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 24 matches)

Label	Polynomial	Discriminant	Galois group	Class group
14.4.3222197555141171.1	x^14 - 7x^13 + 22x^12 - 41x^11 + 46x^10 - 21x^9 - 25x^8 + 61x^7 - 63x^6 + 38x^5 - 9x^4 - 6x^3 + 9x^2 - 5x + 1	\( -\,17^{4}\cdot 131^{5} \)	14T56	Trivial
14.2.4396746947664269.1	x^14 - x^13 - x^12 + 2x^11 + 2x^10 - 9x^9 + 5x^8 + x^7 + 5x^6 - 9x^5 + 2x^4 + 2x^3 - x^2 - x + 1	\( 11^{8}\cdot 29^{5} \)	14T56	Trivial
14.4.7651638724807467.1	x^14 - x^13 - 5x^12 - 2x^11 + 8x^10 + 7x^9 - 3x^8 - 9x^7 - 12x^6 - 11x^5 + 8x^4 + 16x^3 + 5x^2 - 2x - 1	\( -\,3^{13}\cdot 13^{2}\cdot 73^{4} \)	14T56	Trivial
14.2.15046713626495157.1	x^14 - x^13 - x^12 + 9x^11 - 9x^10 - 9x^9 + 32x^8 - 26x^7 - 17x^6 + 48x^5 - 42x^4 + 18x^3 - x^2 - 2x + 1	\( 3^{12}\cdot 73^{4}\cdot 997 \)	14T56	Trivial
14.0.42966894377765007.1	x^14 - 4x^13 + 7x^12 - 13x^11 + 19x^10 - 22x^9 + 31x^8 - 25x^7 + 31x^6 - 22x^5 + 19x^4 - 13x^3 + 7x^2 - 4x + 1	\( -\,3^{13}\cdot 13\cdot 73^{5} \)	14T56	Trivial
14.6.128900683133295021.1	x^14 - 5x^13 + 8x^12 + 6x^11 - 33x^10 + 18x^9 + 47x^8 - 58x^7 - 20x^6 + 36x^5 + 36x^4 - 12x^3 - 44x^2 + 22x - 1	\( 3^{14}\cdot 13\cdot 73^{5} \)	14T56	Trivial
14.0.247267157529083904.1	x^14 + 7x^12 + 24x^10 + 49x^8 + 64x^6 + 48x^4 + 13x^2 + 1	\( -\,2^{14}\cdot 3^{12}\cdot 73^{4} \)	14T56	Trivial
14.6.741801472587251712.1	x^14 - 3x^12 - 3x^10 + 14x^8 - 3x^6 - 15x^4 + 11x^2 - 3	\( 2^{14}\cdot 3^{13}\cdot 73^{4} \)	14T56	Trivial
14.4.3907823013550959364.1	x^14 - 2x^13 - 2x^12 + x^11 - 5x^10 - 3x^9 - 4x^8 - 4x^7 - 4x^6 - 3x^5 - 5x^4 + x^3 - 2x^2 - 2x + 1	\( -\,2^{2}\cdot 149^{4}\cdot 211^{4} \)	14T56	Trivial
14.4.3907823013550959364.2	x^14 - 2x^13 - x^11 + 2x^10 + 2x^8 + 2x^6 + 2x^4 - x^3 - 2x + 1	\( -\,2^{2}\cdot 149^{4}\cdot 211^{4} \)	14T56	Trivial
14.6.6218645434186503125.1	x^14 - 7x^13 + 24x^12 - 53x^11 + 64x^10 - x^9 - 145x^8 + 289x^7 - 231x^6 - 40x^5 + 259x^4 - 252x^3 + 107x^2 - 15x - 1	\( 5^{5}\cdot 6679^{4} \)	14T56	Trivial
14.6.6218645434186503125.2	x^14 - x^13 - 8x^12 - 5x^11 + 29x^10 + 69x^9 - 65x^8 - 195x^7 + 112x^6 + 233x^5 - 80x^4 - 91x^3 + 20x^2 + 5x + 1	\( 5^{5}\cdot 6679^{4} \)	14T56	Trivial
14.8.18562159314367056979.1	x^14 - 3x^13 - 5x^12 + 36x^11 - 38x^10 - 102x^9 + 268x^8 - 69x^7 - 438x^6 + 421x^5 + 114x^4 - 244x^3 + 46x^2 + 29x - 8	\( -\,19\cdot 149^{4}\cdot 211^{4} \)	14T56	Trivial
14.8.22469982327918016343.1	x^14 - 3x^12 - 21x^10 + 75x^8 + 12x^6 - 173x^4 + 21x^2 + 92	\( -\,23\cdot 149^{4}\cdot 211^{4} \)	14T56	Trivial
14.12.31262584108407674912.1	x^14 - 10x^12 + 28x^10 - x^8 - 84x^6 + 107x^4 - 50x^2 + 8	\( -\,2^{5}\cdot 149^{4}\cdot 211^{4} \)	14T56	Trivial
14.10.824550655859252425804.1	x^14 - 2x^13 + 8x^12 - 42x^11 - 7x^10 + 267x^9 - 253x^8 - 293x^7 + 433x^6 + 58x^5 - 257x^4 + 38x^3 + 65x^2 - 6x - 2	\( 2^{2}\cdot 149^{4}\cdot 211^{5} \)	14T56	Trivial
14.10.824550655859252425804.2	x^14 - 3x^13 - 19x^12 + 52x^11 + 138x^10 - 313x^9 - 494x^8 + 820x^7 + 854x^6 - 1067x^5 - 385x^4 + 559x^3 - 127x^2 - 138x + 16	\( 2^{2}\cdot 149^{4}\cdot 211^{5} \)	14T56	Trivial
14.0.4001610765876182388736.1	x^14 + 16x^12 + 101x^10 + 319x^8 + 528x^6 + 438x^4 + 157x^2 + 16	\( -\,2^{12}\cdot 149^{4}\cdot 211^{4} \)	14T56	$[2, 22]$
14.12.4001610765876182388736.1	x^14 - 19x^12 + 113x^10 - 213x^8 + 92x^6 + 91x^4 - 80x^2 + 16	\( -\,2^{12}\cdot 149^{4}\cdot 211^{4} \)	14T56	Trivial
14.2.8003221531752364777472.1	x^14 + 13x^12 + 23x^10 - 103x^8 - 388x^6 - 453x^4 - 212x^2 - 32	\( 2^{13}\cdot 149^{4}\cdot 211^{4} \)	14T56	$[2]$
14.2.8003221531752364777472.2	x^14 + 12x^12 + 51x^10 + 83x^8 + 3x^6 - 127x^4 - 118x^2 - 32	\( 2^{13}\cdot 149^{4}\cdot 211^{4} \)	14T56	Trivial
14.0.63140689505957347344384.1	x^14 + 20x^12 + 123x^10 + 335x^8 + 445x^6 + 276x^4 + 62x^2 + 1	\( -\,2^{14}\cdot 3^{16}\cdot 547^{4} \)	14T56	$[4, 28]$
14.14.101886286793711667200000.1	x^14 - 19x^12 + 116x^10 - 307x^8 + 382x^6 - 218x^4 + 55x^2 - 5	\( 2^{14}\cdot 5^{5}\cdot 6679^{4} \)	14T56	Trivial (GRH)
14.14.101886286793711667200000.2	x^14 - 28x^12 + 255x^10 - 950x^8 + 1368x^6 - 593x^4 + 95x^2 - 5	\( 2^{14}\cdot 5^{5}\cdot 6679^{4} \)	14T56	Trivial (GRH)