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 23 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.74304653885440000000000.8	x^16 - 14x^14 + 101x^12 - 474x^10 + 1576x^8 - 3520x^6 + 5830x^4 - 6050x^2 + 3025	\( 2^{32}\cdot 5^{10}\cdot 11^{6} \)	16T790	Trivial (GRH)
16.4.74304653885440000000000.8	x^16 - 2x^14 - 42x^12 + 118x^10 + 731x^8 - 550x^6 - 2530x^4 + 3025	\( 2^{32}\cdot 5^{10}\cdot 11^{6} \)	16T790	Trivial (GRH)
16.0.74304653885440000000000.9	x^16 + 14x^14 + 101x^12 + 474x^10 + 1576x^8 + 3520x^6 + 5830x^4 + 6050x^2 + 3025	\( 2^{32}\cdot 5^{10}\cdot 11^{6} \)	16T790	Trivial (GRH)
16.4.74304653885440000000000.9	x^16 + 2x^14 - 42x^12 - 118x^10 + 731x^8 + 550x^6 - 2530x^4 + 3025	\( 2^{32}\cdot 5^{10}\cdot 11^{6} \)	16T790	Trivial (GRH)
16.4.208361619975602500000000.1	x^16 - x^15 + 7x^14 + 5x^13 + 7x^12 + 18x^11 - 169x^10 + 291x^9 - 794x^8 - 338x^7 - 805x^6 + 4106x^5 + 8515x^4 - 9672x^3 - 15376x^2 + 5635x + 7729	\( 2^{8}\cdot 5^{10}\cdot 11^{6}\cdot 19^{6} \)	16T790	$[2]$ (GRH)
16.4.208361619975602500000000.2	x^16 - 4x^15 + 19x^14 - 41x^13 + 16x^12 + 73x^11 - 1000x^10 + 1279x^9 - 4131x^8 + 119x^7 - 1971x^6 - 9418x^5 - 329x^4 - 2366x^3 - 16176x^2 + 6557x - 199	\( 2^{8}\cdot 5^{10}\cdot 11^{6}\cdot 19^{6} \)	16T790	Trivial (GRH)
16.0.1857616347136000000000000.5	x^16 + 2x^14 + 25x^12 + 2x^10 + 284x^8 + 528x^6 + 1210x^4 + 2178x^2 + 9801	\( 2^{32}\cdot 5^{12}\cdot 11^{6} \)	16T790	$[4]$ (GRH)
16.0.1857616347136000000000000.6	x^16 - 2x^14 + 25x^12 - 2x^10 + 284x^8 - 528x^6 + 1210x^4 - 2178x^2 + 9801	\( 2^{32}\cdot 5^{12}\cdot 11^{6} \)	16T790	$[4]$ (GRH)
16.4.475549784866816000000000000.1	x^16 - 8x^15 + 40x^14 - 100x^13 + 124x^12 + 152x^11 - 712x^10 + 1900x^9 - 5064x^8 + 11152x^7 - 9952x^6 - 6124x^5 + 18124x^4 - 8176x^3 - 1616x^2 - 1916x - 29	\( 2^{40}\cdot 5^{12}\cdot 11^{6} \)	16T790	$[2]$ (GRH)
16.4.475549784866816000000000000.2	x^16 - 4x^14 - 36x^13 - 130x^12 - 192x^11 + 600x^10 + 3144x^9 + 6147x^8 + 8976x^7 + 21252x^6 + 52800x^5 + 87604x^4 + 95832x^3 + 74052x^2 + 39204x + 9801	\( 2^{40}\cdot 5^{12}\cdot 11^{6} \)	16T790	$[4]$ (GRH)
16.8.739040154910723253702500000000.1	x^16 - 2x^15 - 2x^14 + 42x^13 - 614x^12 + 178x^11 - 9449x^10 - 12791x^9 + 64261x^8 - 303172x^7 + 245065x^6 + 88205x^5 - 264332x^4 + 7809328x^3 - 14277659x^2 + 5204053x + 368009	\( 2^{8}\cdot 5^{10}\cdot 29^{6}\cdot 89^{6} \)	16T790	Trivial (GRH)
16.8.739040154910723253702500000000.2	x^16 - 5x^15 + 8x^14 + 125x^13 - 622x^12 - 1028x^11 + 7296x^10 + 3734x^9 - 67991x^8 - 83954x^7 + 403748x^6 + 748264x^5 - 679622x^4 - 2508605x^3 - 1483482x^2 + 2961393x + 3590449	\( 2^{8}\cdot 5^{10}\cdot 29^{6}\cdot 89^{6} \)	16T790	Trivial (GRH)
16.0.1808302579025794791040000000000.1	x^16 + 28x^14 + 170x^12 - 459x^10 + 34714x^8 + 300350x^6 + 3179290x^4 + 9660625x^2 + 35343025	\( 2^{16}\cdot 5^{10}\cdot 29^{6}\cdot 41^{6} \)	16T790	$[2, 4]$ (GRH)
16.0.1808302579025794791040000000000.2	x^16 - 111x^14 + 5910x^12 - 197473x^10 + 4571039x^8 - 76365265x^6 + 911551490x^4 - 7174634075x^2 + 29723484025	\( 2^{16}\cdot 5^{10}\cdot 29^{6}\cdot 41^{6} \)	16T790	$[2, 4]$ (GRH)
16.0.189194279657145152947840000000000.3	x^16 - 42x^14 - 28x^13 + 885x^12 + 422x^11 + 124x^10 - 139160x^9 + 812973x^8 - 2482800x^7 + 7523736x^6 - 26068944x^5 + 68901995x^4 - 115202696x^3 + 125583512x^2 - 102707850x + 52927601	\( 2^{16}\cdot 5^{10}\cdot 29^{6}\cdot 89^{6} \)	16T790	$[2, 2, 8]$ (GRH)
16.0.189194279657145152947840000000000.4	x^16 - 8x^15 + 31x^14 + 22x^13 - 286x^12 + 1218x^11 + 2835x^10 - 5158x^9 + 31863x^8 + 186018x^7 + 219389x^6 - 1339930x^5 + 3321886x^4 + 5646760x^3 + 27780227x^2 + 147746204x + 266392369	\( 2^{16}\cdot 5^{10}\cdot 29^{6}\cdot 89^{6} \)	16T790	$[2, 2, 8]$ (GRH)
16.0.2442744860101307576054633212890625.3	x^16 - 4x^15 + 96x^14 - 236x^13 + 2231x^12 + 2057x^11 - 19522x^10 + 283427x^9 - 841908x^8 + 3596219x^7 - 2112483x^6 - 3867184x^5 + 179699696x^4 - 919387662x^3 + 5609396159x^2 - 14310734897x + 47938335701	\( 5^{10}\cdot 29^{6}\cdot 41^{6}\cdot 97^{4} \)	16T790	$[2, 2]$ (GRH)
16.0.61068621502532689401365830322265625.2	x^16 - x^15 - 108x^14 + 237x^13 + 6821x^12 + 621x^11 - 224383x^10 - 846849x^9 + 563022x^8 + 14768610x^7 + 66008293x^6 + 249045053x^5 + 655817757x^4 + 844850241x^3 + 2040819419x^2 + 275105310x + 1134395231	\( 5^{12}\cdot 29^{6}\cdot 41^{6}\cdot 97^{4} \)	16T790	$[2, 2, 4]$ (GRH)
16.8.255573021657714643907277003525390625.3	x^16 - 5x^15 - 99x^14 - 319x^13 - 19523x^12 + 121886x^11 + 840025x^10 + 5075165x^9 + 122313650x^8 - 473699896x^7 + 2616789777x^6 - 15749698812x^5 + 16404250745x^4 - 69425863392x^3 + 252708127180x^2 + 184196436709x - 129803237261	\( 5^{10}\cdot 29^{6}\cdot 89^{6}\cdot 97^{4} \)	16T790	$[2]$ (GRH)
16.8.255573021657714643907277003525390625.4	x^16 + 212x^14 - 508x^13 + 5384x^12 - 16080x^11 - 936609x^10 + 4385924x^9 - 34332018x^8 + 59677972x^7 + 458923898x^6 - 3537270704x^5 + 13345340432x^4 + 7085774092x^3 - 116425745573x^2 + 49037720024x + 217181440849	\( 5^{10}\cdot 29^{6}\cdot 89^{6}\cdot 97^{4} \)	16T790	$[2]$ (GRH)
16.0.26706316588122320300180823322240000000000.1	x^16 + 1755x^14 + 1239334x^12 + 451082130x^10 + 89914939054x^8 + 9630554199795x^6 + 507257210716170x^4 + 10352297616322800x^2 + 23508342503733025	\( 2^{16}\cdot 5^{10}\cdot 29^{6}\cdot 89^{6}\cdot 109^{4} \)	16T790	$[2, 2, 2, 2, 2, 2, 6, 4723818]$ (GRH)
16.16.26706316588122320300180823322240000000000.1	x^16 - 1755x^14 + 1239334x^12 - 451082130x^10 + 89914939054x^8 - 9630554199795x^6 + 507257210716170x^4 - 10352297616322800x^2 + 23508342503733025	\( 2^{16}\cdot 5^{10}\cdot 29^{6}\cdot 89^{6}\cdot 109^{4} \)	16T790	$[2]$ (GRH)
16.16.170920426163982849921157269262336000000000000.1	x^16 - 4x^15 - 2242x^14 + 6482x^13 + 1973254x^12 - 3143498x^11 - 875311194x^10 + 185218176x^9 + 206515921983x^8 + 244194385350x^7 - 24824036076810x^6 - 64296287880780x^5 + 1300696765087662x^4 + 5554771415609822x^3 - 18027969452365224x^2 - 127514159553381278x - 171107553307089379	\( 2^{24}\cdot 5^{12}\cdot 29^{6}\cdot 89^{6}\cdot 109^{4} \)	16T790	$[2, 2, 4]$ (GRH)