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 15 matches)

Label	Polynomial	Discriminant	Galois group	Class group
15.1.2059629760000000000000.1	x^15 - 7x^14 + 18x^13 - 29x^12 + 85x^11 - 227x^10 + 274x^9 - 321x^8 + 978x^7 - 1270x^6 + 238x^5 - 96x^4 + 439x^3 + 53x^2 + 190x - 55	\( -\,2^{18}\cdot 5^{13}\cdot 23^{5} \)	15T97	Trivial (GRH)
15.3.3295407616000000000000000.1	x^15 - 12x^10 - 25x^7 + 48x^5 - 125x^3 + 100x^2 - 64	\( 2^{24}\cdot 5^{15}\cdot 23^{5} \)	15T97	Trivial (GRH)
15.1.18817080704000000000000000.1	x^15 + 100x^7 - 160x^6 + 64x^5 + 500x^3 - 1200x^2 + 960x - 256	\( -\,2^{22}\cdot 5^{15}\cdot 43^{5} \)	15T97	Trivial (GRH)
15.3.80609714195072000000000000000.1	x^15 + 120x^11 - 284x^10 + 275x^7 - 2660x^6 + 4368x^5 - 8000x^3 + 19200x^2 + 5120x - 16384	\( 2^{22}\cdot 5^{15}\cdot 229^{5} \)	15T97	Trivial (GRH)
15.3.69512094038728469161467479126016000000.1	x^15 + 234x^13 - 432x^12 + 15904x^11 - 37888x^10 + 488376x^9 + 1975680x^8 + 15375488x^7 - 77250944x^6 + 48684160x^5 - 311662080x^4 + 359769600x^3 - 298598400x^2 + 580608000x - 331776000	\( 2^{18}\cdot 3^{4}\cdot 5^{6}\cdot 13^{2}\cdot 31^{5}\cdot 208094267^{2} \)	15T97	$[2]$ (GRH)
15.3.12508510250549402266838396233711616000000.1	x^15 - 81x^13 + 1163x^11 - 608x^10 - 6705x^9 + 23976x^8 + 253668x^7 - 1670632x^6 + 1782240x^5 + 3051360x^4 - 4986800x^3 - 894400x^2 + 2912000x - 832000	\( 2^{23}\cdot 5^{6}\cdot 13^{4}\cdot 37^{5}\cdot 151^{2}\cdot 457^{2}\cdot 3181^{2} \)	15T97	Trivial (GRH)
15.11.4041163971392929828955494668759105536000000.1	x^15 - 144x^13 - 936x^12 + 5540x^11 + 75392x^10 - 370134x^9 - 1459296x^8 + 10678864x^7 + 27161712x^6 - 73028000x^5 - 285963840x^4 - 324408800x^3 - 168640000x^2 - 41664000x - 3968000	\( 2^{21}\cdot 5^{6}\cdot 31^{4}\cdot 37^{5}\cdot 1387715921^{2} \)	15T97	Trivial (GRH)
15.7.39319960333779840237315944809779298304000000.1	x^15 - 270x^13 - 504x^12 + 7942x^11 - 91568x^10 - 296010x^9 + 2916576x^8 + 6356616x^7 - 16677328x^6 - 58165280x^5 + 4550400x^4 + 153260000x^3 + 171145600x^2 + 70784000x + 10112000	\( 2^{23}\cdot 5^{6}\cdot 37^{5}\cdot 79^{4}\cdot 233^{2}\cdot 857^{2}\cdot 1669^{2} \)	15T97	Trivial (GRH)
15.11.44842222891195545361422304391393705984000000.1	x^15 - 432x^13 - 2592x^12 + 31528x^11 + 680480x^10 - 787680x^9 - 56878848x^8 + 112700512x^7 + 1181988864x^6 - 2781299200x^5 - 5558538240x^4 + 21733222400x^3 - 23532339200x^2 + 10637312000x - 1736704000	\( 2^{28}\cdot 5^{6}\cdot 53^{4}\cdot 71^{5}\cdot 27404129^{2} \)	15T97	Trivial (GRH)
15.7.578449131183957732046721344708617568256000000.1	x^15 - 45x^13 - 864x^12 + 767x^11 + 41952x^10 + 78255x^9 - 634824x^8 - 2333284x^7 + 5757272x^6 + 23688720x^5 - 1929600x^4 - 64990000x^3 - 72574400x^2 - 30016000x - 4288000	\( 2^{23}\cdot 5^{6}\cdot 37^{5}\cdot 67^{4}\cdot 2699^{2}\cdot 658447^{2} \)	15T97	Trivial (GRH)
15.15.248398977558713794925562108830363540177001953125.1	x^15 - 420x^13 - 580x^12 + 71510x^11 + 184558x^10 - 6191100x^9 - 22494140x^8 + 278723315x^7 + 1303942895x^6 - 5695992303x^5 - 35890644050x^4 + 16640248995x^3 + 365694137360x^2 + 693107493395x + 402871723939	\( 5^{13}\cdot 257^{5}\cdot 883^{2}\cdot 15257253491^{2} \)	15T97	Trivial (GRH)
15.5.947121317450814515044219243193351148649984000000.1	x^15 - 387x^13 - 288x^12 + 45388x^11 + 179064x^10 - 2071125x^9 - 11113704x^8 - 23050860x^7 + 297750656x^6 + 836860640x^5 + 553472640x^4 - 1292267200x^3 - 1678700800x^2 + 1329664000	\( -\,2^{15}\cdot 5^{6}\cdot 7^{8}\cdot 23^{5}\cdot 53^{4}\cdot 359^{2}\cdot 7001803^{2} \)	15T97	Trivial (GRH)
15.5.526578703368934513642333503864526678250539093504000000.1	x^15 - 792x^13 - 1152x^12 + 237803x^11 - 541864x^10 - 23582115x^9 + 191481624x^8 - 405543860x^7 - 4433943936x^6 + 12454039840x^5 - 8249235840x^4 - 19260603200x^3 + 25020204800x^2 - 19817984000	\( -\,2^{15}\cdot 5^{6}\cdot 23^{5}\cdot 59^{2}\cdot 157^{2}\cdot 38707^{4}\cdot 910849^{2} \)	15T97	Trivial (GRH)
15.15.11006353820590761829104554853487124581411222177394688000000.1	x^15 - 1926x^13 - 15408x^12 + 1171432x^11 + 19205152x^10 - 128106360x^9 - 5496558912x^8 - 57384566496x^7 - 311196686976x^6 - 1003145984640x^5 - 2022280888320x^4 - 2578386854400x^3 - 2023557580800x^2 - 893684736000x - 170225664000	\( 2^{18}\cdot 3^{10}\cdot 5^{6}\cdot 7^{4}\cdot 11^{2}\cdot 107^{5}\cdot 239^{2}\cdot 1979^{4}\cdot 112901^{2} \)	15T97	Trivial (GRH)
15.9.38583234404050627753560028547647715274328642905059328000000.1	x^15 + 846x^13 - 13536x^12 + 239912x^11 - 6052864x^10 + 82904760x^9 - 959105664x^8 + 12280855424x^7 - 121534297088x^6 + 773045872640x^5 - 3112713584640x^4 + 7937354137600x^3 - 12458714726400x^2 + 11004542976000x - 4192206848000	\( -\,2^{18}\cdot 3^{6}\cdot 5^{6}\cdot 79^{2}\cdot 107^{5}\cdot 1999^{4}\cdot 4987^{2}\cdot 609683^{2} \)	15T97	Trivial (GRH)