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 11 matches)

Label	Polynomial	Discriminant	Galois group	Class group
10.0.6284601413776876558534375.3	x^10 - 3x^9 - 200x^8 + 50x^7 + 17637x^6 + 39445x^5 - 111526x^4 - 277572x^3 + 13054024x^2 + 41505856x + 259861504	\( -\,5^{5}\cdot 11^{9}\cdot 31^{8} \)	$C_{10}$ (as 10T1)	$[5, 323020]$ (GRH)
10.0.58837612521292212217534375.3	x^10 - 3x^9 - 288x^8 + 842x^7 + 30309x^6 - 92907x^5 - 231118x^4 + 2902660x^3 + 22742472x^2 - 121997088x + 574971904	\( -\,5^{5}\cdot 11^{9}\cdot 41^{8} \)	$C_{10}$ (as 10T1)	$[1237220]$ (GRH)
10.0.210523572267483978271484375.1	x^10 - 5x^9 - 180x^8 + 310x^7 + 13085x^6 + 13891x^5 - 237410x^4 - 44500x^3 + 3391800x^2 + 3901600x + 30270976	\( -\,5^{16}\cdot 11^{8}\cdot 23^{5} \)	$C_{10}$ (as 10T1)	$[3744015]$ (GRH)
10.0.404948281009841156005859375.1	x^10 - 5x^9 - 90x^8 - 50x^7 + 11105x^6 + 29011x^5 + 251560x^4 + 1396580x^3 + 21008400x^2 + 38261440x + 533780224	\( -\,5^{17}\cdot 11^{8}\cdot 19^{5} \)	$C_{10}$ (as 10T1)	$[2, 2, 10, 10, 18040]$ (GRH)
10.0.690669632728369005581442727.1	x^10 - 3x^9 - 524x^8 + 3626x^7 + 71277x^6 - 771947x^5 + 787334x^4 + 6027876x^3 + 13955416x^2 + 5675680x + 30499072	\( -\,7^{5}\cdot 11^{8}\cdot 61^{8} \)	$C_{10}$ (as 10T1)	$[5, 443405]$ (GRH)
10.0.1412611925092978197588034375.1	x^10 - 3x^9 - 464x^8 + 3482x^7 + 60405x^6 - 780539x^5 + 2991794x^4 - 14072892x^3 + 100633384x^2 - 67799648x + 1054936576	\( -\,5^{5}\cdot 11^{9}\cdot 61^{8} \)	$C_{10}$ (as 10T1)	$[2722420]$ (GRH)
10.0.2412342113372980700918909375.3	x^10 - x^9 + 474x^8 + 54x^7 + 109561x^6 - 68025x^5 + 8870412x^4 - 23104764x^3 + 157170784x^2 - 1045275584x + 1689938944	\( -\,5^{5}\cdot 11^{9}\cdot 41^{9} \)	$C_{10}$ (as 10T1)	$[10, 507100]$ (GRH)
10.0.34979630064734673309326171875.2	x^10 - 4615x^7 - 4970x^6 + 296354x^5 + 13287650x^4 + 135006500x^3 + 1053034370x^2 + 3428920860x + 3628410199	\( -\,5^{17}\cdot 71^{9} \)	$C_{10}$ (as 10T1)	$[4, 16, 16, 16, 80]$ (GRH)
10.0.327217385234372376075381080064.1	x^10 - 2x^9 - 505x^8 - 1552x^7 + 76072x^6 + 557872x^5 - 110392x^4 - 666304x^3 + 37976784x^2 - 47220384x + 225499504	\( -\,2^{15}\cdot 3^{5}\cdot 11^{8}\cdot 61^{8} \)	$C_{10}$ (as 10T1)	$[2, 10, 10, 10, 710]$ (GRH)
10.2.822287695938095069212060016640000000.1	x^10 - 950x^8 + 361000x^6 - 633864x^5 - 68590000x^4 - 1204341600x^3 + 6516050000x^2 - 114412452000x - 147164007376	\( 2^{19}\cdot 3^{8}\cdot 5^{7}\cdot 7^{8}\cdot 11^{8}\cdot 19^{5} \)	$F_{5}\times C_2$ (as 10T5)	$[10, 10, 12880]$ (GRH)
10.0.9625493923037926853032751929716796875.1	x^10 - 5034897x^5 + 8450062600203	\( -\,3^{9}\cdot 5^{10}\cdot 7^{8}\cdot 233^{8} \)	$F_{5}\times C_2$ (as 10T5)	$[5, 15, 17670]$ (GRH)