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
15.3.352917739133440000000000000000.1	x^15 + 20x^11 - 16x^10 + 25x^7 - 40x^6 + 16x^5 - 125x^3 + 300x^2 - 240x + 64	\( 2^{24}\cdot 5^{16}\cdot 13^{10} \)	15T98	Trivial (GRH)
15.7.4329686169519589168622500000000000000.1	x^15 - 5x^11 - 4x^10 - 1100x^7 - 1760x^6 - 704x^5 + 8000x^3 + 19200x^2 + 15360x + 4096	\( 2^{14}\cdot 5^{16}\cdot 7^{10}\cdot 19^{10} \)	15T98	$[3]$ (GRH)
15.7.199789376587969000000000000000000000000.1	x^15 - 110x^13 - 180x^12 + 3485x^11 + 7528x^10 - 41050x^9 - 185620x^8 + 693510x^7 + 2174580x^6 - 16746956x^5 + 18406300x^4 + 87814465x^3 - 146316600x^2 - 82482960x + 86138816	\( 2^{24}\cdot 5^{24}\cdot 7^{10}\cdot 29^{4} \)	15T98	Trivial (GRH)
15.7.21081131822384482680088939852611594757696000000.1	x^15 - 936x^13 - 7488x^12 + 193772x^11 + 3324992x^10 + 12209760x^9 - 126963072x^8 - 1735002176x^7 - 9717254656x^6 - 31462307840x^5 - 63453265920x^4 - 80902246400x^3 - 63493324800x^2 - 28041216000x - 5341184000	\( 2^{12}\cdot 5^{6}\cdot 31^{10}\cdot 97^{2}\cdot 163^{4}\cdot 245981^{2} \)	15T98	Trivial (GRH)
15.11.6242427558646320395593447809832981520060416000000.1	x^15 - 126x^13 - 1008x^12 - 47968x^11 - 737248x^10 - 5886360x^9 - 48520512x^8 - 378179296x^7 - 1954203776x^6 - 6255936640x^5 - 12603064320x^4 - 16068774400x^3 - 12611020800x^2 - 5569536000x - 1060864000	\( 2^{18}\cdot 5^{6}\cdot 7^{4}\cdot 19^{10}\cdot 37^{4}\cdot 1481^{2}\cdot 158699^{2} \)	15T98	Trivial (GRH)
15.7.47320369987690955076753433023568430483460751360000.1	x^15 - 1026x^13 - 8208x^12 + 229632x^11 + 3920352x^10 + 9892440x^9 - 257694912x^8 - 3119550496x^7 - 17240494976x^6 - 55720224640x^5 - 112357048320x^4 - 143254054400x^3 - 112427980800x^2 - 49652736000x - 9457664000	\( 2^{18}\cdot 5^{4}\cdot 13^{10}\cdot 2131^{2}\cdot 2309^{4}\cdot 127399^{2} \)	15T98	Trivial (GRH)
15.11.1556733003528499930254458732658332584781471296000000.1	x^15 + 36x^13 - 144x^12 - 32503x^11 + 261104x^10 - 2848725x^9 + 25958664x^8 - 124445806x^7 + 333271318x^6 - 536215885x^5 + 540397440x^4 - 344500525x^3 + 135184650x^2 - 29851500x + 2843000	\( 2^{12}\cdot 5^{6}\cdot 7^{10}\cdot 13^{2}\cdot 71^{2}\cdot 337^{2}\cdot 2843^{4}\cdot 116719^{2} \)	15T98	Trivial (GRH)
15.11.978816588753356030957478208479888197420687527936000000.1	x^15 - 1656x^13 - 13248x^12 + 756052x^11 + 12494272x^10 - 34227000x^9 - 2397580992x^8 - 25615490336x^7 - 139353010816x^6 - 449403866240x^5 - 906009477120x^4 - 1155152550400x^3 - 906581452800x^2 - 400382976000x - 76263424000	\( 2^{18}\cdot 5^{6}\cdot 7^{10}\cdot 13^{2}\cdot 43^{4}\cdot 433^{4}\cdot 631^{2}\cdot 323441^{2} \)	15T98	Trivial (GRH)
15.15.1970267782154216617690093863120316160444627676893184000000.1	x^15 - 2106x^13 - 16848x^12 + 1129752x^11 + 18581472x^10 - 78499800x^9 - 4227619392x^8 - 44677501536x^7 - 242693414016x^6 - 782507994240x^5 - 1577524101120x^4 - 2011326630400x^3 - 1578520012800x^2 - 697138176000x - 132788224000	\( 2^{18}\cdot 3^{20}\cdot 5^{6}\cdot 17^{6}\cdot 1907^{4}\cdot 657388279^{2} \)	15T98	Trivial (GRH)
15.15.33146623676447473240676184720625960099206358036156416000000.1	x^15 - 2106x^13 - 16848x^12 + 1275552x^11 + 20914272x^10 - 114496200x^9 - 5385465792x^8 - 56522264736x^7 - 306744441216x^6 - 988894842240x^5 - 1993571205120x^4 - 2541782310400x^3 - 1994829772800x^2 - 880997376000x - 167809024000	\( 2^{18}\cdot 3^{20}\cdot 5^{6}\cdot 19^{2}\cdot 53^{4}\cdot 773^{4}\cdot 1510646329^{2} \)	15T98	Trivial (GRH)
15.3.634826879298290317710532545900028146989740835908935880704000000.1	x^15 - 1044x^13 - 16704x^12 + 133652x^11 + 6281344x^10 + 89085240x^9 + 1072877184x^8 + 14132201344x^7 + 140824572928x^6 + 896700835840x^5 + 3610996899840x^4 + 9207966105600x^3 + 14453106278400x^2 + 12766150656000x + 4863295488000	\( 2^{18}\cdot 3^{6}\cdot 5^{6}\cdot 41^{2}\cdot 61^{10}\cdot 773^{4}\cdot 4261^{2}\cdot 165379^{2} \)	15T98	Trivial (GRH)
15.11.2606494027779061551579411214493333175014953976893624414572544000000.1	x^15 - 5274x^13 - 84384x^12 + 7855432x^11 + 261499904x^10 - 819354600x^9 - 171313992576x^8 - 3704165887616x^7 - 40366806612992x^6 - 260417811445760x^5 - 1050040215797760x^4 - 2677580453478400x^3 - 4202812479897600x^2 - 3712263389184000x - 1414195576832000	\( 2^{18}\cdot 5^{6}\cdot 13^{10}\cdot 79^{2}\cdot 103^{4}\cdot 6547^{4}\cdot 1891234619^{2} \)	15T98	Trivial (GRH)