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 9 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.2751882854400000000.3	x^16 - x^14 - 7x^12 - 7x^10 + 15x^8 + 42x^6 + 42x^4 + 20x^2 + 4	\( 2^{30}\cdot 3^{8}\cdot 5^{8} \)	$(C_2\times C_4).C_2^4$ (as 16T205)	Trivial
16.0.44030125670400000000.4	x^16 - 10x^14 + 42x^12 - 84x^10 + 60x^8 + 56x^6 - 112x^4 + 32x^2 + 64	\( 2^{34}\cdot 3^{8}\cdot 5^{8} \)	$(C_2\times C_4).C_2^4$ (as 16T205)	Trivial
16.8.8098041718374400000000.1	x^16 - 6x^14 - 12x^13 - 35x^12 - 80x^11 - 66x^10 + 88x^9 + 188x^8 + 248x^7 + 608x^6 + 244x^5 - 1146x^4 - 960x^3 + 542x^2 + 488x - 71	\( 2^{32}\cdot 5^{8}\cdot 13^{6} \)	$(C_2\times C_4).C_2^4$ (as 16T205)	Trivial (GRH)
16.8.54742762016210944000000.1	x^16 - 16x^14 - 8x^13 + 103x^12 + 112x^11 - 296x^10 - 616x^9 + 115x^8 + 1596x^7 + 1310x^6 - 1956x^5 - 2773x^4 + 1128x^3 + 2016x^2 - 460x - 647	\( 2^{32}\cdot 5^{6}\cdot 13^{8} \)	$(C_2\times C_4).C_2^4$ (as 16T205)	Trivial (GRH)
16.8.2800444573576914534400000000.1	x^16 - 6x^15 - 23x^14 + 76x^13 - 214x^12 + 1002x^11 + 7538x^10 - 10546x^9 - 15990x^8 + 3618x^7 - 308637x^6 - 190596x^5 + 65402x^4 - 242146x^3 + 1530257x^2 - 1648578x - 238999	\( 2^{24}\cdot 5^{8}\cdot 13^{6}\cdot 97^{4} \)	$(C_2\times C_4).C_2^4$ (as 16T205)	Trivial (GRH)
16.0.7478711585794844262400000000.1	x^16 + 70x^14 - 4x^13 + 2168x^12 - 424x^11 + 37270x^10 - 19988x^9 + 363790x^8 - 431008x^7 + 1914202x^6 - 4225052x^5 + 5723512x^4 - 16426168x^3 + 17099594x^2 - 16351756x + 29319889	\( 2^{32}\cdot 5^{8}\cdot 13^{6}\cdot 31^{4} \)	$(C_2\times C_4).C_2^4$ (as 16T205)	$[2, 2, 2, 410]$ (GRH)
16.8.7478711585794844262400000000.1	x^16 - 4x^15 - 14x^14 - 16x^13 - 511x^12 + 244x^11 - 678x^10 - 8760x^9 + 21998x^8 - 24488x^7 + 153132x^6 - 214428x^5 - 62674x^4 + 3390956x^3 - 8339980x^2 + 4371640x + 185071	\( 2^{32}\cdot 5^{8}\cdot 13^{6}\cdot 31^{4} \)	$(C_2\times C_4).C_2^4$ (as 16T205)	$[2]$ (GRH)
16.0.213599481601886546978406400000000.1	x^16 + 358x^14 - 156x^13 + 45729x^12 - 23504x^11 + 2585058x^10 - 599248x^9 + 73676772x^8 + 9111128x^7 + 1089726432x^6 + 539705140x^5 + 7851350618x^4 + 7498045776x^3 + 24982140462x^2 + 39039125944x + 59243323961	\( 2^{32}\cdot 5^{8}\cdot 13^{10}\cdot 31^{4} \)	$(C_2\times C_4).C_2^4$ (as 16T205)	$[2, 2, 2, 2, 31588]$ (GRH)
16.16.214070583463493396843509212774400000000.1	x^16 - 4x^15 - 1584x^14 + 6976x^13 + 968618x^12 - 4501752x^11 - 291746664x^10 + 1378342360x^9 + 46041170792x^8 - 211911186816x^7 - 3734495952480x^6 + 15875325749312x^5 + 142907859799296x^4 - 518503792322688x^3 - 2292621554536112x^2 + 5400237968704032x + 12924181690872944	\( 2^{32}\cdot 5^{8}\cdot 13^{6}\cdot 41^{4}\cdot 311^{4} \)	$(C_2\times C_4).C_2^4$ (as 16T205)	$[2]$ (GRH)