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 26 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.4.439804651110400000000.5	x^16 + 4x^14 - 4x^12 - 36x^10 - 38x^8 + 32x^6 + 76x^4 + 40x^2 + 4	\( 2^{50}\cdot 5^{8} \)	16T869	Trivial (GRH)
16.4.439804651110400000000.6	x^16 - 4x^14 - 4x^12 + 36x^10 - 38x^8 - 32x^6 + 76x^4 - 40x^2 + 4	\( 2^{50}\cdot 5^{8} \)	16T869	Trivial (GRH)
16.0.6794121672126852235264.8	x^16 - 8x^14 + 40x^12 - 200x^10 + 729x^8 - 1564x^6 + 1870x^4 - 1156x^2 + 289	\( 2^{48}\cdot 17^{6} \)	16T869	$[2]$
16.0.27176486688507408941056.12	x^16 - 20x^14 + 176x^12 - 896x^10 + 3000x^8 - 6936x^6 + 9520x^4 - 4624x^2 + 1156	\( 2^{50}\cdot 17^{6} \)	16T869	$[2]$ (GRH)
16.8.778257078845440000000000.1	x^16 - 2x^15 - 7x^14 - 14x^13 + 35x^12 + 156x^11 + 22x^10 - 132x^9 - 493x^8 - 426x^7 + 561x^6 + 498x^5 - 55x^4 - 32x^3 + 896x^2 - 768x - 256	\( 2^{24}\cdot 5^{10}\cdot 41^{6} \)	16T869	$[2]$ (GRH)
16.0.778257078845440000000000.7	x^16 - 6x^15 + 23x^14 - 68x^13 + 148x^12 - 258x^11 + 486x^10 - 654x^9 + 1183x^8 - 2462x^7 + 3094x^6 - 5146x^5 + 6498x^4 - 4324x^3 + 5227x^2 - 822x + 3231	\( 2^{24}\cdot 5^{10}\cdot 41^{6} \)	16T869	$[4]$ (GRH)
16.8.32031814824091254112890625.1	x^16 - 6x^15 + x^14 + 72x^13 - 181x^12 - 130x^11 + 1282x^10 - 1608x^9 - 2531x^8 + 9006x^7 - 3368x^6 - 15236x^5 + 18694x^4 + 9802x^3 - 16078x^2 - 1020x + 2531	\( 5^{8}\cdot 13^{10}\cdot 29^{6} \)	16T869	$[2]$ (GRH)
16.0.199233812184432640000000000.1	x^16 - 4x^15 + 6x^14 + 40x^13 - 150x^12 + 132x^11 + 594x^10 - 104x^9 - 3567x^8 + 6672x^7 + 5120x^6 - 58576x^5 + 169744x^4 - 276992x^3 + 276928x^2 - 162432x + 45504	\( 2^{32}\cdot 5^{10}\cdot 41^{6} \)	16T869	$[2, 2, 4]$ (GRH)
16.16.51003855919214755840000000000.2	x^16 - 56x^14 + 1182x^12 - 11964x^10 + 62931x^8 - 174660x^6 + 249690x^4 - 168100x^2 + 42025	\( 2^{40}\cdot 5^{10}\cdot 41^{6} \)	16T869	$[2]$ (GRH)
16.0.51003855919214755840000000000.4	x^16 + 56x^14 + 1182x^12 + 11964x^10 + 62931x^8 + 174660x^6 + 249690x^4 + 168100x^2 + 42025	\( 2^{40}\cdot 5^{10}\cdot 41^{6} \)	16T869	$[2, 2, 2, 364]$ (GRH)
16.12.96143571830568172203282530304.1	x^16 - 40x^14 + 142x^12 + 3080x^10 - 19062x^8 + 13192x^6 + 74302x^4 - 75272x^2 + 9409	\( 2^{44}\cdot 3^{8}\cdot 97^{6} \)	16T869	Trivial (GRH)
16.4.96143571830568172203282530304.1	x^16 + 40x^14 + 142x^12 - 3080x^10 - 19062x^8 - 13192x^6 + 74302x^4 + 75272x^2 + 9409	\( 2^{44}\cdot 3^{8}\cdot 97^{6} \)	16T869	$[2]$ (GRH)
16.12.513620296716624855040000000000.1	x^16 - 2x^15 - x^14 + 18x^13 - 719x^12 + 176x^11 + 9972x^10 + 1964x^9 - 41518x^8 - 28648x^7 + 25448x^6 + 50352x^5 + 45396x^4 - 54496x^3 - 20304x^2 + 9216x + 2416	\( 2^{28}\cdot 5^{10}\cdot 241^{6} \)	16T869	Trivial (GRH)
16.4.513620296716624855040000000000.1	x^16 - 18x^14 - 92x^13 - 635x^12 - 1304x^11 - 4824x^10 - 5484x^9 - 11879x^8 + 2512x^7 + 10910x^6 + 73664x^5 + 82950x^4 + 145832x^3 + 95148x^2 + 62824x - 128476	\( 2^{28}\cdot 5^{10}\cdot 241^{6} \)	16T869	$[2, 2]$ (GRH)
16.0.816061694707436093440000000000.1	x^16 + 80x^14 + 2516x^12 + 39920x^10 + 340044x^8 + 1515360x^6 + 3171760x^4 + 2689600x^2 + 672400	\( 2^{44}\cdot 5^{10}\cdot 41^{6} \)	16T869	$[2, 2, 2, 1458]$ (GRH)
16.16.816061694707436093440000000000.1	x^16 - 80x^14 + 2516x^12 - 39920x^10 + 340044x^8 - 1515360x^6 + 3171760x^4 - 2689600x^2 + 672400	\( 2^{44}\cdot 5^{10}\cdot 41^{6} \)	16T869	$[2]$ (GRH)
16.8.816061694707436093440000000000.1	x^16 + 12x^14 - 896x^12 - 8272x^10 + 143156x^8 - 190240x^6 - 1036480x^4 + 1344800x^2 + 672400	\( 2^{44}\cdot 5^{10}\cdot 41^{6} \)	16T869	$[2]$ (GRH)
16.8.816061694707436093440000000000.2	x^16 - 28x^14 - 1156x^12 - 9052x^10 - 11074x^8 + 68060x^6 + 58220x^4 - 168100x^2 + 42025	\( 2^{44}\cdot 5^{10}\cdot 41^{6} \)	16T869	$[2]$ (GRH)
16.8.816061694707436093440000000000.3	x^16 + 36x^14 - 204x^12 - 7924x^10 + 25566x^8 + 369820x^6 - 1255420x^4 + 840500x^2 + 42025	\( 2^{44}\cdot 5^{10}\cdot 41^{6} \)	16T869	Trivial (GRH)
16.8.816061694707436093440000000000.4	x^16 + 64x^14 + 886x^12 - 2416x^10 - 59384x^8 + 186960x^6 + 355880x^4 - 1344800x^2 + 672400	\( 2^{44}\cdot 5^{10}\cdot 41^{6} \)	16T869	$[2]$ (GRH)
16.8.816061694707436093440000000000.5	x^16 + 28x^14 - 1156x^12 + 9052x^10 - 11074x^8 - 68060x^6 + 58220x^4 + 168100x^2 + 42025	\( 2^{44}\cdot 5^{10}\cdot 41^{6} \)	16T869	$[2]$ (GRH)
16.8.816061694707436093440000000000.6	x^16 - 36x^14 - 204x^12 + 7924x^10 + 25566x^8 - 369820x^6 - 1255420x^4 - 840500x^2 + 42025	\( 2^{44}\cdot 5^{10}\cdot 41^{6} \)	16T869	Trivial (GRH)
16.0.22168695080663051109329457381376.1	x^16 + 24x^14 + 324x^12 + 3584x^10 - 3928x^8 - 244528x^6 + 926840x^4 - 1008032x^2 + 611524	\( 2^{50}\cdot 13^{8}\cdot 17^{6} \)	16T869	$[2, 2, 4]$ (GRH)
16.0.22168695080663051109329457381376.2	x^16 - 24x^14 + 324x^12 - 3584x^10 - 3928x^8 + 244528x^6 + 926840x^4 + 1008032x^2 + 611524	\( 2^{50}\cdot 13^{8}\cdot 17^{6} \)	16T869	$[2, 2, 4]$ (GRH)
16.8.8146439662885973461565440000000000.1	x^16 + 40x^14 - 168x^13 - 346x^12 - 5112x^11 - 15384x^10 + 49452x^9 + 148909x^8 + 1730976x^7 + 2055924x^6 - 3305052x^5 - 12392604x^4 - 97021992x^3 + 44381336x^2 + 147258708x - 5857289	\( 2^{32}\cdot 5^{10}\cdot 761^{6} \)	16T869	$[2, 2, 2]$ (GRH)
16.8.8146439662885973461565440000000000.2	x^16 - 48x^14 - 168x^13 - 126x^12 + 6120x^11 + 39236x^10 + 32604x^9 - 395743x^8 - 2599968x^7 - 7009552x^6 + 4897716x^5 + 71862392x^4 + 209915832x^3 + 352409812x^2 + 298136964x + 125995759	\( 2^{32}\cdot 5^{10}\cdot 761^{6} \)	16T869	$[2, 4]$ (GRH)