Global number field search results

Further refine search

Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying all 30 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.10460890548900000000.1	x^16 - 5x^15 + 8x^14 + 2x^13 - 3x^12 - 80x^11 + 227x^10 - 192x^9 - 125x^8 + 264x^7 + 230x^6 - 875x^5 + 858x^4 - 295x^3 - 55x^2 + 37x + 19	\( 2^{8}\cdot 3^{10}\cdot 5^{8}\cdot 11^{6} \)	16T1220	Trivial
16.0.10460890548900000000.2	x^16 - 4x^15 + 8x^14 - 21x^13 + 46x^12 - 50x^11 + 43x^10 - 29x^9 - 40x^8 - 29x^7 + 211x^6 - 75x^5 - 108x^4 + 10x^3 + 28x^2 + 9x + 1	\( 2^{8}\cdot 3^{10}\cdot 5^{8}\cdot 11^{6} \)	16T1220	$[2]$
16.0.33260226740224000000.1	x^16 - 12x^14 - 12x^13 + 58x^12 + 88x^11 - 72x^10 - 200x^9 - 100x^8 - 64x^7 - 124x^6 + 208x^5 + 844x^4 + 1056x^3 + 680x^2 + 232x + 34	\( 2^{44}\cdot 5^{6}\cdot 11^{2} \)	16T1220	Trivial
16.0.33260226740224000000.2	x^16 - 4x^15 + 8x^13 - 4x^12 + 16x^11 + 72x^10 + 16x^9 - 240x^8 - 480x^7 - 240x^6 + 592x^5 + 1192x^4 + 960x^3 + 432x^2 + 96x + 8	\( 2^{44}\cdot 5^{6}\cdot 11^{2} \)	16T1220	Trivial
16.4.72584947302400000000.1	x^16 - 4x^13 - 24x^9 - 14x^8 - 32x^7 - 32x^6 - 32x^5 + 44x^4 + 128x^3 + 112x^2 + 48x + 4	\( 2^{40}\cdot 5^{8}\cdot 13^{2} \)	16T1220	Trivial
16.4.72584947302400000000.2	x^16 + 4x^14 - 4x^13 - 10x^12 - 32x^11 - 44x^10 - 28x^9 + 15x^8 + 112x^7 + 216x^6 + 260x^5 + 200x^4 + 104x^3 + 36x^2 + 8x + 1	\( 2^{40}\cdot 5^{8}\cdot 13^{2} \)	16T1220	Trivial
16.0.52554919692301559136256.1	x^16 - 4x^15 + 18x^14 - 56x^13 + 173x^12 - 392x^11 + 954x^10 - 2164x^9 + 3866x^8 - 7096x^7 + 12564x^6 - 16304x^5 + 20066x^4 - 28280x^3 + 30324x^2 - 17608x + 4132	\( 2^{38}\cdot 17^{6}\cdot 89^{2} \)	16T1220	$[2]$
16.0.52554919692301559136256.2	x^16 + 4x^14 - 12x^13 - 15x^12 - 20x^11 + 388x^10 - 328x^9 - 615x^8 + 120x^7 + 5212x^6 - 8076x^5 - 15x^4 + 2332x^3 + 8332x^2 - 10768x + 3464	\( 2^{38}\cdot 17^{6}\cdot 89^{2} \)	16T1220	$[2]$
16.12.174125907386032334045184.1	x^16 - 8x^15 + 12x^14 + 48x^13 - 116x^12 - 132x^11 + 292x^10 + 704x^9 - 951x^8 - 2124x^7 + 3844x^6 + 312x^5 - 4794x^4 + 4244x^3 - 1036x^2 - 656x + 337	\( 2^{40}\cdot 3^{8}\cdot 17^{6} \)	16T1220	Trivial (GRH)
16.8.174125907386032334045184.1	x^16 - 4x^13 - 24x^12 - 56x^11 - 64x^10 + 168x^9 + 623x^8 + 640x^7 - 284x^6 - 1416x^5 - 1532x^4 - 784x^3 - 184x^2 - 12x + 1	\( 2^{40}\cdot 3^{8}\cdot 17^{6} \)	16T1220	Trivial
16.8.174125907386032334045184.2	x^16 - 8x^15 + 24x^14 - 16x^13 - 128x^12 + 564x^11 - 1432x^10 + 2980x^9 - 5127x^8 + 6868x^7 - 7960x^6 + 8652x^5 - 7498x^4 + 5100x^3 - 3512x^2 + 1996x - 503	\( 2^{40}\cdot 3^{8}\cdot 17^{6} \)	16T1220	Trivial
16.4.174125907386032334045184.3	x^16 - 8x^15 + 32x^14 - 76x^13 + 66x^12 + 232x^11 - 1172x^10 + 3128x^9 - 6098x^8 + 9416x^7 - 12560x^6 + 14552x^5 - 13276x^4 + 8304x^3 - 2360x^2 - 496x + 292	\( 2^{40}\cdot 3^{8}\cdot 17^{6} \)	16T1220	Trivial
16.12.557121553975260619997184.1	x^16 - 16x^14 - 20x^13 + 62x^12 + 200x^11 + 180x^10 - 264x^9 - 680x^8 - 560x^7 - 1788x^6 - 4336x^5 - 3608x^4 - 192x^3 + 984x^2 + 288x - 18	\( 2^{44}\cdot 3^{8}\cdot 13^{6} \)	16T1220	Trivial (GRH)
16.4.557121553975260619997184.1	x^16 + 16x^14 - 12x^13 + 78x^12 - 40x^11 - 44x^10 + 568x^9 - 2088x^8 + 4112x^7 - 5620x^6 + 6192x^5 - 7528x^4 + 9152x^3 - 7464x^2 + 3264x - 578	\( 2^{44}\cdot 3^{8}\cdot 13^{6} \)	16T1220	Trivial
16.8.307757468400156944014204800390625.1	x^16 - 8x^15 - 16x^14 + 252x^13 - 1021x^12 + 2486x^11 + 22853x^10 - 130094x^9 + 41755x^8 + 628878x^7 - 2436777x^6 + 4548148x^5 - 2534855x^4 - 1509366x^3 + 9752220x^2 - 8384456x + 4669264	\( 5^{8}\cdot 13^{2}\cdot 29^{6}\cdot 97^{8} \)	16T1220	Trivial (GRH)
16.8.192348417750098090008878000244140625.1	x^16 - 2x^15 - 9x^14 - 3x^13 - 5329x^12 + 5969x^11 + 23059x^10 - 57699x^9 + 6616977x^8 - 6636719x^7 - 30238421x^6 + 108400439x^5 - 598924089x^4 + 291344387x^3 + 696989411x^2 - 1291737162x - 80946349	\( 5^{12}\cdot 13^{2}\cdot 29^{6}\cdot 97^{8} \)	16T1220	Trivial (GRH)
16.12.258824030924531989915946237128515625.1	x^16 - 4x^15 - 21x^14 + 36x^13 - 1456x^12 + 8554x^11 + 57458x^10 - 285532x^9 - 699575x^8 + 3307352x^7 + 2828733x^6 - 13679900x^5 - 1078209x^4 + 9483892x^3 + 5607282x^2 + 1110642x - 167749	\( 5^{8}\cdot 13^{2}\cdot 29^{8}\cdot 97^{8} \)	16T1220	$[2]$ (GRH)
16.12.258824030924531989915946237128515625.2	x^16 - 2x^15 - 27x^14 + 70x^13 - 1228x^12 - 2362x^11 + 41679x^10 + 58828x^9 - 292439x^8 - 620902x^7 + 28717x^6 + 3272810x^5 + 291102x^4 - 4573696x^3 + 312549x^2 + 1178370x - 3389	\( 5^{8}\cdot 13^{2}\cdot 29^{8}\cdot 97^{8} \)	16T1220	$[2]$ (GRH)
16.0.372286265552058761987916010000000000.1	x^16 - 2x^15 - 14x^14 + 49x^13 - 1435x^12 + 3947x^11 + 7085x^10 + 134109x^9 - 461910x^8 + 1785594x^7 + 22643979x^6 - 205130504x^5 + 1402119634x^4 - 2806521416x^3 + 7424247588x^2 - 6349974312x + 5672327056	\( 2^{10}\cdot 5^{10}\cdot 41^{6}\cdot 97^{8} \)	16T1220	$[58]$ (GRH)
16.0.372286265552058761987916010000000000.2	x^16 - 4x^15 + 105x^14 - 157x^13 + 4415x^12 + 8141x^11 + 158184x^10 + 495646x^9 + 6060244x^8 + 6804645x^7 + 141296160x^6 - 18177834x^5 + 1472323023x^4 - 726339735x^3 + 5298257835x^2 - 1353001077x + 4908433609	\( 2^{10}\cdot 5^{10}\cdot 41^{6}\cdot 97^{8} \)	16T1220	$[58]$ (GRH)
16.8.33118016836326980261932928527132262400.1	x^16 - 16x^14 - 648x^12 + 6152x^10 + 58666x^8 - 117840x^6 - 542088x^4 + 317160x^2 + 27225	\( 2^{50}\cdot 3^{10}\cdot 5^{2}\cdot 109^{8} \)	16T1220	$[2]$ (GRH)
16.8.33118016836326980261932928527132262400.2	x^16 - 8x^14 - 168x^12 + 1120x^10 + 5290x^8 - 28776x^6 - 16488x^4 + 93600x^2 + 27225	\( 2^{50}\cdot 3^{10}\cdot 5^{2}\cdot 109^{8} \)	16T1220	$[2]$ (GRH)
16.4.161765019327832493697466398205322265625.1	x^16 - 8x^15 + 150x^14 - 910x^13 + 2815x^12 - 5424x^11 - 460598x^10 + 2331975x^9 - 25428140x^8 + 87696510x^7 - 456607633x^6 + 1072701854x^5 - 2845882150x^4 + 4001565485x^3 - 4522732490x^2 + 2686818563x - 233420339	\( 5^{12}\cdot 13^{2}\cdot 29^{8}\cdot 97^{8} \)	16T1220	$[4]$ (GRH)
16.4.161765019327832493697466398205322265625.2	x^16 - 6x^15 - 24x^14 + 486x^13 - 13097x^12 + 75084x^11 - 627886x^10 + 2570953x^9 - 9369992x^8 + 29169414x^7 + 2512621x^6 - 36928272x^5 + 878892788x^4 - 2189230097x^3 + 2780443254x^2 - 1460860467x + 926982331	\( 5^{12}\cdot 13^{2}\cdot 29^{8}\cdot 97^{8} \)	16T1220	$[4]$ (GRH)
16.8.3097409343524676827553991309957483462656.1	x^16 + 16x^14 + 8x^12 - 548x^10 + 49x^8 + 4352x^6 - 3190x^4 - 2992x^2 + 121	\( 2^{48}\cdot 3^{12}\cdot 11^{6}\cdot 43^{8} \)	16T1220	$[4]$ (GRH)
16.8.374786530566485896134032948504855498981376.1	x^16 + 100x^14 + 1694x^12 - 12716x^10 - 127655x^8 + 1043504x^6 - 1639792x^4 - 1288408x^2 + 1771561	\( 2^{48}\cdot 3^{12}\cdot 11^{8}\cdot 43^{8} \)	16T1220	$[2, 8]$ (GRH)
16.0.13742275226577042645713355852595855360000000000.1	x^16 - 6x^14 - 9166x^12 + 1705860x^10 + 581558100x^8 + 71673084000x^6 + 6640477030400x^4 + 408443341848000x^2 + 13594580577640000	\( 2^{30}\cdot 5^{10}\cdot 41^{6}\cdot 359^{8} \)	16T1220	$[2, 2, 2, 6, 144]$ (GRH)
16.0.13742275226577042645713355852595855360000000000.2	x^16 + 234x^14 + 46558x^12 + 3312588x^10 + 517543324x^8 + 51447741360x^6 + 2284011012880x^4 + 178926406536000x^2 + 13594580577640000	\( 2^{30}\cdot 5^{10}\cdot 41^{6}\cdot 359^{8} \)	16T1220	$[2, 2, 2, 6, 144]$ (GRH)
16.0.6787686212645735395617770359527756187429905390010541799040000000000.1	x^16 + 99927x^14 + 3348619917x^12 + 49805057274891x^10 + 358242690060063549x^8 + 1226168211290116622980x^6 + 1723001890065898798219360x^4 + 675683468660538284973587200x^2 + 45933415411470942405369606400	\( 2^{16}\cdot 5^{10}\cdot 101^{10}\cdot 673^{8}\cdot 1229^{4} \)	16T1220	n/a
16.0.6787686212645735395617770359527756187429905390010541799040000000000.2	x^16 + 105511x^14 + 4286485093x^12 + 83745030765827x^10 + 788070267257863489x^8 + 2989272107913514337760x^6 + 2340628252707564433358240x^4 + 591998115627081544732705600x^2 + 45933415411470942405369606400	\( 2^{16}\cdot 5^{10}\cdot 101^{10}\cdot 673^{8}\cdot 1229^{4} \)	16T1220	n/a