Trivial
14.6.5139738988203125.1	x^14 - 4x^13 - x^12 + 24x^11 - 26x^10 - 27x^9 + 63x^8 - 34x^7 - x^6 + 23x^5 - 35x^4 + 16x^3 - x^2 + 2x + 1	\( 5^{7}\cdot 256493^{2} \)	$S_7\times C_2$ (as 14T49)	Trivial
14.6.29283534866328125.1	x^14 - x^13 + 2x^12 + x^11 - 6x^10 + 7x^9 - 14x^8 - 36x^7 - 24x^6 - 12x^5 + 2x^4 + 5x^3 + 4x^2 + x - 1	\( 5^{7}\cdot 71^{2}\cdot 8623^{2} \)	$S_7\times C_2$ (as 14T49)	Trivial
14.10.81799439172384353.1	x^14 - 4x^13 - 2x^12 + 26x^11 - 21x^10 - 59x^9 + 86x^8 + 63x^7 - 114x^6 - 49x^5 + 61x^4 + 30x^3 - 9x^2 - 7x - 1	\( 7^{2}\cdot 17^{7}\cdot 2017^{2} \)	$S_7\times C_2$ (as 14T49)	Trivial
14.0.121781095161992523.1	x^14 - 3x^13 + 12x^12 - 13x^11 + 40x^10 - 31x^9 + 97x^8 - 37x^7 + 108x^6 - 23x^5 + 89x^4 - 4x^3 + 10x^2 + 1	\( -\,3^{7}\cdot 43^{2}\cdot 173539^{2} \)	$S_7\times C_2$ (as 14T49)	Trivial
14.0.153874832821917507.1	x^14 - 2x^13 + 9x^12 - 8x^11 + 36x^10 - 27x^9 + 92x^8 - 32x^7 + 125x^6 - 39x^5 + 105x^4 + 6x^3 + 14x^2 - 2x + 1	\( -\,3^{7}\cdot 8388019^{2} \)	$S_7\times C_2$ (as 14T49)	Trivial
14.10.415656167718828125.1	x^14 - 9x^12 - 4x^11 + 16x^10 + 36x^9 + 8x^8 - 64x^7 - 11x^6 + 40x^5 - 13x^4 - 7x^3 + 10x^2 - x - 1	\( 5^{7}\cdot 107^{2}\cdot 21557^{2} \)	$S_7\times C_2$ (as 14T49)	Trivial
14.14.19195235171446953125.1	x^14 - x^13 - 21x^12 + 22x^11 + 145x^10 - 138x^9 - 433x^8 + 371x^7 + 560x^6 - 449x^5 - 244x^4 + 194x^3 + 4x^2 - 11x + 1	\( 5^{7}\cdot 13^{2}\cdot 1205753^{2} \)	$S_7\times C_2$ (as 14T49)	Trivial (GRH)
14.14.31671389178003828125.1	x^14 - x^13 - 19x^12 + 14x^11 + 107x^10 - 53x^9 - 240x^8 + 87x^7 + 241x^6 - 66x^5 - 108x^4 + 22x^3 + 19x^2 - 2x - 1	\( 5^{7}\cdot 71^{2}\cdot 283583^{2} \)	$S_7\times C_2$ (as 14T49)	Trivial (GRH)