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 )

Label	Polynomial	Discriminant	Galois group	Class group
16.0.842099397638721574979305472.1	x^16 + 51x^14 + 1071x^12 + 12104x^10 + 79951x^8 + 310318x^6 + 661946x^4 + 624172x^2 + 76313	\( 2^{16}\cdot 17^{15}\cdot 67^{2} \)	16T1223	$[2, 2, 2, 160]$ (GRH)
16.0.842099397638721574979305472.2	x^16 + 51x^14 + 986x^12 + 9486x^10 + 49980x^8 + 148869x^6 + 248608x^4 + 216410x^2 + 76313	\( 2^{16}\cdot 17^{15}\cdot 67^{2} \)	16T1223	$[2, 2, 2, 132]$ (GRH)
16.0.842099397638721574979305472.3	x^16 + 51x^14 + 969x^12 + 9452x^10 + 52751x^8 + 172652x^6 + 318002x^4 + 284750x^2 + 76313	\( 2^{16}\cdot 17^{15}\cdot 67^{2} \)	16T841	$[2, 2, 2, 148]$ (GRH)
16.0.1173621921239636377600000000.1	x^16 + 36x^14 - 28x^13 + 551x^12 - 812x^11 + 5292x^10 - 7616x^9 + 41399x^8 - 21780x^7 + 237130x^6 + 39612x^5 + 871247x^4 + 452756x^3 + 1745324x^2 + 996728x + 1038209	\( 2^{32}\cdot 5^{8}\cdot 7^{4}\cdot 13^{4}\cdot 101^{2} \)	16T1123	$[2, 614]$ (GRH)
16.0.1230789518357685955321724928.1	x^16 + 51x^14 + 1071x^12 + 11934x^10 + 75735x^8 + 272646x^6 + 520506x^4 + 446148x^2 + 111537	\( 2^{16}\cdot 3^{8}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[2, 2, 386]$ (GRH)
16.0.1473063013603449241600000000.1	x^16 - 8x^15 + 28x^14 - 56x^13 + 154x^12 - 560x^11 + 2224x^10 - 6368x^9 + 19101x^8 - 43784x^7 + 99796x^6 - 167312x^5 + 300592x^4 - 363464x^3 + 519304x^2 - 359648x + 444959	\( 2^{44}\cdot 5^{8}\cdot 11^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[3, 3, 120]$ (GRH)
16.0.1506456681949104716472385536.4	x^16 + 4x^14 + 118x^12 - 24x^11 + 1124x^10 + 840x^9 + 9255x^8 + 2592x^7 + 56524x^6 + 3360x^5 + 222298x^4 - 65208x^3 + 639668x^2 - 261816x + 747358	\( 2^{48}\cdot 3^{8}\cdot 13^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[3, 3, 240]$ (GRH)
16.0.1782866513792016000000000000.3	x^16 - 8x^15 + 54x^14 - 238x^13 + 1036x^12 - 3486x^11 + 11912x^10 - 32324x^9 + 91167x^8 - 201062x^7 + 475958x^6 - 829962x^5 + 1646891x^4 - 2095374x^3 + 3402871x^2 - 2467436x + 3167221	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 19^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[2, 4, 16, 16]$ (GRH)
16.0.1928062066067290240000000000.1	x^16 + 48x^14 + 943x^12 + 9883x^10 + 59836x^8 + 209680x^6 + 396095x^4 + 324200x^2 + 40525	\( 2^{16}\cdot 5^{10}\cdot 29^{4}\cdot 1621^{3} \)	16T1561	$[2, 564]$ (GRH)
16.0.1936190195826058295484765625.1	x^16 - 7x^15 + 71x^14 - 336x^13 + 1790x^12 - 6320x^11 + 23130x^10 - 65833x^9 + 193101x^8 - 470475x^7 + 1146942x^6 - 2228506x^5 + 3869799x^4 - 4706434x^3 + 4766774x^2 - 2465349x + 1254661	\( 5^{8}\cdot 13^{4}\cdot 19^{2}\cdot 29^{8}\cdot 31^{2} \)	$C_2^3.C_2^4.C_2$ (as 16T608)	$[2, 2, 336]$ (GRH)
16.0.1996961573765376000000000000.1	x^16 + 49x^14 + 987x^12 + 10477x^10 + 62235x^8 + 201538x^6 + 317672x^4 + 190896x^2 + 26896	\( 2^{20}\cdot 3^{8}\cdot 5^{12}\cdot 29^{4}\cdot 41^{2} \)	16T781	$[2, 2, 296]$ (GRH)
16.0.2334966419615122175401076753.2	x^16 - x^15 + 52x^14 - 52x^13 + 1123x^12 - 1123x^11 + 13057x^10 - 13057x^9 + 88792x^8 - 88792x^7 + 361438x^6 - 361438x^5 + 881944x^4 - 881944x^3 + 1328092x^2 - 1328092x + 1439629	\( 13^{8}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[2, 2, 2, 226]$ (GRH)
16.0.2359562117249079705600000000.5	x^16 - 8x^15 + 28x^14 - 56x^13 + 140x^12 - 476x^11 + 2262x^10 - 7328x^9 + 23357x^8 - 54124x^7 + 123426x^6 - 206968x^5 + 355430x^4 - 416728x^3 + 541996x^2 - 360952x + 344644	\( 2^{32}\cdot 3^{8}\cdot 5^{8}\cdot 11^{8} \)	$C_2^4$ (as 16T3)	$[2, 2, 8, 48]$ (GRH)
16.0.2434427958226796953600000000.1	x^16 + 62x^14 + 1557x^12 + 20582x^10 + 153773x^8 + 638206x^6 + 1309128x^4 + 943504x^2 + 190096	\( 2^{20}\cdot 5^{8}\cdot 29^{8}\cdot 109^{2} \)	16T984	$[2, 2, 522]$ (GRH)
16.0.2859655432078149808865465089.6	x^16 - 6x^15 + 40x^14 - 152x^13 + 705x^12 - 2142x^11 + 7860x^10 - 19323x^9 + 60042x^8 - 119410x^7 + 322825x^6 - 498338x^5 + 1197274x^4 - 1299079x^3 + 2829154x^2 - 1635129x + 3329789	\( 17^{14}\cdot 19^{8} \)	$C_8\times C_2$ (as 16T5)	$[5, 520]$ (GRH)
16.0.3998912675022684800000000000.1	x^16 + 58x^14 + 1201x^12 + 11385x^10 + 56550x^8 + 153400x^6 + 219250x^4 + 143125x^2 + 28625	\( 2^{16}\cdot 5^{11}\cdot 101^{4}\cdot 229^{3} \)	16T1770	$[2, 2, 432]$ (GRH)
16.0.4039286225255792640000000000.1	x^16 + 42x^14 - 52x^13 + 756x^12 - 1472x^11 + 7508x^10 - 16676x^9 + 46796x^8 - 95208x^7 + 178960x^6 - 290664x^5 + 366131x^4 - 393256x^3 + 422098x^2 - 242772x + 311609	\( 2^{32}\cdot 3^{4}\cdot 5^{10}\cdot 29^{4}\cdot 41^{2} \)	16T799	$[2, 2, 2, 148]$ (GRH)
16.0.4076113365999630907663712256.1	x^16 + 68x^14 - 24x^13 + 1534x^12 - 216x^11 + 14408x^10 + 36x^9 + 70945x^8 - 1920x^7 + 181556x^6 + 5796x^5 + 274372x^4 + 73728x^3 + 163352x^2 + 74100x + 204241	\( 2^{40}\cdot 3^{12}\cdot 17^{8} \)	$(C_2\times D_4):C_4$ (as 16T120)	$[2, 2, 2, 170]$ (GRH)
16.0.4310472359920663782400000000.1	x^16 - 2x^15 + 27x^14 - 44x^13 + 452x^12 - 644x^11 + 5131x^10 - 6202x^9 + 42489x^8 - 42728x^7 + 257239x^6 - 204038x^5 + 1104650x^4 - 624150x^3 + 3070971x^2 - 944592x + 4250681	\( 2^{16}\cdot 5^{8}\cdot 17^{14} \)	$C_8\times C_2$ (as 16T5)	$[40, 80]$ (GRH)
16.0.4361204616626257617397743616.1	x^16 + 48x^14 - 48x^13 + 880x^12 - 1504x^11 + 9104x^10 - 18864x^9 + 63084x^8 - 138624x^7 + 292784x^6 - 507040x^5 + 958208x^4 - 1261120x^3 + 1259280x^2 - 608640x + 222722	\( 2^{72}\cdot 31^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T565)	$[2, 2, 2, 148]$ (GRH)
16.0.4361204616626257617397743616.2	x^16 + 48x^14 - 80x^13 + 808x^12 - 2304x^11 + 8640x^10 - 21136x^9 + 57456x^8 - 120320x^7 + 257456x^6 - 419232x^5 + 588936x^4 - 573184x^3 + 526720x^2 - 330144x + 210878	\( 2^{72}\cdot 31^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T565)	$[2, 2, 2, 144]$ (GRH)
16.0.4442777237269582873600000000.1	x^16 + 55x^14 + 1229x^12 + 14475x^10 + 97712x^8 + 383925x^6 + 845081x^4 + 921785x^2 + 346921	\( 2^{16}\cdot 5^{8}\cdot 19^{2}\cdot 29^{8}\cdot 31^{2} \)	16T860	$[2, 2, 586]$ (GRH)
16.0.4732099199699517440000000000.1	x^16 + 62x^14 + 1543x^12 + 20412x^10 + 157716x^8 + 727930x^6 + 1948310x^4 + 2739600x^2 + 1541025	\( 2^{40}\cdot 5^{10}\cdot 761^{3} \)	16T1398	$[2, 708]$ (GRH)
16.0.5057816008568976000000000000.1	x^16 + 66x^14 + 1734x^12 + 23112x^10 + 164484x^8 + 601344x^6 + 992061x^4 + 544968x^2 + 68121	\( 2^{16}\cdot 3^{12}\cdot 5^{12}\cdot 29^{6} \)	$(C_2\times D_4).C_2^3$ (as 16T322)	$[2, 2, 2, 212]$ (GRH)
16.0.5357808174640126287142780928.1	x^16 + 85x^14 + 2720x^12 + 41531x^10 + 311899x^8 + 1087983x^6 + 1861704x^4 + 1531309x^2 + 485537	\( 2^{16}\cdot 13^{4}\cdot 17^{15} \)	$C_{16} : C_2$ (as 16T22)	$[2, 2, 6, 102]$ (GRH)
16.0.5760649700315136000000000000.4	x^16 - 8x^15 + 24x^14 - 28x^13 + 112x^12 - 672x^11 + 2154x^10 - 4324x^9 + 11499x^8 - 28016x^7 + 70602x^6 - 123900x^5 + 296066x^4 - 413680x^3 + 760490x^2 - 570320x + 1060195	\( 2^{24}\cdot 3^{8}\cdot 5^{12}\cdot 11^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[4, 4, 4, 16]$ (GRH)
16.0.5760649700315136000000000000.5	x^16 - 4x^15 - 4x^14 + 24x^13 + 126x^12 - 368x^11 + 998x^10 - 278x^9 + 5507x^8 - 5336x^7 + 60702x^6 - 65514x^5 + 337471x^4 - 293202x^3 + 975099x^2 - 500742x + 1094031	\( 2^{24}\cdot 3^{8}\cdot 5^{12}\cdot 11^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[2, 2, 2, 8, 24]$ (GRH)
16.0.6191171251706894745600000000.1	x^16 + 44x^14 + 818x^12 + 8172x^10 + 48275x^8 + 174324x^6 + 401870x^4 + 546296x^2 + 421201	\( 2^{36}\cdot 3^{8}\cdot 5^{8}\cdot 7^{4}\cdot 11^{4} \)	$C_2\times Q_8:C_2^2$ (as 16T69)	$[2, 2, 2, 156]$ (GRH)
16.0.7314611834454016000000000000.6	x^16 + 8x^14 - 20x^13 + 194x^12 + 200x^11 + 2992x^10 + 1920x^9 + 23426x^8 + 24320x^7 + 225310x^6 + 384060x^5 + 1509355x^4 + 1962800x^3 + 4390350x^2 + 3039300x + 4174025	\( 2^{32}\cdot 5^{12}\cdot 17^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[3, 24, 24]$ (GRH)
16.0.7478711585794844262400000000.1	x^16 + 70x^14 - 4x^13 + 2168x^12 - 424x^11 + 37270x^10 - 19988x^9 + 363790x^8 - 431008x^7 + 1914202x^6 - 4225052x^5 + 5723512x^4 - 16426168x^3 + 17099594x^2 - 16351756x + 29319889	\( 2^{32}\cdot 5^{8}\cdot 13^{6}\cdot 31^{4} \)	$(C_2\times C_4).C_2^4$ (as 16T205)	$[2, 2, 2, 410]$ (GRH)
16.0.7921586895449647259644140625.1	x^16 - 8x^15 + 82x^14 - 400x^13 + 2138x^12 - 6903x^11 + 23397x^10 - 54193x^9 + 122896x^8 - 215474x^7 + 376822x^6 - 532544x^5 + 741836x^4 - 830694x^3 + 842431x^2 - 553149x + 226071	\( 5^{8}\cdot 19^{8}\cdot 103^{6} \)	$Q_8:C_2^2.D_6$ (as 16T754)	$[2, 2, 404]$ (GRH)
16.0.8979181539709000089600000000.4	x^16 - 12x^14 + 14x^12 - 336x^10 + 3649x^8 + 25788x^6 + 121716x^4 - 112320x^2 + 129600	\( 2^{32}\cdot 3^{8}\cdot 5^{8}\cdot 13^{8} \)	$C_2^4$ (as 16T3)	$[2, 4, 4, 48]$ (GRH)
16.0.8979181539709000089600000000.9	x^16 - 4x^14 - 36x^13 + 104x^12 + 456x^11 + 2346x^10 + 3756x^9 + 14201x^8 + 32856x^7 + 146358x^6 + 348468x^5 + 885224x^4 + 1326168x^3 + 2009246x^2 + 1544424x + 1332841	\( 2^{32}\cdot 3^{8}\cdot 5^{8}\cdot 13^{8} \)	$C_2^4$ (as 16T3)	$[2, 4, 8, 48]$ (GRH)
16.0.8979181539709000089600000000.22	x^16 - 4x^15 + 30x^14 - 56x^13 + 371x^12 - 588x^11 + 3614x^10 - 4076x^9 + 18768x^8 - 39664x^7 + 32116x^6 - 34272x^5 + 43695x^4 - 20088x^3 + 9072x^2 - 14580x + 6561	\( 2^{32}\cdot 3^{8}\cdot 5^{8}\cdot 13^{8} \)	$C_2^4$ (as 16T3)	$[4, 4, 4, 24]$ (GRH)
16.0.9167390055669127803424473088.1	x^16 + 48x^14 + 943x^12 + 9756x^10 + 56971x^8 + 187080x^6 + 325596x^4 + 266256x^2 + 79507	\( 2^{20}\cdot 43^{5}\cdot 2777^{4} \)	16T1666	$[2, 1006]$ (GRH)
16.0.9670824485325868057600000000.1	x^16 + 56x^14 + 1281x^12 + 15589x^10 + 110298x^8 + 463897x^6 + 1129849x^4 + 1453837x^2 + 755161	\( 2^{16}\cdot 5^{8}\cdot 11^{2}\cdot 29^{8}\cdot 79^{2} \)	16T860	$[2, 2, 850]$ (GRH)
16.0.10455582754471936000000000000.1	x^16 - 4x^15 + 52x^14 - 204x^13 + 1478x^12 - 5224x^11 + 25196x^10 - 69432x^9 + 224498x^8 - 402184x^7 + 874144x^6 - 743520x^5 + 1448468x^4 + 35312x^3 + 1960928x^2 + 899376x + 1069756	\( 2^{40}\cdot 5^{12}\cdot 79^{4} \)	$C_2^4:C_2^2.C_2$ (as 16T317)	$[2, 2, 2, 2, 170]$ (GRH)
16.0.11246496478350875289234440192.1	x^16 + 48x^14 + 910x^12 + 8876x^10 + 48315x^8 + 146964x^6 + 231234x^4 + 146812x^2 + 4913	\( 2^{40}\cdot 17^{3}\cdot 113^{6} \)	16T1638	$[2, 2, 344]$ (GRH)
16.0.11463919801532416000000000000.1	x^16 - 6x^15 + 64x^14 - 340x^13 + 1948x^12 - 8352x^11 + 33828x^10 - 113188x^9 + 352922x^8 - 904216x^7 + 2222292x^6 - 4249040x^5 + 8233280x^4 - 10858344x^3 + 16315160x^2 - 11583064x + 13011916	\( 2^{28}\cdot 5^{12}\cdot 41^{2}\cdot 101^{4} \)	16T1161	$[2, 2, 2, 130]$ (GRH)
16.0.11463919801532416000000000000.2	x^16 + 32x^14 - 8x^13 + 482x^12 - 252x^11 + 3724x^10 - 1724x^9 + 15990x^8 + 1164x^7 + 40612x^6 + 86476x^5 + 67782x^4 + 165288x^3 + 3152x^2 - 46464x + 581341	\( 2^{28}\cdot 5^{12}\cdot 41^{2}\cdot 101^{4} \)	16T1161	$[2, 2, 2, 144]$ (GRH)
16.0.11819246862071129702400000000.1	x^16 - 8x^15 + 68x^14 - 336x^13 + 1658x^12 - 5944x^11 + 20368x^10 - 54408x^9 + 136411x^8 - 272568x^7 + 489568x^6 - 690440x^5 + 875066x^4 - 834912x^3 + 406796x^2 - 71320x + 1065439	\( 2^{62}\cdot 3^{8}\cdot 5^{8} \)	$C_8\times C_2$ (as 16T5)	$[42, 42]$ (GRH)
16.0.11819246862071129702400000000.2	x^16 - 8x^15 + 44x^14 - 168x^13 + 630x^12 - 1960x^11 + 5980x^10 - 14984x^9 + 38313x^8 - 79760x^7 + 174976x^6 - 292528x^5 + 551472x^4 - 686544x^3 + 1108840x^2 - 804304x + 1110334	\( 2^{62}\cdot 3^{8}\cdot 5^{8} \)	$C_8\times C_2$ (as 16T5)	$[7, 560]$ (GRH)
16.0.12136551081312256000000000000.1	x^16 - 4x^15 + 52x^14 - 240x^13 + 1440x^12 - 5716x^11 + 22796x^10 - 69300x^9 + 204159x^8 - 453580x^7 + 997404x^6 - 1441988x^5 + 2287980x^4 - 1475320x^3 + 2075448x^2 - 2010692x + 4536281	\( 2^{44}\cdot 5^{12}\cdot 41^{4} \)	$C_2^4.C_2^3$ (as 16T268)	$[2, 2, 2, 382]$ (GRH)
16.0.12518258881906239078400000000.1	x^16 + 38x^14 + 589x^12 + 4916x^10 + 24263x^8 + 72420x^6 + 126683x^4 + 116522x^2 + 41209	\( 2^{40}\cdot 5^{8}\cdot 7^{2}\cdot 29^{6} \)	16T1228	$[2, 924]$ (GRH)
16.0.12518258881906239078400000000.2	x^16 + 52x^14 + 1074x^12 + 11194x^10 + 61958x^8 + 177860x^6 + 253143x^4 + 167678x^2 + 41209	\( 2^{40}\cdot 5^{8}\cdot 7^{2}\cdot 29^{6} \)	16T1228	$[2, 972]$ (GRH)
16.0.12688106723977199129600000000.1	x^16 + 81x^14 + 2406x^12 + 34724x^10 + 267248x^8 + 1121762x^6 + 2480479x^4 + 2537877x^2 + 791381	\( 2^{16}\cdot 5^{8}\cdot 29^{6}\cdot 941^{3} \)	16T1477	$[2, 2056]$ (GRH)
16.0.12882531132048216201998893056.4	x^16 + 12x^14 + 218x^12 - 24x^11 + 2624x^10 + 1008x^9 + 24297x^8 + 5952x^7 + 166628x^6 + 9744x^5 + 766944x^4 - 149280x^3 + 2362076x^2 - 716904x + 3186913	\( 2^{48}\cdot 3^{8}\cdot 17^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[2, 4, 4, 40]$ (GRH)
16.0.13185833497340017023096726049.1	x^16 - 6x^15 + 48x^14 - 194x^13 + 1027x^12 - 3286x^11 + 13568x^10 - 35071x^9 + 121104x^8 - 251532x^7 + 749631x^6 - 1200952x^5 + 3154322x^4 - 3529051x^3 + 8317312x^2 - 4933595x + 10693577	\( 17^{14}\cdot 23^{8} \)	$C_8\times C_2$ (as 16T5)	$[7, 7, 105]$ (GRH)
16.0.14442699262227065915043741696.1	x^16 + 60x^14 + 1344x^12 + 14832x^10 + 87840x^8 + 282744x^6 + 477360x^4 + 374544x^2 + 93636	\( 2^{50}\cdot 3^{12}\cdot 17^{6} \)	$(C_2\times D_4).C_2^3$ (as 16T293)	$[2, 2, 586]$ (GRH)
16.0.14870286751307494933959540736.1	x^16 + 64x^14 + 1592x^12 + 19760x^10 + 132106x^8 + 474032x^6 + 838456x^4 + 582336x^2 + 113569	\( 2^{60}\cdot 337^{4} \)	16T1263	$[2, 1388]$ (GRH)

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