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 24 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.492857375909216256.3	x^16 - 4x^15 + 4x^14 + 2x^12 - 12x^11 + 36x^10 - 52x^9 + 50x^8 - 40x^7 + 12x^6 + 4x^5 - 10x^4 + 8x^3 + 4x^2 + 1	\( 2^{28}\cdot 3^{8}\cdot 23^{4} \)	$C_2\times C_2^2:S_4:C_2$ (as 16T724)	Trivial
16.0.674314151379664896.2	x^16 - 8x^15 + 30x^14 - 70x^13 + 124x^12 - 198x^11 + 300x^10 - 400x^9 + 456x^8 - 458x^7 + 414x^6 - 324x^5 + 206x^4 - 100x^3 + 35x^2 - 8x + 1	\( 2^{16}\cdot 3^{8}\cdot 199^{4} \)	$C_2\times C_2^2:S_4:C_2$ (as 16T724)	Trivial
16.0.1063333314324135936.1	x^16 - 2x^15 - 4x^14 + 18x^13 - 72x^11 + 66x^10 + 62x^9 - 53x^8 - 80x^7 + 32x^6 + 70x^5 - 15x^4 - 32x^3 + 3x^2 + 6x + 1	\( 2^{16}\cdot 3^{8}\cdot 223^{4} \)	$C_2\times C_2^2:S_4:C_2$ (as 16T724)	Trivial
16.0.1557143660844140625.1	x^16 - x^15 - 2x^14 + x^13 + 4x^12 - 2x^11 - 2x^10 - 6x^9 + 5x^8 + 12x^7 - 3x^6 - 19x^5 + 9x^4 + 8x^3 - 3x^2 - 2x + 1	\( 3^{8}\cdot 5^{8}\cdot 157^{4} \)	$C_2\times C_2^2:S_4:C_2$ (as 16T724)	Trivial
16.0.3847195656649179136.1	x^16 + 4x^14 + 4x^12 - 6x^10 + 14x^8 - 4x^6 + 9x^4 - 6x^2 + 1	\( 2^{32}\cdot 173^{4} \)	$C_2\times C_2^2:S_4:C_2$ (as 16T724)	Trivial
16.0.10172435817406640625.1	x^16 - 7x^15 + 27x^14 - 63x^13 + 115x^12 - 167x^11 + 216x^10 - 243x^9 + 258x^8 - 243x^7 + 216x^6 - 167x^5 + 115x^4 - 63x^3 + 27x^2 - 7x + 1	\( 3^{8}\cdot 5^{8}\cdot 251^{4} \)	$C_2\times C_2^2:S_4:C_2$ (as 16T724)	$[2]$
16.0.38557145113600000000.2	x^16 + x^14 + 4x^12 - 4x^10 + 10x^8 - 4x^6 + 4x^4 - 4x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 197^{4} \)	$C_2\times C_2^2:S_4:C_2$ (as 16T724)	Trivial
16.0.55725627801600000000.8	x^16 - 2x^15 + 6x^14 - 10x^13 + 12x^12 + 6x^10 + 10x^9 - 3x^8 + 8x^7 + 34x^6 + 6x^5 + 18x^4 + 66x^3 + 72x^2 + 36x + 9	\( 2^{28}\cdot 3^{12}\cdot 5^{8} \)	$C_2\times C_2^2:S_4:C_2$ (as 16T724)	Trivial
16.0.81094542259068665856.2	x^16 - 6x^15 + 20x^14 - 48x^13 + 84x^12 - 84x^11 + 46x^10 - 61x^8 + 174x^7 - 212x^6 + 96x^5 + 45x^4 - 90x^3 + 173x^2 - 234x + 169	\( 2^{16}\cdot 3^{8}\cdot 659^{4} \)	$C_2\times C_2^2:S_4:C_2$ (as 16T724)	$[2]$
16.0.169941440847545368576.1	x^16 - 4x^15 + 10x^14 - 24x^13 + 44x^12 - 92x^11 + 192x^10 - 288x^9 + 398x^8 - 336x^7 + 144x^6 - 104x^5 - 32x^4 - 128x^3 + 152x^2 + 80x + 68	\( 2^{36}\cdot 223^{4} \)	$C_2\times C_2^2:S_4:C_2$ (as 16T724)	Trivial
16.0.186110712217600000000.2	x^16 - 4x^14 + 3x^12 + 4x^10 + 13x^8 - 42x^6 + 72x^4 - 32x^2 + 16	\( 2^{24}\cdot 5^{8}\cdot 73^{4} \)	$C_2\times C_2^2:S_4:C_2$ (as 16T724)	Trivial
16.0.196520024473600000000.2	x^16 - 2x^15 + 5x^14 - 14x^13 + 13x^12 - 24x^11 + 32x^10 - 12x^9 + 42x^8 + 12x^7 + 32x^6 + 24x^5 + 13x^4 + 14x^3 + 5x^2 + 2x + 1	\( 2^{28}\cdot 5^{8}\cdot 37^{4} \)	$C_2\times C_2^2:S_4:C_2$ (as 16T724)	Trivial
16.8.318890714258290507776.2	x^16 - 8x^15 + 24x^14 - 24x^13 - 40x^12 + 152x^11 - 200x^10 + 104x^9 + 108x^8 - 336x^7 + 352x^6 - 112x^5 - 120x^4 + 144x^3 - 32x^2 - 16x + 4	\( 2^{36}\cdot 3^{8}\cdot 29^{4} \)	$C_2\times C_2^2:S_4:C_2$ (as 16T724)	Trivial
16.8.1031221647769600000000.1	x^16 - 8x^14 - 8x^13 + 28x^12 + 24x^11 - 24x^10 + 8x^9 + 22x^8 - 96x^7 - 136x^6 + 8x^5 + 96x^4 + 112x^3 + 88x^2 + 32x + 4	\( 2^{40}\cdot 5^{8}\cdot 7^{4} \)	$C_2\times C_2^2:S_4:C_2$ (as 16T724)	Trivial (GRH)
16.8.3144320391577600000000.1	x^16 - 4x^14 + 36x^12 - 136x^10 + 78x^8 + 52x^6 - 16x^4 - 8x^2 + 1	\( 2^{32}\cdot 5^{8}\cdot 37^{4} \)	$C_2\times C_2^2:S_4:C_2$ (as 16T724)	Trivial (GRH)
16.8.5036593283481600000000.1	x^16 - 2x^15 - 3x^14 - 10x^13 + 10x^12 + 52x^11 + 43x^10 - 64x^9 - 154x^8 + 30x^7 + 219x^6 + 36x^5 - 477x^4 - 370x^3 - 14x^2 + 28x + 4	\( 2^{20}\cdot 3^{8}\cdot 5^{8}\cdot 37^{4} \)	$C_2\times C_2^2:S_4:C_2$ (as 16T724)	Trivial (GRH)
16.0.7947193069254687890625.1	x^16 - x^15 - 6x^14 + 13x^13 + 20x^12 - 56x^11 - 9x^10 + 112x^9 - 32x^8 - 51x^7 + 90x^6 - 246x^5 + 241x^4 - 20x^2 - 50x + 25	\( 3^{8}\cdot 5^{8}\cdot 1327^{4} \)	$C_2\times C_2^2:S_4:C_2$ (as 16T724)	$[2]$
16.0.15772350630880634535936.1	x^16 - 6x^15 + 17x^14 - 32x^13 + 46x^12 - 38x^11 + 16x^10 - 12x^9 + 58x^8 + 120x^7 + 520x^6 + 884x^5 + 1302x^4 + 1524x^3 + 1320x^2 + 672x + 169	\( 2^{16}\cdot 3^{8}\cdot 23^{4}\cdot 107^{4} \)	$C_2\times C_2^2:S_4:C_2$ (as 16T724)	$[2]$
16.0.18022783261081600000000.1	x^16 - 2x^15 + 16x^13 - 20x^12 - 74x^11 + 274x^10 - 386x^9 + 146x^8 + 386x^7 - 426x^6 - 814x^5 + 2567x^4 - 3054x^3 + 1970x^2 - 684x + 101	\( 2^{24}\cdot 5^{8}\cdot 229^{4} \)	$C_2\times C_2^2:S_4:C_2$ (as 16T724)	$[4]$
16.0.36041103880170174939136.1	x^16 + 20x^14 + 156x^12 + 604x^10 + 1220x^8 + 1240x^6 + 564x^4 + 88x^2 + 4	\( 2^{36}\cdot 23^{4}\cdot 37^{4} \)	$C_2\times C_2^2:S_4:C_2$ (as 16T724)	$[2, 2]$
16.0.8273769005056000000000000.1	x^16 + 4x^14 + 32x^12 - 88x^10 + 70x^8 + 188x^6 + 92x^4 + 16x^2 + 1	\( 2^{32}\cdot 5^{12}\cdot 53^{4} \)	$C_2\times C_2^2:S_4:C_2$ (as 16T724)	Trivial (GRH)
16.16.40430096994638233600000000.1	x^16 - 28x^14 + 290x^12 - 1392x^10 + 3195x^8 - 3320x^6 + 1378x^4 - 196x^2 + 1	\( 2^{36}\cdot 5^{8}\cdot 197^{4} \)	$C_2\times C_2^2:S_4:C_2$ (as 16T724)	Trivial (GRH)
16.0.73821320237390233600000000.1	x^16 - 4x^15 + 14x^14 - 64x^13 + 178x^12 - 332x^11 + 758x^10 - 908x^9 + 1407x^8 - 1344x^7 + 1242x^6 - 924x^5 + 488x^4 - 192x^3 + 56x^2 - 8x + 1	\( 2^{36}\cdot 5^{8}\cdot 229^{4} \)	$C_2\times C_2^2:S_4:C_2$ (as 16T724)	$[2, 4]$ (GRH)
16.16.73821320237390233600000000.1	x^16 - 30x^14 - 4x^13 + 302x^12 + 84x^11 - 1226x^10 - 344x^9 + 2030x^8 + 344x^7 - 1226x^6 - 84x^5 + 302x^4 + 4x^3 - 30x^2 + 1	\( 2^{36}\cdot 5^{8}\cdot 229^{4} \)	$C_2\times C_2^2:S_4:C_2$ (as 16T724)	Trivial (GRH)