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 18 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.1048576000000000000.5	x^16 - 2x^14 + 6x^12 - 16x^10 + 24x^8 - 28x^6 + 19x^4 - 4x^2 + 1	\( 2^{32}\cdot 5^{12} \)	$(C_2\times C_8):C_2^2$ (as 16T75)	Trivial (GRH)
16.0.1048576000000000000.7	x^16 - 2x^12 + 4x^8 - 3x^4 + 1	\( 2^{32}\cdot 5^{12} \)	$(C_2\times C_8):C_2^2$ (as 16T75)	Trivial
16.4.16777216000000000000.1	x^16 - 12x^12 + 54x^8 - 108x^4 + 1	\( 2^{36}\cdot 5^{12} \)	$(C_2\times C_8):C_2^2$ (as 16T75)	Trivial (GRH)
16.4.16777216000000000000.5	x^16 - 4x^14 - 16x^12 + 72x^10 + 24x^8 - 176x^6 - 64x^4 - 32x^2 + 16	\( 2^{36}\cdot 5^{12} \)	$(C_2\times C_8):C_2^2$ (as 16T75)	Trivial (GRH)
16.4.268435456000000000000.2	x^16 - 4x^15 + 8x^14 - 20x^13 + 30x^12 - 72x^11 + 240x^10 - 424x^9 + 766x^8 - 1480x^7 + 1760x^6 - 1176x^5 + 488x^4 - 144x^3 + 32x^2 - 4	\( 2^{40}\cdot 5^{12} \)	$(C_2\times C_8):C_2^2$ (as 16T75)	Trivial (GRH)
16.4.268435456000000000000.3	x^16 - 4x^15 + 4x^14 + 12x^13 - 48x^12 + 60x^11 + 68x^10 - 396x^9 + 559x^8 - 84x^7 - 696x^6 + 884x^5 - 622x^4 + 288x^3 - 56x^2 + 1	\( 2^{40}\cdot 5^{12} \)	$(C_2\times C_8):C_2^2$ (as 16T75)	Trivial (GRH)
16.0.268435456000000000000.6	x^16 - 4x^15 + 4x^14 - 12x^13 + 68x^12 - 108x^11 + 32x^10 - 88x^9 + 401x^8 - 452x^7 + 244x^6 - 192x^5 + 570x^4 - 616x^3 + 420x^2 - 148x + 31	\( 2^{40}\cdot 5^{12} \)	$(C_2\times C_8):C_2^2$ (as 16T75)	$[2]$ (GRH)
16.0.268435456000000000000.7	x^16 - 4x^15 + 4x^14 - 8x^13 + 32x^12 - 40x^11 + 8x^10 - 16x^9 + 109x^8 - 24x^7 - 16x^6 - 16x^5 + 168x^4 + 148x^3 + 104x^2 - 120x + 31	\( 2^{40}\cdot 5^{12} \)	$(C_2\times C_8):C_2^2$ (as 16T75)	$[2]$ (GRH)
16.0.383854225736338134765625.1	x^16 - x^15 - 2x^14 + 56x^12 + 45x^11 + 92x^10 - 262x^9 - 19x^8 - 280x^7 + 950x^6 + 375x^5 + 700x^4 - 750x^3 + 625x + 625	\( 5^{12}\cdot 11^{6}\cdot 31^{6} \)	$(C_2\times C_8):C_2^2$ (as 16T75)	$[4, 4]$ (GRH)
16.0.383854225736338134765625.2	x^16 - 4x^15 - 5x^14 + 25x^13 + 76x^12 - 255x^11 - 201x^10 + 635x^9 + 1486x^8 - 2500x^7 - 1610x^6 + 766x^5 + 6016x^4 - 5965x^3 + 2390x^2 - 375x + 25	\( 5^{12}\cdot 11^{6}\cdot 31^{6} \)	$(C_2\times C_8):C_2^2$ (as 16T75)	$[2, 4]$ (GRH)
16.8.616308629868476806640625.1	x^16 - 24x^14 + 244x^12 - 1278x^10 + 3204x^8 - 2436x^6 - 899x^4 - 252x^2 + 16	\( 3^{12}\cdot 5^{12}\cdot 41^{6} \)	$(C_2\times C_8):C_2^2$ (as 16T75)	Trivial (GRH)
16.8.616308629868476806640625.2	x^16 - 6x^15 + 12x^14 - 27x^13 + 67x^12 - 90x^11 - 177x^10 + 216x^9 + 75x^8 + 69x^7 - 102x^6 - 135x^5 + 292x^4 + 117x^3 - 33x^2 - 9x + 1	\( 3^{12}\cdot 5^{12}\cdot 41^{6} \)	$(C_2\times C_8):C_2^2$ (as 16T75)	Trivial (GRH)
16.0.49331181715456000000000000.1	x^16 - 6x^14 + 34x^12 - 192x^10 + 924x^8 - 1164x^6 + 731x^4 - 228x^2 + 361	\( 2^{32}\cdot 5^{12}\cdot 19^{6} \)	$(C_2\times C_8):C_2^2$ (as 16T75)	$[12]$ (GRH)
16.0.49331181715456000000000000.2	x^16 - 8x^14 + 71x^12 - 624x^10 + 3719x^8 - 10272x^6 + 12299x^4 + 1064x^2 + 361	\( 2^{32}\cdot 5^{12}\cdot 19^{6} \)	$(C_2\times C_8):C_2^2$ (as 16T75)	$[12]$ (GRH)
16.0.789298907447296000000000000.1	x^16 + 4x^14 + 104x^12 + 8x^10 + 2204x^8 - 6704x^6 + 69296x^4 - 64768x^2 + 364816	\( 2^{36}\cdot 5^{12}\cdot 19^{6} \)	$(C_2\times C_8):C_2^2$ (as 16T75)	$[2, 78]$ (GRH)
16.16.789298907447296000000000000.1	x^16 - 48x^14 + 806x^12 - 5784x^10 + 19399x^8 - 29832x^6 + 19334x^4 - 5016x^2 + 361	\( 2^{36}\cdot 5^{12}\cdot 19^{6} \)	$(C_2\times C_8):C_2^2$ (as 16T75)	Trivial (GRH)
16.0.789298907447296000000000000.2	x^16 + 48x^14 + 806x^12 + 5784x^10 + 19399x^8 + 29832x^6 + 19334x^4 + 5016x^2 + 361	\( 2^{36}\cdot 5^{12}\cdot 19^{6} \)	$(C_2\times C_8):C_2^2$ (as 16T75)	$[2, 78]$ (GRH)
16.16.789298907447296000000000000.2	x^16 - 44x^14 + 704x^12 - 5028x^10 + 15934x^8 - 20756x^6 + 10496x^4 - 1692x^2 + 81	\( 2^{36}\cdot 5^{12}\cdot 19^{6} \)	$(C_2\times C_8):C_2^2$ (as 16T75)	Trivial (GRH)