Global number field search results

Further refine search

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
14.2.74266439531269141.1	x^14 - 6x^13 + 17x^12 - 31x^11 + 46x^10 - 66x^9 + 97x^8 - 142x^7 + 128x^6 - 59x^5 + 89x^4 - 79x^3 - 2x^2 - 19x + 13	\( 13^{6}\cdot 109^{5} \)	14T42	Trivial
14.2.965463713906498833.1	x^14 - 5x^13 + 18x^12 - 35x^11 + 43x^10 - 23x^9 - 3x^8 - 65x^7 + 163x^6 - 168x^5 + 12x^4 + 175x^3 - 180x^2 + 13x - 13	\( 13^{7}\cdot 109^{5} \)	14T42	Trivial
14.4.25473388759225315363.1	x^14 - 3x^13 - 2x^12 + x^11 + 30x^10 + 45x^9 - 200x^8 - 45x^7 + 257x^6 - 121x^5 + 614x^4 + 323x^3 - 1565x^2 - 559x + 523	\( -\,7^{3}\cdot 13^{6}\cdot 109^{5} \)	14T42	Trivial
14.4.162420703254885611367.1	x^14 - 6x^13 + 9x^12 + 25x^11 - 80x^10 + 104x^9 - 425x^8 + 1261x^7 + 5x^6 - 4607x^5 + 6299x^4 + 754x^3 - 5512x^2 + 702x + 1453	\( -\,3^{7}\cdot 13^{6}\cdot 109^{5} \)	14T42	Trivial
14.14.23255329393129696526336.1	x^14 - 33x^12 - 12x^11 + 347x^10 + 268x^9 - 1307x^8 - 1596x^7 + 1210x^6 + 2592x^5 + 962x^4 - 232x^3 - 174x^2 - 16x + 2	\( 2^{26}\cdot 809^{5} \)	14T42	Trivial
14.6.23255329393129696526336.1	x^14 - 11x^12 - 35x^10 + 357x^8 + 971x^6 - 401x^4 - 1769x^2 - 809	\( 2^{26}\cdot 809^{5} \)	14T42	Trivial
14.6.23255329393129696526336.2	x^14 - 5x^13 + 4x^12 + 19x^11 - 68x^10 + 139x^9 - 171x^8 + 100x^7 + 82x^6 - 458x^5 + 800x^4 - 698x^3 + 204x^2 + 186x + 22	\( 2^{26}\cdot 809^{5} \)	14T42	$[2]$
14.0.372085270290075144421376.1	x^14 + 13x^12 - 10x^11 + 103x^10 - 258x^9 + 513x^8 - 1060x^7 + 3590x^6 - 3072x^5 + 4146x^4 - 3444x^3 + 5982x^2 - 2140x + 1454	\( -\,2^{30}\cdot 809^{5} \)	14T42	$[2, 80]$ (GRH)
14.8.372085270290075144421376.1	x^14 - 22x^12 - 22x^11 + 192x^10 + 368x^9 - 942x^8 - 2056x^7 + 2479x^6 + 5908x^5 - 2018x^4 - 8254x^3 - 530x^2 + 3732x - 398	\( -\,2^{30}\cdot 809^{5} \)	14T42	Trivial
14.8.372085270290075144421376.2	x^14 + 8x^12 - 156x^10 - 300x^8 + 4660x^6 + 2128x^4 - 28928x^2 + 12944	\( -\,2^{30}\cdot 809^{5} \)	14T42	Trivial
14.0.1488341081160300577685504.1	x^14 + 43x^12 + 642x^10 + 4466x^8 + 15508x^6 + 25684x^4 + 16796x^2 + 3236	\( -\,2^{32}\cdot 809^{5} \)	14T42	$[2, 254]$ (GRH)
14.14.1488341081160300577685504.1	x^14 - 29x^12 + 337x^10 - 1993x^8 + 6279x^6 - 10007x^4 + 6709x^2 - 809	\( 2^{32}\cdot 809^{5} \)	14T42	Trivial (GRH)