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
16.0.9199792113324180635648.1	x^16 - 5x^14 + 23x^12 - 57x^10 + 62x^8 - 43x^6 + 55x^4 - 51x^2 + 17	\( 2^{28}\cdot 17^{11} \)	16T1113	Trivial
16.0.9199792113324180635648.2	x^16 + 6x^14 + 12x^12 + 19x^10 + 28x^8 - 2x^6 + 42x^4 - 17x^2 + 17	\( 2^{28}\cdot 17^{11} \)	16T1113	Trivial
16.4.147196673813186890170368.3	x^16 + 4x^14 - 5x^12 - 38x^10 + 10x^8 + 158x^6 - 121x^4 - 340x^2 + 17	\( 2^{32}\cdot 17^{11} \)	16T1113	Trivial
16.4.147196673813186890170368.4	x^16 - 4x^14 - 5x^12 + 38x^10 + 10x^8 - 158x^6 - 121x^4 + 340x^2 + 17	\( 2^{32}\cdot 17^{11} \)	16T1113	Trivial
16.4.59190897027263214111328125.1	x^16 - 7x^15 + 5x^14 + 80x^13 - 235x^12 - 81x^11 + 1787x^10 - 3595x^9 - 2745x^8 + 19795x^7 - 32268x^6 + 31406x^5 - 5735x^4 + 44260x^3 - 32500x^2 - 2048x + 92111	\( 3^{4}\cdot 5^{15}\cdot 41^{6}\cdot 71^{2} \)	16T1113	$[2]$ (GRH)
16.4.59190897027263214111328125.2	x^16 - x^15 - 30x^14 + 55x^13 + 285x^12 - 878x^11 - 527x^10 + 5950x^9 - 6675x^8 - 16515x^7 + 36668x^6 + 21267x^5 - 45635x^4 - 92185x^3 - 30260x^2 + 17764x + 34621	\( 3^{4}\cdot 5^{15}\cdot 41^{6}\cdot 71^{2} \)	16T1113	$[2]$ (GRH)
16.4.48763989276665152618408203125.1	x^16 - 2x^15 - 35x^14 + 140x^13 + 95x^12 - 3201x^11 + 13312x^10 + 22360x^9 - 285830x^8 + 81435x^7 + 2562842x^6 - 1161819x^5 - 9809590x^4 - 2753750x^3 + 6343430x^2 + 35305612x + 35181701	\( 5^{15}\cdot 41^{6}\cdot 18341^{2} \)	16T1113	Trivial (GRH)
16.4.48763989276665152618408203125.2	x^16 - 5x^15 + 50x^14 - 300x^13 + 690x^12 - 3875x^11 + 7280x^10 + 2515x^9 + 94800x^8 - 23525x^7 - 82960x^6 - 908045x^5 - 9182675x^4 + 22946630x^3 - 47630820x^2 + 62556615x - 17707745	\( 5^{15}\cdot 41^{6}\cdot 18341^{2} \)	16T1113	Trivial (GRH)
16.4.1278076597085555502017391343173632.1	x^16 + 184x^14 + 9744x^12 + 196432x^10 + 1204306x^8 - 6498968x^6 - 87742452x^4 - 184271568x^2 + 207386978	\( 2^{67}\cdot 17^{6}\cdot 599^{2} \)	16T1113	$[2]$ (GRH)
16.4.1278076597085555502017391343173632.2	x^16 + 96x^14 + 2020x^12 - 70560x^10 - 3717076x^8 - 57999200x^6 - 346080720x^4 - 446748576x^2 + 829547912	\( 2^{67}\cdot 17^{6}\cdot 599^{2} \)	16T1113	$[2]$ (GRH)
16.8.10258099857515326057366623132581888.1	x^16 - 112x^14 - 324x^12 + 301424x^10 - 4852020x^8 - 110083488x^6 + 1591476112x^4 + 7317952736x^2 + 6658118408	\( 2^{67}\cdot 17^{6}\cdot 1697^{2} \)	16T1113	$[2, 2]$ (GRH)
16.8.10258099857515326057366623132581888.2	x^16 - 88x^14 - 2092x^12 + 75544x^10 + 1164966x^8 - 15334664x^6 - 204541196x^4 - 95086304x^2 + 1664529602	\( 2^{67}\cdot 17^{6}\cdot 1697^{2} \)	16T1113	$[2, 2]$ (GRH)
16.0.21393065423814767306817757436903948288.1	x^16 + 552x^14 + 119208x^12 + 13044640x^10 + 774656338x^8 + 24581085768x^6 + 376003596236x^4 + 2094807147552x^2 + 3471343735202	\( 2^{67}\cdot 7^{2}\cdot 17^{6}\cdot 11071^{2} \)	16T1113	$[2, 2, 2, 2, 2177408]$ (GRH)
16.0.21393065423814767306817757436903948288.2	x^16 + 472x^14 + 88780x^12 + 8569912x^10 + 456984038x^8 + 13450643240x^6 + 205334750052x^4 + 1420420813840x^2 + 3471343735202	\( 2^{67}\cdot 7^{2}\cdot 17^{6}\cdot 11071^{2} \)	16T1113	$[2, 2, 2, 2, 1501776]$ (GRH)
16.12.115143422370815907323395348998014369792.1	x^16 - 192x^14 - 17164x^12 + 6285536x^10 - 448461620x^8 + 4519999040x^6 + 503537363856x^4 - 12587964743712x^2 + 74734946110472	\( 2^{67}\cdot 17^{6}\cdot 23^{2}\cdot 7817^{2} \)	16T1113	Trivial (GRH)
16.12.115143422370815907323395348998014369792.2	x^16 - 336x^14 + 29588x^12 + 540680x^10 - 144580170x^8 + 2481964568x^6 + 85749047868x^4 - 2645562716896x^2 + 18683736527618	\( 2^{67}\cdot 17^{6}\cdot 23^{2}\cdot 7817^{2} \)	16T1113	Trivial (GRH)
16.16.4292702462281032366933505959381142863872.1	x^16 - 696x^14 + 189762x^12 - 25837780x^10 + 1884364081x^8 - 75799317308x^6 + 1672904683652x^4 - 18901405129856x^2 + 85165710013832	\( 2^{53}\cdot 383^{2}\cdot 1217^{6} \)	16T1113	Trivial (GRH)
16.16.4292702462281032366933505959381142863872.2	x^16 - 636x^14 + 156618x^12 - 19276476x^10 + 1283010849x^8 - 46430899784x^6 + 875091198288x^4 - 7985667216384x^2 + 27809211433088	\( 2^{53}\cdot 383^{2}\cdot 1217^{6} \)	16T1113	Trivial (GRH)
16.8.1072976581893572471636613847437598787096281088.1	x^16 + 2112x^14 - 335372x^12 - 2092104320x^10 - 99624248436x^8 + 576976513783936x^6 - 4032319635459760x^4 - 12392713672696488160x^2 + 696425773826392185608	\( 2^{67}\cdot 17^{6}\cdot 548837153^{2} \)	16T1113	$[2, 2]$ (GRH)
16.8.1072976581893572471636613847437598787096281088.2	x^16 - 2536x^14 - 3656200x^12 + 332530944x^10 + 1263201268434x^8 + 179252047961656x^6 - 54996144938520724x^4 - 6455576794872506880x^2 + 174106443456598046402	\( 2^{67}\cdot 17^{6}\cdot 548837153^{2} \)	16T1113	$[2, 2]$ (GRH)