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 20 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.4.6879707136000000000000.4	x^16 - 6x^14 + 5x^12 + 26x^10 - 36x^8 - 4x^6 - 30x^4 + 14x^2 + 1	\( 2^{32}\cdot 3^{8}\cdot 5^{12} \)	$C_2^3.C_2^4.C_2$ (as 16T467)	Trivial (GRH)
16.4.6879707136000000000000.5	x^16 + 6x^14 - 2x^12 - 10x^10 + 11x^8 + 10x^6 - 18x^4 - 8x^2 + 1	\( 2^{32}\cdot 3^{8}\cdot 5^{12} \)	$C_2^3.C_2^4.C_2$ (as 16T467)	Trivial (GRH)
16.0.152274770176000000000000.1	x^16 - 3x^14 + 40x^12 - 368x^10 + 2369x^8 - 9512x^6 + 22040x^4 - 26912x^2 + 13456	\( 2^{20}\cdot 5^{12}\cdot 29^{6} \)	$C_2^3.C_2^4.C_2$ (as 16T467)	$[2]$ (GRH)
16.0.245635219456000000000000.1	x^16 + 22x^14 + 278x^12 + 1984x^10 + 9440x^8 + 22264x^6 + 25168x^4 - 63888x^2 + 234256	\( 2^{36}\cdot 5^{12}\cdot 11^{4} \)	$C_2^3.C_2^4.C_2$ (as 16T467)	Trivial (GRH)
16.0.245635219456000000000000.2	x^16 - 22x^14 + 278x^12 - 1984x^10 + 9440x^8 - 22264x^6 + 25168x^4 + 63888x^2 + 234256	\( 2^{36}\cdot 5^{12}\cdot 11^{4} \)	$C_2^3.C_2^4.C_2$ (as 16T467)	Trivial (GRH)
16.8.770891024016000000000000.1	x^16 - 6x^15 + 2x^14 + 54x^13 - 142x^12 + 154x^11 - 54x^10 - 388x^9 + 443x^8 - 56x^7 + 2074x^6 - 770x^5 - 1507x^4 + 398x^3 + 363x^2 - 26x - 19	\( 2^{16}\cdot 3^{4}\cdot 5^{12}\cdot 29^{6} \)	$C_2^3.C_2^4.C_2$ (as 16T467)	Trivial (GRH)
16.0.1216026685696000000000000.2	x^16 - 13x^14 + 147x^12 - 1215x^10 + 5461x^8 - 7380x^6 - 13612x^4 + 26896x^2 + 26896	\( 2^{20}\cdot 5^{12}\cdot 41^{6} \)	$C_2^3.C_2^4.C_2$ (as 16T467)	$[2]$ (GRH)
16.8.1947839620325062500000000.1	x^16 - 6x^15 + x^14 + 48x^13 - 63x^12 - 136x^11 + 232x^10 + 463x^9 - 369x^8 - 877x^7 + 1637x^6 + 2724x^5 - 703x^4 - 2902x^3 - 1779x^2 - 411x - 29	\( 2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 41^{6} \)	$C_2^3.C_2^4.C_2$ (as 16T467)	Trivial (GRH)
16.8.19757093783472562500000000.1	x^16 + 10x^14 - 42x^13 - 19x^12 - 330x^11 + 64x^10 - 309x^9 + 1606x^8 + 1422x^7 + 16307x^6 + 16914x^5 - 34228x^4 - 4947x^3 + 2024x^2 - 93x + 1	\( 2^{8}\cdot 3^{12}\cdot 5^{12}\cdot 29^{6} \)	$C_2^3.C_2^4.C_2$ (as 16T467)	Trivial (GRH)
16.0.498646942803216000000000000.1	x^16 - 17x^14 + 79x^12 + 62x^10 - 579x^8 - 7790x^6 + 36490x^4 + 84050x^2 + 42025	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 41^{6} \)	$C_2^3.C_2^4.C_2$ (as 16T467)	$[2, 2]$ (GRH)
16.0.498646942803216000000000000.2	x^16 + 23x^14 + 189x^12 + 467x^10 + 3666x^8 + 2495x^6 + 17165x^4 - 12300x^2 + 42025	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 41^{6} \)	$C_2^3.C_2^4.C_2$ (as 16T467)	$[2, 2]$ (GRH)
16.8.498646942803216000000000000.4	x^16 - 13x^14 - 35x^12 + 542x^10 - 171x^8 - 2732x^6 + 190x^4 + 4018x^2 + 1681	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 41^{6} \)	$C_2^3.C_2^4.C_2$ (as 16T467)	Trivial (GRH)
16.0.2229454910146816000000000000.1	x^16 + 58x^14 + 1688x^12 + 31581x^10 + 412915x^8 + 3826086x^6 + 24464748x^4 + 98504648x^2 + 197009296	\( 2^{20}\cdot 5^{12}\cdot 11^{4}\cdot 29^{6} \)	$C_2^3.C_2^4.C_2$ (as 16T467)	$[2]$ (GRH)
16.0.2229454910146816000000000000.2	x^16 - 63x^14 + 1798x^12 - 31196x^10 + 377825x^8 - 3430526x^6 + 22920788x^4 - 98504648x^2 + 197009296	\( 2^{20}\cdot 5^{12}\cdot 11^{4}\cdot 29^{6} \)	$C_2^3.C_2^4.C_2$ (as 16T467)	$[2]$ (GRH)
16.8.6847016061481864788618324763213824.1	x^16 + 72x^14 - 160x^13 - 3048x^12 - 23232x^11 - 255872x^10 - 545552x^9 + 3043444x^8 + 33122208x^7 + 217453872x^6 + 341051488x^5 - 3246277392x^4 - 14285640128x^3 - 3013742336x^2 + 72795641824x + 100457697148	\( 2^{64}\cdot 3^{4}\cdot 7^{6}\cdot 79^{4} \)	$C_2^3.C_2^4.C_2$ (as 16T467)	$[2, 2]$ (GRH)
16.8.6847016061481864788618324763213824.2	x^16 + 40x^14 - 16x^13 - 6516x^12 + 16064x^11 - 46000x^10 - 1009872x^9 + 11342580x^8 - 12091152x^7 - 162023704x^6 + 1510348640x^5 - 1449183488x^4 - 16401426768x^3 + 39182469104x^2 - 36835875024x + 12419943838	\( 2^{64}\cdot 3^{4}\cdot 7^{6}\cdot 79^{4} \)	$C_2^3.C_2^4.C_2$ (as 16T467)	$[2]$ (GRH)
16.16.144374905963274060169216000000000000.1	x^16 - 140x^14 + 7098x^12 - 164200x^10 + 1877899x^8 - 10550760x^6 + 27229752x^4 - 29599020x^2 + 9418761	\( 2^{48}\cdot 3^{4}\cdot 5^{12}\cdot 11^{10} \)	$C_2^3.C_2^4.C_2$ (as 16T467)	$[2]$ (GRH)
16.16.144374905963274060169216000000000000.2	x^16 - 140x^14 + 7978x^12 - 236360x^10 + 3839419x^8 - 32869320x^6 + 129267072x^4 - 185630940x^2 + 9418761	\( 2^{48}\cdot 3^{4}\cdot 5^{12}\cdot 11^{10} \)	$C_2^3.C_2^4.C_2$ (as 16T467)	$[2]$ (GRH)
16.0.6116821298063232221593993216000000000000.1	x^16 + 924x^14 - 340x^13 + 272760x^12 - 31440x^11 + 33633576x^10 - 5455480x^9 + 2023819954x^8 - 364995040x^7 + 63031672656x^6 - 23051035280x^5 + 1004385747460x^4 - 766557135840x^3 + 6946284261904x^2 - 9033027884240x + 11940059568116	\( 2^{40}\cdot 5^{12}\cdot 11^{8}\cdot 571^{4} \)	$C_2^3.C_2^4.C_2$ (as 16T467)	$[2, 2, 2, 2, 2, 2, 2, 1661828]$ (GRH)
16.0.6116821298063232221593993216000000000000.2	x^16 + 884x^14 - 460x^13 + 279960x^12 - 283240x^11 + 37499896x^10 - 58510080x^9 + 2032000719x^8 - 3943978960x^7 + 53612475676x^6 - 98903155760x^5 + 744323000990x^4 - 1183776575800x^3 + 5126676453884x^2 - 5348496829980x + 10362339067001	\( 2^{40}\cdot 5^{12}\cdot 11^{8}\cdot 571^{4} \)	$C_2^3.C_2^4.C_2$ (as 16T467)	$[2, 2, 2, 2, 2, 2, 2, 1455270]$ (GRH)