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 16 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.27330294579200000000000.1	x^16 + 4x^14 - x^12 - 2x^10 + 26x^8 - 30x^6 + 26x^4 - 10x^2 + 5	\( 2^{32}\cdot 5^{11}\cdot 19^{4} \)	16T1433	Trivial
16.4.27330294579200000000000.1	x^16 - 10x^14 + 46x^12 - 102x^10 + 94x^8 - 6x^6 - 69x^4 + 40x^2 + 5	\( 2^{32}\cdot 5^{11}\cdot 19^{4} \)	16T1433	Trivial
16.0.27330294579200000000000.2	x^16 - 8x^14 + 31x^12 - 74x^10 + 111x^8 - 100x^6 + 49x^4 - 10x^2 + 5	\( 2^{32}\cdot 5^{11}\cdot 19^{4} \)	16T1433	Trivial
16.4.27330294579200000000000.2	x^16 + 4x^14 - x^12 - 22x^10 - 19x^8 + 10x^6 + 41x^4 + 30x^2 + 5	\( 2^{32}\cdot 5^{11}\cdot 19^{4} \)	16T1433	Trivial
16.4.21823047807795200000000000.3	x^16 - 10x^14 + x^12 + 198x^10 - 391x^8 + 794x^6 - 2349x^4 + 1260x^2 + 5	\( 2^{32}\cdot 5^{11}\cdot 101^{4} \)	16T1433	Trivial (GRH)
16.4.21823047807795200000000000.4	x^16 + 4x^14 - 6x^12 - 2x^10 + 46x^8 - 110x^6 + 101x^4 - 40x^2 + 5	\( 2^{32}\cdot 5^{11}\cdot 101^{4} \)	16T1433	Trivial (GRH)
16.0.3562076463236043104722092032.1	x^16 - 16x^14 + 140x^12 - 752x^10 + 2732x^8 - 7104x^6 + 11440x^4 - 8160x^2 + 2312	\( 2^{67}\cdot 17^{6} \)	16T1433	$[2, 2]$ (GRH)
16.8.3562076463236043104722092032.1	x^16 - 16x^14 - 60x^12 + 1784x^10 - 5594x^8 - 3288x^6 + 4220x^4 + 3264x^2 + 578	\( 2^{67}\cdot 17^{6} \)	16T1433	Trivial (GRH)
16.0.3562076463236043104722092032.2	x^16 - 20x^12 - 8x^10 + 246x^8 - 584x^6 + 780x^4 - 272x^2 + 578	\( 2^{67}\cdot 17^{6} \)	16T1433	$[2, 2]$ (GRH)
16.8.3562076463236043104722092032.2	x^16 + 8x^14 - 76x^12 - 216x^10 + 1334x^8 + 1064x^6 - 5068x^4 + 2176x^2 + 578	\( 2^{67}\cdot 17^{6} \)	16T1433	Trivial (GRH)
16.0.70367540303366615290376880128.1	x^16 - 18x^14 - 8x^13 + 51x^12 - 680x^11 - 2796x^10 + 5424x^9 + 60652x^8 + 159744x^7 - 125676x^6 - 733488x^5 + 467446x^4 + 6066512x^3 + 20419528x^2 + 6548432x + 2485852	\( 2^{45}\cdot 7^{4}\cdot 97^{6} \)	16T1433	$[2, 6]$ (GRH)
16.0.70367540303366615290376880128.2	x^16 - 6x^14 - 520x^12 - 2200x^11 - 1332x^10 + 9896x^9 + 80197x^8 + 480168x^7 + 1622334x^6 + 4107528x^5 + 11430398x^4 + 22638336x^3 + 34893252x^2 + 55615680x + 61140096	\( 2^{45}\cdot 7^{4}\cdot 97^{6} \)	16T1433	$[2, 6]$ (GRH)
16.0.11230100681627560957071852383825297408.1	x^16 + 560x^14 + 126364x^12 + 15027760x^10 + 1023306828x^8 + 40118683872x^6 + 846231957776x^4 + 7669495426592x^2 + 7289004894728	\( 2^{67}\cdot 17^{4}\cdot 977^{4} \)	16T1433	$[2, 2, 2, 2, 2208864]$ (GRH)
16.16.11230100681627560957071852383825297408.1	x^16 - 560x^14 + 126364x^12 - 15027760x^10 + 1023306828x^8 - 40118683872x^6 + 846231957776x^4 - 7669495426592x^2 + 7289004894728	\( 2^{67}\cdot 17^{4}\cdot 977^{4} \)	16T1433	Trivial (GRH)
16.0.11230100681627560957071852383825297408.2	x^16 + 624x^14 + 134420x^12 + 13270424x^10 + 656438310x^8 + 16233495912x^6 + 188794381852x^4 + 984799023648x^2 + 1822251223682	\( 2^{67}\cdot 17^{4}\cdot 977^{4} \)	16T1433	$[2, 2, 2, 2, 1634032]$ (GRH)
16.16.11230100681627560957071852383825297408.2	x^16 - 624x^14 + 134420x^12 - 13270424x^10 + 656438310x^8 - 16233495912x^6 + 188794381852x^4 - 984799023648x^2 + 1822251223682	\( 2^{67}\cdot 17^{4}\cdot 977^{4} \)	16T1433	Trivial (GRH)