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 12 matches)

Label	Polynomial	Discriminant	Galois group	Class group
15.1.6401597515801839.1	x^15 - x^14 - x^13 + 2x^12 - 4x^11 - x^10 + 3x^9 + 3x^8 + 12x^7 - 2x^6 - 14x^5 + 7x^4 + 11x^3 - 6x^2 + 1	\( -\,3^{9}\cdot 13^{3}\cdot 23^{6} \)	$S_5 \times S_3$ (as 15T29)	Trivial
15.1.24118280788986467.1	x^15 - 2x^14 + 6x^12 - 13x^11 + 13x^10 - x^9 - 21x^8 + 40x^7 - 41x^6 + 29x^5 - 18x^4 + 13x^3 - 7x^2 + x + 1	\( -\,59^{6}\cdot 83^{3} \)	$S_5 \times S_3$ (as 15T29)	Trivial
15.3.98765528526263521.1	x^15 - 3x^14 + 7x^13 - 12x^12 + 8x^11 - 2x^10 - 17x^9 + 36x^8 - 49x^7 + 54x^6 - 41x^5 + 30x^4 - 17x^3 + 8x^2 - 5x + 3	\( 13^{3}\cdot 31^{6}\cdot 37^{3} \)	$S_5 \times S_3$ (as 15T29)	Trivial
15.3.137631064560062464.1	x^15 - x^14 - 2x^13 + 3x^12 + 11x^11 - 5x^10 - 14x^9 - 5x^8 - 10x^7 + 22x^6 + 14x^5 + 2x^4 - 13x^3 - 5x^2 + 1	\( 2^{12}\cdot 23^{6}\cdot 61^{3} \)	$S_5 \times S_3$ (as 15T29)	Trivial
15.5.78524595786905053696.1	x^15 - 4x^13 - 4x^12 + 13x^11 + 4x^10 - 43x^9 + 89x^8 - 67x^7 - 64x^6 + 90x^5 - 9x^4 - 26x^3 + 13x^2 - 1	\( -\,2^{9}\cdot 31^{6}\cdot 557^{3} \)	$S_5 \times S_3$ (as 15T29)	Trivial
15.5.91411367382133293359.1	x^15 - 2x^14 - 3x^13 + 18x^12 + 16x^11 - 40x^10 - 33x^9 + 101x^8 + 52x^7 - 96x^6 - 59x^5 + 32x^4 + 23x^3 - 12x^2 + 1	\( -\,23^{5}\cdot 61^{3}\cdot 397^{3} \)	$S_5 \times S_3$ (as 15T29)	Trivial
15.9.100133149236970913792.1	x^15 - 6x^14 + 7x^13 + 26x^12 - 82x^11 + 70x^10 + 29x^9 - 100x^8 + 78x^7 + 2x^6 - 69x^5 + 42x^4 + 29x^3 - 26x^2 - 4x + 4	\( -\,2^{18}\cdot 37^{6}\cdot 53^{3} \)	$S_5 \times S_3$ (as 15T29)	Trivial
15.9.171959209292585208832.1	x^15 - 5x^13 - 17x^12 - 24x^11 + 61x^10 + 214x^9 + 111x^8 - 303x^7 - 468x^6 - 151x^5 + 176x^4 + 200x^3 + 82x^2 + 15x + 1	\( -\,2^{10}\cdot 13^{3}\cdot 31^{3}\cdot 37^{6} \)	$S_5 \times S_3$ (as 15T29)	Trivial
15.3.295785383589955843072.1	x^15 - 7x^13 - 7x^12 + 38x^11 + 49x^10 - 108x^9 - 55x^8 + 345x^7 + 82x^6 - 375x^5 - 18x^4 + 34x^3 + 12x^2 - 3x - 1	\( 2^{10}\cdot 37^{5}\cdot 1609^{3} \)	$S_5 \times S_3$ (as 15T29)	Trivial
15.3.2623285411012023287821.1	x^15 - 8x^13 - 3x^12 + 48x^11 + 24x^10 - 187x^9 - 32x^8 + 736x^7 + 60x^6 - 992x^5 + 8x^4 + 65x^3 - 16x^2 - 4x + 1	\( 229^{5}\cdot 1609^{3} \)	$S_5 \times S_3$ (as 15T29)	Trivial (GRH)
15.15.555278804074785034747904.1	x^15 - 2x^14 - 28x^13 + 22x^12 + 204x^11 - 144x^10 - 578x^9 + 424x^8 + 672x^7 - 448x^6 - 374x^5 + 192x^4 + 96x^3 - 32x^2 - 8x + 2	\( 2^{14}\cdot 37^{5}\cdot 7877^{3} \)	$S_5 \times S_3$ (as 15T29)	Trivial (GRH)
15.15.792952227088888747277125.1	x^15 - 35x^13 - 18x^12 + 403x^11 + 337x^10 - 1759x^9 - 1406x^8 + 3449x^7 + 2048x^6 - 2850x^5 - 1077x^4 + 761x^3 + 123x^2 - 13x - 1	\( 5^{3}\cdot 229^{6}\cdot 353^{3} \)	$S_5 \times S_3$ (as 15T29)	Trivial (GRH)