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 matches 1-50 of 307)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.53852247105234794897624209945600000000.1	x^16 + 692x^14 + 195021x^12 + 29476446x^10 + 2631730033x^8 + 142943828127x^6 + 4635153016019x^4 + 82392759879901x^2 + 617051226286141	\( 2^{16}\cdot 5^{8}\cdot 101^{8}\cdot 181^{5} \)	16T1022	$[2, 2, 2, 2, 2, 5542900]$ (GRH)
16.0.53852247105234794897624209945600000000.2	x^16 + 905x^14 + 292559x^12 + 46835215x^10 + 4188988837x^8 + 217813282150x^6 + 6476220131501x^4 + 100585999361780x^2 + 617051226286141	\( 2^{16}\cdot 5^{8}\cdot 101^{8}\cdot 181^{5} \)	16T1022	$[2, 2, 2, 2, 2, 5542900]$ (GRH)
16.0.124072986059627688411885857786694729728.1	x^16 + 784x^14 + 233444x^12 + 35068304x^10 + 2901858458x^8 + 133415695888x^6 + 3219023669900x^4 + 35156129966736x^2 + 131686311606833	\( 2^{66}\cdot 113^{3}\cdot 1039^{4} \)	16T859	$[2, 2, 2, 2, 6505842]$ (GRH)
16.0.593480012330142368753575683686400000000.1	x^16 + 966x^14 + 336865x^12 + 54096892x^10 + 4564529155x^8 + 213414926004x^6 + 5474328578946x^4 + 70645633332048x^2 + 352375894935684	\( 2^{38}\cdot 3^{4}\cdot 5^{8}\cdot 31^{2}\cdot 89^{4}\cdot 33641^{2} \)	16T1605	$[2, 2, 2, 2, 20522460]$ (GRH)
16.0.656523274126409603991207936000000000000.74	x^16 + 780x^14 + 188370x^12 + 19164600x^10 + 930852000x^8 + 22422582000x^6 + 257859693000x^4 + 1249258140000x^2 + 1873887210000	\( 2^{44}\cdot 3^{8}\cdot 5^{12}\cdot 13^{12} \)	$C_4\times C_2^2$ (as 16T2)	$[2, 2, 2, 2, 4, 4, 20, 40, 680]$ (GRH)
16.0.3245499096990365116593765338925510950912.1	x^16 + 1040x^14 + 413632x^12 + 81233056x^10 + 8399650146x^8 + 453293070296x^6 + 12271932633428x^4 + 147376666008656x^2 + 526630603644098	\( 2^{67}\cdot 17^{6}\cdot 977^{4} \)	16T937	$[2, 2, 2, 2, 2, 17397908]$ (GRH)
16.0.3245499096990365116593765338925510950912.2	x^16 + 1080x^14 + 445108x^12 + 89721256x^10 + 9481842342x^8 + 527214969352x^6 + 14588368338164x^4 + 174011003239136x^2 + 526630603644098	\( 2^{67}\cdot 17^{6}\cdot 977^{4} \)	16T937	$[2, 2, 2, 2, 2, 13352508]$ (GRH)
16.0.4377879877971569095410685630463959105536.1	x^16 + 492x^14 + 87822x^12 + 7199928x^10 + 282271716x^8 + 5280868224x^6 + 42978947328x^4 + 105408221184x^2 + 45174951936	\( 2^{44}\cdot 3^{8}\cdot 41^{14} \)	$C_8\times C_2$ (as 16T5)	$[2, 2, 2, 2, 8006728]$ (GRH)
16.0.6116821298063232221593993216000000000000.1	x^16 + 924x^14 - 340x^13 + 272760x^12 - 31440x^11 + 33633576x^10 - 5455480x^9 + 2023819954x^8 - 364995040x^7 + 63031672656x^6 - 23051035280x^5 + 1004385747460x^4 - 766557135840x^3 + 6946284261904x^2 - 9033027884240x + 11940059568116	\( 2^{40}\cdot 5^{12}\cdot 11^{8}\cdot 571^{4} \)	$C_2^3.C_2^4.C_2$ (as 16T467)	$[2, 2, 2, 2, 2, 2, 2, 1661828]$ (GRH)
16.0.6116821298063232221593993216000000000000.2	x^16 + 884x^14 - 460x^13 + 279960x^12 - 283240x^11 + 37499896x^10 - 58510080x^9 + 2032000719x^8 - 3943978960x^7 + 53612475676x^6 - 98903155760x^5 + 744323000990x^4 - 1183776575800x^3 + 5126676453884x^2 - 5348496829980x + 10362339067001	\( 2^{40}\cdot 5^{12}\cdot 11^{8}\cdot 571^{4} \)	$C_2^3.C_2^4.C_2$ (as 16T467)	$[2, 2, 2, 2, 2, 2, 2, 1455270]$ (GRH)
16.0.6386440838157604973770860952468990607569.2	x^16 - x^15 + 64x^14 + 320x^13 - 2278x^12 - 14002x^11 - 143032x^10 - 1270944x^9 - 2564467x^8 + 11757259x^7 + 259046624x^6 + 2375245912x^5 + 13322733808x^4 + 53673234160x^3 + 167744328448x^2 + 361157329920x + 401292214272	\( 17^{14}\cdot 41^{14} \)	$C_8\times C_2$ (as 16T5)	$[17, 22055052]$ (GRH)
16.0.7591625588243699460514311988838400000000.24	x^16 + 1020x^14 + 313650x^12 + 42687000x^10 + 2809080000x^8 + 87783750000x^6 + 1290421125000x^4 + 7900537500000x^2 + 11850806250000	\( 2^{44}\cdot 3^{8}\cdot 5^{8}\cdot 17^{14} \)	$C_8\times C_2$ (as 16T5)	$[2, 2, 2, 2, 2, 2, 2423618]$ (GRH)
16.0.10504372386022553663859326976000000000000.29	x^16 + 520x^14 + 72280x^12 + 4123600x^10 + 108831775x^8 + 1340170000x^6 + 7634575000x^4 + 17850625000x^2 + 11156640625	\( 2^{48}\cdot 3^{8}\cdot 5^{12}\cdot 13^{12} \)	$C_4\times C_2^2$ (as 16T2)	$[2, 2, 2, 4, 4, 40, 47560]$ (GRH)
16.0.10504372386022553663859326976000000000000.63	x^16 + 520x^14 + 98020x^12 + 8382400x^10 + 342457375x^8 + 7034794000x^6 + 72361490500x^4 + 337876630000x^2 + 509831700625	\( 2^{48}\cdot 3^{8}\cdot 5^{12}\cdot 13^{12} \)	$C_4\times C_2^2$ (as 16T2)	$[2, 2, 2, 2, 4, 4, 808520]$ (GRH)
16.0.10504372386022553663859326976000000000000.66	x^16 + 624x^14 + 148356x^12 + 17010864x^10 + 991343691x^8 + 27910775880x^6 + 314044277040x^4 + 936943605000x^2 + 566850881025	\( 2^{48}\cdot 3^{8}\cdot 5^{12}\cdot 13^{12} \)	$C_4^2$ (as 16T4)	$[2, 2, 4, 8, 408, 4080]$ (GRH)
16.0.10504372386022553663859326976000000000000.111	x^16 + 520x^14 + 109460x^12 + 11965200x^10 + 725842325x^8 + 24327381000x^6 + 426030156500x^4 + 3372768490000x^2 + 8400432722500	\( 2^{48}\cdot 3^{8}\cdot 5^{12}\cdot 13^{12} \)	$C_4\times C_2^2$ (as 16T2)	$[2, 2, 2, 8, 24, 83640]$ (GRH)
16.0.10794315587750478004949812183658374627328.1	x^16 + 748x^14 + 218042x^12 + 32039832x^10 + 2528793520x^8 + 103688499024x^6 + 1891077591304x^4 + 9615126068768x^2 + 9853649041808	\( 2^{44}\cdot 11^{8}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[2, 2, 65218052]$ (GRH)
16.0.23031458444917227413688756615157796306944.9	x^16 + 1144x^14 + 446732x^12 + 71980480x^10 + 5062477134x^8 + 169837942560x^6 + 2708915183832x^4 + 17810338909792x^2 + 24489216000964	\( 2^{62}\cdot 11^{8}\cdot 13^{12} \)	$C_8\times C_2$ (as 16T5)	$[3, 6, 6, 1579782]$ (GRH)
16.0.23462097005834430807696998400000000000000.1	x^16 - 8x^15 + 412x^14 - 1764x^13 + 63806x^12 - 47388x^11 + 4670180x^10 + 16709548x^9 + 173831769x^8 + 1709712244x^7 + 5006084840x^6 + 60097040484x^5 + 247939978456x^4 + 656088145268x^3 + 8329269294588x^2 - 1393015120376x + 75558851901361	\( 2^{40}\cdot 3^{8}\cdot 5^{14}\cdot 41^{2}\cdot 563021^{2} \)	16T1162	$[2, 2, 4, 31435684]$ (GRH)
16.0.24313966763341113270967730176000000000000.20	x^16 + 192x^14 + 17916x^12 + 1013056x^10 + 38045364x^8 + 973354368x^6 + 17044358464x^4 + 186876209664x^2 + 1092493210176	\( 2^{48}\cdot 5^{12}\cdot 29^{12} \)	$C_4^2$ (as 16T4)	$[2, 4, 8, 1927120]$ (GRH)
16.0.28273563576220552539381170176000000000000.19	x^16 + 740x^14 + 210530x^12 + 29844200x^10 + 2305396000x^8 + 99381186000x^6 + 2334546117000x^4 + 27325267380000x^2 + 122963703210000	\( 2^{44}\cdot 5^{12}\cdot 37^{12} \)	$C_4\times C_2^2$ (as 16T2)	$[2, 10, 10, 10, 59170]$ (GRH)
16.0.31633787341870088027340013568000000000000.1	x^16 + 880x^14 + 314600x^12 + 58564000x^10 + 6039412500x^8 + 338207100000x^6 + 9300695250000x^4 + 97435855000000x^2 + 77437145761250	\( 2^{79}\cdot 5^{12}\cdot 11^{8} \)	$C_{16}$ (as 16T1)	$[2, 306799748]$ (GRH)
16.0.31633787341870088027340013568000000000000.2	x^16 + 880x^14 + 314600x^12 + 58564000x^10 + 6039412500x^8 + 338207100000x^6 + 9300695250000x^4 + 97435855000000x^2 + 257498605801250	\( 2^{79}\cdot 5^{12}\cdot 11^{8} \)	$C_{16}$ (as 16T1)	$[2, 90566276]$ (GRH)
16.0.36612584972217083233681138272216794791936.7	x^16 + 32x^14 - 328x^13 + 4356x^12 - 16400x^11 + 294176x^10 - 556944x^9 - 2998808x^8 - 63183296x^7 + 314280384x^6 - 3101634256x^5 + 33449145528x^4 - 43796710368x^3 + 499235025024x^2 - 291056903424x + 1694656660932	\( 2^{48}\cdot 7^{8}\cdot 41^{12} \)	$C_4\times C_2^2$ (as 16T2)	$[2, 4, 4, 8, 24, 24, 840]$ (GRH)
16.0.41077163661333146216005633381666283061248.1	x^16 + 884x^14 + 304538x^12 + 52886184x^10 + 4933055920x^8 + 239047344432x^6 + 5152444842376x^4 + 30960620275936x^2 + 37497509782928	\( 2^{44}\cdot 13^{8}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[2, 2, 2, 2, 2, 2, 2, 2, 2, 528068]$ (GRH)
16.0.41077163661333146216005633381666283061248.2	x^16 + 884x^14 + 304538x^12 + 52886184x^10 + 5041816208x^8 + 267325019312x^6 + 7394864460360x^4 + 83938440196832x^2 + 37497509782928	\( 2^{44}\cdot 13^{8}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[2, 2, 2, 2, 2, 2, 2, 2, 28, 34972]$ (GRH)
16.0.96909452923685986042145406976000000000000.9	x^16 + 288x^14 + 32916x^12 + 1621984x^10 + 17935164x^8 - 768301248x^6 + 6889679824x^4 - 24932542464x^2 + 35571468816	\( 2^{44}\cdot 5^{12}\cdot 41^{12} \)	$C_4^2$ (as 16T4)	$[4, 20, 20, 40, 7400]$ (GRH)
16.0.96909452923685986042145406976000000000000.20	x^16 + 820x^14 + 214430x^12 + 24542600x^10 + 1390691300x^8 + 40249864000x^6 + 576730928000x^4 + 3616974080000x^2 + 7233948160000	\( 2^{44}\cdot 5^{12}\cdot 41^{12} \)	$C_4\times C_2^2$ (as 16T2)	$[2, 2, 2, 2, 2, 2, 52, 53300]$ (GRH)
16.0.96909452923685986042145406976000000000000.22	x^16 - 288x^14 + 39396x^12 - 3310304x^10 + 185330844x^8 - 7050027072x^6 + 177390624784x^4 - 2681723402496x^2 + 18451182794256	\( 2^{44}\cdot 5^{12}\cdot 41^{12} \)	$C_4^2$ (as 16T4)	$[2, 2, 2, 4, 40, 156880]$ (GRH)
16.0.101075408216203634510751650650521600000000.1	x^16 + 1168x^14 - 1716x^13 + 511010x^12 - 1113408x^11 + 112405248x^10 - 267407364x^9 + 13586028503x^8 - 29544777456x^7 + 903868150860x^6 - 1458109683324x^5 + 30925819337576x^4 - 25388246588088x^3 + 490041878843476x^2 - 119034342218376x + 3136651030534129	\( 2^{40}\cdot 3^{4}\cdot 5^{8}\cdot 13^{8}\cdot 1249^{2}\cdot 1511^{2} \)	16T1547	$[2, 2, 2, 2, 2, 31008660]$ (GRH)
16.0.101075408216203634510751650650521600000000.2	x^16 - 4x^15 + 516x^14 - 2936x^13 + 107194x^12 - 641420x^11 + 11627920x^10 - 66371504x^9 + 728118680x^8 - 3717247748x^7 + 27035672060x^6 - 114044064440x^5 + 572310574986x^4 - 1784176112812x^3 + 6210498313016x^2 - 11384486485632x + 25628389555519	\( 2^{40}\cdot 3^{4}\cdot 5^{8}\cdot 13^{8}\cdot 1249^{2}\cdot 1511^{2} \)	16T1547	$[2, 2, 2, 2, 2, 29994700]$ (GRH)
16.0.129057635000142890828743303810252800000000.1	x^16 + 1020x^14 + 405450x^12 + 81243000x^10 + 8743950000x^8 + 488903850000x^6 + 12159082125000x^4 + 84303382500000x^2 + 117810956250000	\( 2^{44}\cdot 3^{8}\cdot 5^{8}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[2, 2, 2, 90180868]$ (GRH)
16.0.138870981735380017471819830544433646927872.1	x^16 + 560x^14 + 118048x^12 + 12132848x^10 + 644338394x^8 + 16821430696x^6 + 178643373076x^4 + 563622068800x^2 + 135973824098	\( 2^{67}\cdot 7^{14}\cdot 193^{4} \)	16T1188	$[2, 2, 2, 2, 2, 2, 2408144]$ (GRH)
16.0.138870981735380017471819830544433646927872.2	x^16 + 784x^14 + 194516x^12 + 21761432x^10 + 1214654686x^8 + 33084444456x^6 + 362054171164x^4 + 467806317104x^2 + 135973824098	\( 2^{67}\cdot 7^{14}\cdot 193^{4} \)	16T1188	$[2, 2, 2, 2, 2, 2, 2583840]$ (GRH)
16.0.138870981735380017471819830544433646927872.3	x^16 + 448x^14 + 73388x^12 + 5577768x^10 + 217602126x^8 + 4457348896x^6 + 45900154748x^4 + 197267724080x^2 + 135973824098	\( 2^{67}\cdot 7^{14}\cdot 193^{4} \)	16T1230	$[2, 2, 2, 2, 2, 4, 1486716]$ (GRH)
16.0.138870981735380017471819830544433646927872.4	x^16 + 560x^14 + 123928x^12 + 13756064x^10 + 800459128x^8 + 23105342400x^6 + 282979163040x^4 + 1397782730624x^2 + 2175581185568	\( 2^{67}\cdot 7^{14}\cdot 193^{4} \)	16T1230	$[2, 2, 2, 2, 2, 4, 933928]$ (GRH)
16.0.238796025103060449638782189092971852333056.22	x^16 + 88x^14 - 208x^13 + 8368x^12 - 20800x^11 + 638672x^10 - 1465568x^9 + 36424504x^8 - 70097664x^7 + 1387466400x^6 - 2216400576x^5 + 35413540288x^4 - 40748008704x^3 + 535089365184x^2 - 352153340032x + 4121239940624	\( 2^{44}\cdot 13^{12}\cdot 17^{12} \)	$C_4^2$ (as 16T4)	$[2, 2, 2, 2, 4, 120, 15600]$ (GRH)
16.0.238796025103060449638782189092971852333056.28	x^16 + 884x^14 + 259454x^12 + 31648968x^10 + 1869438116x^8 + 55955375424x^6 + 811007540096x^4 + 4885387839488x^2 + 9770775678976	\( 2^{44}\cdot 13^{12}\cdot 17^{12} \)	$C_4\times C_2^2$ (as 16T2)	$[2, 2, 2, 4, 4, 8, 312, 1560]$ (GRH)
16.0.260647664583545828058954286602649600000000.3	x^16 + 820x^14 + 243950x^12 + 33333000x^10 + 2178022500x^8 + 67912400000x^6 + 921188000000x^4 + 3765440000000x^2 + 2689600000000	\( 2^{44}\cdot 5^{8}\cdot 41^{14} \)	$C_8\times C_2$ (as 16T5)	$[2, 2, 4, 4, 4, 8, 112712]$ (GRH)
16.0.262686006513622818702917369856000000000000.33	x^16 + 680x^14 + 146540x^12 + 10635200x^10 + 129406975x^8 + 599386000x^6 + 1176663500x^4 + 835210000x^2 + 52200625	\( 2^{48}\cdot 3^{8}\cdot 5^{12}\cdot 17^{12} \)	$C_4\times C_2^2$ (as 16T2)	$[2, 2, 2, 4, 156, 22620]$ (GRH)
16.0.262686006513622818702917369856000000000000.35	x^16 + 680x^14 + 175100x^12 + 21732800x^10 + 1371644575x^8 + 41396938000x^6 + 452278497500x^4 + 10857730000x^2 + 52200625	\( 2^{48}\cdot 3^{8}\cdot 5^{12}\cdot 17^{12} \)	$C_4\times C_2^2$ (as 16T2)	$[2, 2, 2, 2, 10, 30, 45240]$ (GRH)
16.0.262686006513622818702917369856000000000000.56	x^16 + 488x^14 + 71756x^12 + 2873344x^10 + 14583259x^8 - 687937848x^6 + 3865158504x^4 - 409240944x^2 + 89663714721	\( 2^{48}\cdot 3^{8}\cdot 5^{12}\cdot 17^{12} \)	$C_4^2$ (as 16T4)	$[2, 2, 2, 2, 20, 120, 6960]$ (GRH)
16.0.262686006513622818702917369856000000000000.63	x^16 + 328x^14 + 39116x^12 + 2154304x^10 + 64573714x^8 + 1108555112x^6 + 10689323324x^4 + 57170356256x^2 + 244628170801	\( 2^{48}\cdot 3^{8}\cdot 5^{12}\cdot 17^{12} \)	$C_4^2$ (as 16T4)	$[2, 2, 8, 8, 40, 19720]$ (GRH)
16.0.262686006513622818702917369856000000000000.76	x^16 + 680x^14 + 151640x^12 + 13814200x^10 + 615403825x^8 + 14090484000x^6 + 157766256000x^4 + 721621440000x^2 + 1082432160000	\( 2^{48}\cdot 3^{8}\cdot 5^{12}\cdot 17^{12} \)	$C_4\times C_2^2$ (as 16T2)	$[2, 2, 2, 4, 156, 22620]$ (GRH)
16.0.262686006513622818702917369856000000000000.77	x^16 + 680x^14 + 179180x^12 + 23004400x^10 + 1481016625x^8 + 44275956000x^6 + 526005432000x^4 + 1443242880000x^2 + 1082432160000	\( 2^{48}\cdot 3^{8}\cdot 5^{12}\cdot 17^{12} \)	$C_4\times C_2^2$ (as 16T2)	$[2, 2, 2, 4, 580, 7540]$ (GRH)
16.0.262686006513622818702917369856000000000000.91	x^16 + 680x^14 + 146540x^12 + 13640800x^10 + 619088575x^8 + 14709522000x^6 + 184097479500x^4 + 1127533500000x^2 + 2642656640625	\( 2^{48}\cdot 3^{8}\cdot 5^{12}\cdot 17^{12} \)	$C_4\times C_2^2$ (as 16T2)	$[2, 2, 2, 2, 10, 30, 26520]$ (GRH)
16.0.262686006513622818702917369856000000000000.104	x^16 + 816x^14 + 236232x^12 + 30712608x^10 + 2042084115x^8 + 71545582152x^6 + 1241503524972x^4 + 8539740283104x^2 + 8022993935121	\( 2^{48}\cdot 3^{8}\cdot 5^{12}\cdot 17^{12} \)	$C_4^2$ (as 16T4)	$[2, 4, 60, 60, 120, 120]$ (GRH)
16.0.262686006513622818702917369856000000000000.110	x^16 + 680x^14 + 175100x^12 + 21964000x^10 + 1449674575x^8 + 49994688000x^6 + 828516037500x^4 + 5524914150000x^2 + 10152029750625	\( 2^{48}\cdot 3^{8}\cdot 5^{12}\cdot 17^{12} \)	$C_4\times C_2^2$ (as 16T2)	$[2, 2, 2, 4, 348, 29580]$ (GRH)
16.0.262686006513622818702917369856000000000000.126	x^16 + 816x^14 + 272952x^12 + 48191328x^10 + 4808091555x^8 + 267911510472x^6 + 7592642387532x^4 + 82436842630224x^2 + 31301238752001	\( 2^{48}\cdot 3^{8}\cdot 5^{12}\cdot 17^{12} \)	$C_4^2$ (as 16T4)	$[2, 4, 4, 4, 24, 45240]$ (GRH)
16.0.262686006513622818702917369856000000000000.134	x^16 + 816x^14 + 268056x^12 + 45194976x^10 + 4120428771x^8 + 195172069320x^6 + 4151692426860x^4 + 29152604149200x^2 + 50975958665025	\( 2^{48}\cdot 3^{8}\cdot 5^{12}\cdot 17^{12} \)	$C_4^2$ (as 16T4)	$[2, 20, 20, 20, 120, 120]$ (GRH)