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
15.1.82170576019287109375.1	x^15 - 5x^12 + 10x^11 - 12x^10 + 10x^9 - 20x^8 + 40x^7 - 60x^6 + 73x^5 - 65x^4 + 35x^3 - 35x^2 + 30x - 9	\( -\,5^{16}\cdot 7^{5}\cdot 179^{2} \)	15T60	Trivial
15.5.15156539194683074951171875.1	x^15 - 15x^13 - 10x^12 + 90x^11 + 102x^10 - 175x^9 - 370x^8 - 35x^7 + 695x^6 + 44x^5 - 650x^4 + 230x^3 + 100x^2 - 30x - 13	\( -\,5^{18}\cdot 331^{5} \)	15T60	$[2]$
15.7.44896833821697857666015625.1	x^15 - x^14 - 4x^13 - 35x^12 - 24x^11 - 71x^10 + 899x^9 + 1896x^8 - 6905x^7 - 1614x^6 + 18939x^5 - 416x^4 - 14084x^3 - 28970x^2 + 3401x - 97	\( 3^{8}\cdot 5^{14}\cdot 257^{5} \)	15T60	Trivial (GRH)
15.5.162898479450432992353906688.1	x^15 - 4x^14 + 3x^13 + 31x^12 - 238x^11 + 18x^10 + 1638x^9 + 1328x^8 - 5925x^7 - 35370x^6 - 57629x^5 - 1757x^4 + 40493x^3 - 3994x^2 - 1285x + 157	\( -\,2^{12}\cdot 17^{2}\cdot 23^{5}\cdot 149^{2}\cdot 31033^{2} \)	15T60	Trivial (GRH)
15.3.3224617669058799027915587584.1	x^15 - 3x^14 + 17x^13 - 59x^12 + 141x^11 - 855x^10 + 1009x^9 - 3187x^8 + 2782x^7 + 1286x^6 + 49598x^5 + 48878x^4 - 68572x^3 + 29412x^2 - 34368x + 26272	\( 2^{26}\cdot 19^{2}\cdot 79^{5}\cdot 6577^{2} \)	15T60	Trivial (GRH)
15.3.17518045204015625000000000000.1	x^15 - 10x^13 - 50x^12 + 135x^11 - 384x^10 + 1625x^9 - 1320x^8 + 4090x^7 - 17380x^6 + 30184x^5 - 30800x^4 + 16840x^3 + 73840x^2 - 74240x + 26944	\( 2^{12}\cdot 5^{18}\cdot 257^{5} \)	15T60	Trivial (GRH)
15.7.30882301570945259777553578125.1	x^15 - 4x^14 + 11x^13 - 38x^12 + 139x^11 - 206x^10 - 2038x^9 + 7767x^8 - 9664x^7 - 5430x^6 + 20708x^5 + 7092x^4 - 3218x^3 - 4097x^2 - 3552x - 188	\( 5^{6}\cdot 11^{12}\cdot 229^{5} \)	15T60	$[5]$ (GRH)
15.1.27100824264108518067277197633767.1	x^15 - 3x^14 + 3x^13 - x^12 - 425x^11 + 693x^10 + 7789x^9 - 6982x^8 + 12820x^7 - 13720x^6 - 246544x^5 + 179744x^4 + 961600x^3 - 477440x^2 + 76800x - 4096	\( -\,11^{4}\cdot 17^{2}\cdot 23^{5}\cdot 997556191^{2} \)	15T60	Trivial (GRH)
15.11.296854871574412530032892056987579392.1	x^15 - x^14 - 28x^13 - 79x^12 - 1100x^11 + 1753x^10 + 15805x^9 + 2562x^8 + 38320x^7 - 121800x^6 - 728448x^5 + 301216x^4 + 1038400x^3 - 167680x^2 - 76800x + 4096	\( 2^{10}\cdot 37^{5}\cdot 151^{2}\cdot 44269^{2}\cdot 305873^{2} \)	15T60	Trivial (GRH)
15.11.1593894329827244387250162786359001088.1	x^15 - 4x^14 - 98x^13 + 222x^12 + 2460x^11 - 1774x^10 - 6038x^9 - 36416x^8 - 276240x^7 + 345120x^6 + 980608x^5 + 64640x^4 + 3744000x^3 - 2539520x^2 + 204800x + 32768	\( 2^{14}\cdot 37^{5}\cdot 252949^{2}\cdot 4682551^{2} \)	15T60	Trivial (GRH)
15.15.13279976064852192427125304206928000000.1	x^15 - 164x^13 - 14x^12 + 10897x^11 + 1462x^10 - 375108x^9 - 53828x^8 + 7054867x^7 + 792140x^6 - 68813252x^5 - 2895510x^4 + 272475995x^3 - 17391330x^2 + 297900x - 1080	\( 2^{10}\cdot 5^{6}\cdot 17^{2}\cdot 37^{5}\cdot 4441^{2}\cdot 1449121^{2} \)	15T60	Trivial (GRH)
15.15.29469615804756686585980269796501500928.1	x^15 - x^14 - 155x^13 + 121x^12 + 9150x^11 - 5424x^10 - 259640x^9 + 113792x^8 + 3704800x^7 - 1186880x^6 - 25716480x^5 + 5849088x^4 + 70144000x^3 - 10485760x^2 - 8192000x + 262144	\( 2^{10}\cdot 37^{5}\cdot 20371966273189^{2} \)	15T60	Trivial (GRH)