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
16.0.39660142577319936000000000000.48	x^16 + 112x^14 + 5145x^12 + 124852x^10 + 1714314x^8 + 13176688x^6 + 51765560x^4 + 79060128x^2 + 5764801	\( 2^{32}\cdot 3^{8}\cdot 5^{12}\cdot 7^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[4, 40, 80]$ (GRH)
16.0.55574059317587781018003767296.2	x^16 - 2x^15 + 56x^14 - 36x^13 + 1298x^12 + 246x^11 + 17477x^10 + 11672x^9 + 149104x^8 + 117458x^7 + 784597x^6 + 588454x^5 + 2445840x^4 + 1448666x^3 + 3937755x^2 + 2216914x + 1884046	\( 2^{16}\cdot 43^{2}\cdot 2777^{6} \)	16T1683	$[4, 2936]$ (GRH)
16.0.80778036035458232960000000000.1	x^16 + 66x^14 + 1741x^12 + 24271x^10 + 195396x^8 + 917220x^6 + 2360880x^4 + 2730825x^2 + 578225	\( 2^{16}\cdot 5^{10}\cdot 101^{5}\cdot 229^{3} \)	16T1642	$[2, 2, 2526]$ (GRH)
16.0.82115019702009856000000000000.4	x^16 - 8x^15 + 60x^14 - 280x^13 + 1364x^12 - 4908x^11 + 18698x^10 - 54220x^9 + 170261x^8 - 399988x^7 + 1060918x^6 - 1966724x^5 + 4429644x^4 - 5961476x^3 + 11232934x^2 - 8526276x + 12941281	\( 2^{32}\cdot 5^{12}\cdot 23^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[3, 30, 120]$ (GRH)
16.0.92144280422466145326820294656.2	x^16 + 86x^14 + 2902x^12 + 49411x^10 + 453495x^8 + 2216251x^6 + 5273394x^4 + 4825962x^2 + 1003941	\( 2^{16}\cdot 3^{5}\cdot 19^{6}\cdot 103^{7} \)	16T1674	$[2, 2, 2996]$ (GRH)
16.0.104894763301569312486400000000.1	x^16 + 76x^14 + 2245x^12 + 33403x^10 + 273118x^8 + 1259002x^6 + 3175017x^4 + 3889260x^2 + 1600189	\( 2^{16}\cdot 5^{8}\cdot 31^{3}\cdot 41^{3}\cdot 1259^{3} \)	16T1871	$[2, 2, 2564]$ (GRH)
16.0.115446638528641004057600000000.1	x^16 + 85x^14 + 2709x^12 + 41896x^10 + 344677x^8 + 1544032x^6 + 3659235x^4 + 4140999x^2 + 1652141	\( 2^{16}\cdot 5^{8}\cdot 1652141^{3} \)	16T1872	$[2, 5530]$ (GRH)
16.0.125015544363803099161600000000.1	x^16 + 87x^14 + 3102x^12 + 58812x^10 + 639588x^8 + 3982276x^6 + 13169203x^4 + 18412939x^2 + 2627641	\( 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 1621^{4} \)	16T1275	$[11400]$ (GRH)
16.0.143607939176308221946269182689.1	x^16 - 6x^15 + 64x^14 - 278x^13 + 1839x^12 - 6330x^11 + 31872x^10 - 88467x^9 + 366078x^8 - 810784x^7 + 2860699x^6 - 4845620x^5 + 14901406x^4 - 17463475x^3 + 47580730x^2 - 29325087x + 72060551	\( 17^{14}\cdot 31^{8} \)	$C_8\times C_2$ (as 16T5)	$[3, 3, 3, 765]$ (GRH)
16.0.144621385476274636765576298496.6	x^16 - 8x^15 + 60x^14 - 280x^13 + 1366x^12 - 4920x^11 + 18684x^10 - 54040x^9 + 169095x^8 - 396536x^7 + 1046676x^6 - 1935192x^5 + 4326842x^4 - 5804824x^3 + 11026220x^2 - 8393144x + 13286974	\( 2^{48}\cdot 3^{8}\cdot 23^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[4, 40, 120]$ (GRH)
16.0.153215432545895383062469140625.2	x^16 - 3x^15 + 82x^14 - 205x^13 + 2798x^12 - 5607x^11 + 52307x^10 - 84419x^9 + 591665x^8 - 830772x^7 + 4121484x^6 - 5423962x^5 + 17725464x^4 - 17389496x^3 + 45696860x^2 - 28773927x + 50639329	\( 5^{8}\cdot 29^{8}\cdot 941^{4} \)	$C_2.C_2\wr C_2^2$ (as 16T394)	$[2, 2, 3248]$ (GRH)
16.0.157685109830355016729600000000.1	x^16 + 94x^14 + 3466x^12 + 64966x^10 + 672448x^8 + 3914768x^6 + 12530639x^4 + 20148678x^2 + 12313081	\( 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 29^{10} \)	$C_4.C_2^2:D_4$ (as 16T305)	$[2, 2, 2, 1654]$ (GRH)
16.0.186947103756597696921600000000.12	x^16 - 8x^15 + 44x^14 - 168x^13 + 684x^12 - 2284x^11 + 9374x^10 - 28984x^9 + 104261x^8 - 263116x^7 + 750810x^6 - 1433520x^5 + 3188158x^4 - 4245960x^3 + 7275852x^2 - 5355144x + 6851556	\( 2^{32}\cdot 3^{8}\cdot 5^{8}\cdot 19^{8} \)	$C_2^4$ (as 16T3)	$[4, 8, 8, 48]$ (GRH)
16.0.236118324143482260684800000000.1	x^16 + 80x^14 + 2600x^12 + 44000x^10 + 412500x^8 + 2100000x^6 + 5250000x^4 + 5000000x^2 + 781250	\( 2^{79}\cdot 5^{8} \)	$C_{16}$ (as 16T1)	$[11458]$ (GRH)
16.0.269708720716852904093994140625.4	x^16 - x^15 - 15x^14 + 47x^13 + 255x^12 - 1999x^11 + 4971x^10 - 6331x^9 - 3164x^8 + 22124x^7 - 12352x^6 - 29264x^5 + 196928x^4 - 293824x^3 + 335616x^2 - 212992x + 65536	\( 3^{8}\cdot 5^{12}\cdot 17^{14} \)	$C_8\times C_2$ (as 16T5)	$[2, 17520]$ (GRH)
16.0.303413777032806400000000000000.1	x^16 - 8x^15 + 116x^14 - 552x^13 + 4636x^12 - 17024x^11 + 97564x^10 - 298656x^9 + 1206042x^8 - 3186136x^7 + 8682804x^6 - 17888024x^5 + 34056956x^4 - 49012432x^3 + 62192636x^2 - 51389008x + 32169161	\( 2^{44}\cdot 5^{14}\cdot 41^{4} \)	$(C_2\times D_4).C_2^3$ (as 16T315)	$[2, 2, 2, 2, 942]$ (GRH)
16.0.307604973831348243481600000000.1	x^16 + 99x^14 + 3773x^12 + 73404x^10 + 804493x^8 + 5096286x^6 + 18172908x^4 + 33258186x^2 + 24019801	\( 2^{16}\cdot 5^{8}\cdot 13^{4}\cdot 29^{10} \)	$OD_{16}:C_2^2$ (as 16T106)	$[2, 2, 2, 2330]$ (GRH)
16.0.315082116699567604562361581568.1	x^16 + 102x^14 + 4284x^12 + 95472x^10 + 1211760x^8 + 8724672x^6 + 33312384x^4 + 57106944x^2 + 28553472	\( 2^{24}\cdot 3^{8}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[2, 2, 4162]$ (GRH)
16.0.361145675909660668917421441024.1	x^16 - 8x^15 + 60x^14 - 280x^13 + 1366x^12 - 4920x^11 + 18684x^10 - 54040x^9 + 169097x^8 - 396544x^7 + 1046352x^6 - 1934192x^5 + 4331632x^4 - 5816080x^3 + 11014984x^2 - 8376112x + 13289086	\( 2^{62}\cdot 23^{8} \)	$C_8\times C_2$ (as 16T5)	$[30840]$ (GRH)
16.0.379165883956039466757862890625.4	x^16 - 6x^15 + 72x^14 - 320x^13 + 2329x^12 - 8230x^11 + 45140x^10 - 128635x^9 + 576030x^8 - 1307274x^7 + 4968321x^6 - 8598346x^5 + 28370042x^4 - 33852655x^3 + 98545822x^2 - 61631729x + 160839449	\( 5^{8}\cdot 7^{8}\cdot 17^{14} \)	$C_8\times C_2$ (as 16T5)	$[24272]$ (GRH)
16.0.379681744835278131840000000000.1	x^16 + 101x^14 + 3757x^12 + 70889x^10 + 762106x^8 + 4851165x^6 + 18017505x^4 + 35937000x^2 + 29648025	\( 2^{16}\cdot 3^{4}\cdot 5^{10}\cdot 11^{4}\cdot 29^{8} \)	$C_2^4.C_2^3$ (as 16T329)	$[2, 2, 2, 2, 1640]$ (GRH)
16.0.396154108207169536000000000000.12	x^16 + 112x^14 + 5096x^12 + 120736x^10 + 1582259x^8 + 11159848x^6 + 37177084x^4 + 39530064x^2 + 5764801	\( 2^{48}\cdot 5^{12}\cdot 7^{8} \)	$C_4^2$ (as 16T4)	$[2, 8, 1360]$ (GRH)
16.0.396154108207169536000000000000.14	x^16 + 64x^14 + 1544x^12 + 18048x^10 + 116179x^8 + 467336x^6 + 1590796x^4 + 4533712x^2 + 7612081	\( 2^{48}\cdot 5^{12}\cdot 7^{8} \)	$C_4^2$ (as 16T4)	$[2, 2, 2, 10, 170]$ (GRH)
16.0.428196565723310037401600000000.1	x^16 + 78x^14 - 60x^13 + 2453x^12 - 3192x^11 + 41698x^10 - 66432x^9 + 417537x^8 - 703088x^7 + 2478520x^6 - 3941164x^5 + 8382885x^4 - 11014656x^3 + 14677804x^2 - 10467112x + 5722919	\( 2^{32}\cdot 5^{8}\cdot 761^{5} \)	16T1163	$[2, 2, 3198]$ (GRH)
16.0.456413827530756096000000000000.7	x^16 - 8x^15 + 40x^14 - 140x^13 + 616x^12 - 2240x^11 + 8426x^10 - 23980x^9 + 78891x^8 - 192320x^7 + 561050x^6 - 1090292x^5 + 2866466x^4 - 4102400x^3 + 9158010x^2 - 7262120x + 14611195	\( 2^{24}\cdot 3^{8}\cdot 5^{12}\cdot 19^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[2, 4, 16, 80]$ (GRH)
16.0.488022614316879794822906640625.2	x^16 - 4x^15 + 44x^14 - 144x^13 + 1097x^12 - 3400x^11 + 18491x^10 - 52652x^9 + 222830x^8 - 586952x^7 + 1901988x^6 - 4222836x^5 + 10063831x^4 - 16091218x^3 + 22963320x^2 - 12168844x + 25104719	\( 5^{8}\cdot 13^{4}\cdot 29^{6}\cdot 271181^{2} \)	16T1177	$[6, 1920]$ (GRH)
16.0.524546382716993536000000000000.5	x^16 + 32x^14 - 20x^13 + 770x^12 + 80x^11 + 14572x^10 + 6960x^9 + 190844x^8 + 143120x^7 + 1964998x^6 + 2116800x^5 + 14613895x^4 + 14908160x^3 + 60000708x^2 + 36634200x + 94703321	\( 2^{32}\cdot 5^{12}\cdot 29^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[4, 16, 240]$ (GRH)
16.0.538148993119091792281600000000.2	x^16 - 8x^15 + 52x^14 - 224x^13 + 1054x^12 - 3776x^11 + 15772x^10 - 48632x^9 + 177651x^8 - 452912x^7 + 1377556x^6 - 2717984x^5 + 6750322x^4 - 9418640x^3 + 18896152x^2 - 14576384x + 23710844	\( 2^{44}\cdot 5^{8}\cdot 23^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[2, 40, 240]$ (GRH)
16.0.577233192643205020288000000000.1	x^16 + 101x^14 + 3986x^12 + 78850x^10 + 834858x^8 + 4716149x^6 + 13451454x^4 + 17742385x^2 + 8260705	\( 2^{16}\cdot 5^{9}\cdot 1652141^{3} \)	16T1888	$[2, 9024]$ (GRH)
16.0.613394685213405714841600000000.1	x^16 + 72x^14 + 2052x^12 + 29918x^10 + 242638x^8 + 1121148x^6 + 2895067x^4 + 3839542x^2 + 2019241	\( 2^{40}\cdot 5^{8}\cdot 7^{4}\cdot 29^{6} \)	$D_4.C_2^3.C_2$ (as 16T264)	$[2, 2, 2740]$ (GRH)
16.0.613394685213405714841600000000.2	x^16 + 96x^14 + 3664x^12 + 71322x^10 + 755974x^8 + 4289544x^6 + 11756031x^4 + 11876718x^2 + 2019241	\( 2^{40}\cdot 5^{8}\cdot 7^{4}\cdot 29^{6} \)	$D_4.C_2^3.C_2$ (as 16T264)	$[2, 2, 3140]$ (GRH)
16.0.672331416948912400000000000000.2	x^16 - 2x^15 + 49x^14 + 18x^13 + 1033x^12 + 1768x^11 + 16241x^10 + 34754x^9 + 169508x^8 + 362188x^7 + 1138799x^6 + 2001274x^5 + 4821683x^4 + 7255146x^3 + 12306656x^2 + 10628644x + 8643461	\( 2^{16}\cdot 5^{14}\cdot 29^{6}\cdot 41^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T646)	$[2, 2, 2, 2, 792]$ (GRH)
16.0.697708606768276588334338277376.4	x^16 + 112x^14 + 5096x^12 + 120736x^10 + 1584660x^8 + 11294304x^6 + 39530064x^4 + 52706752x^2 + 5764801	\( 2^{64}\cdot 3^{8}\cdot 7^{8} \)	$C_8\times C_2$ (as 16T5)	$[2, 2, 2, 2482]$ (GRH)
16.0.697708606768276588334338277376.6	x^16 + 80x^14 + 2600x^12 + 44000x^10 + 412500x^8 + 2100000x^6 + 5250000x^4 + 5000000x^2 + 14371681	\( 2^{64}\cdot 3^{8}\cdot 7^{8} \)	$C_8\times C_2$ (as 16T5)	$[2, 8, 1168]$ (GRH)
16.0.766992641892445428121600000000.5	x^16 - 8x^15 + 84x^14 - 448x^13 + 2650x^12 - 10440x^11 + 42320x^10 - 125624x^9 + 372741x^8 - 835472x^7 + 2002148x^6 - 3512472x^5 + 8820932x^4 - 12559848x^3 + 24807628x^2 - 19004192x + 22430641	\( 2^{48}\cdot 5^{8}\cdot 17^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[4, 4, 4, 312]$ (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)
16.0.835586729888343128721772773376.1	x^16 - 8x^15 + 96x^14 - 400x^13 + 2668x^12 - 6304x^11 + 33752x^10 - 44128x^9 + 246024x^8 - 180656x^7 + 1196888x^6 - 721360x^5 + 3884800x^4 - 2790640x^3 + 7393712x^2 - 5546400x + 6575522	\( 2^{62}\cdot 7^{6}\cdot 17^{2}\cdot 73^{2} \)	16T1086	$[2, 2, 2, 1876]$ (GRH)
16.0.835586729888343128721772773376.2	x^16 + 64x^14 + 2224x^12 - 592x^11 + 41104x^10 - 36672x^9 + 458360x^8 - 600224x^7 + 3274368x^6 - 4535584x^5 + 13795312x^4 - 14357632x^3 + 26002080x^2 - 13908224x + 16366712	\( 2^{62}\cdot 7^{6}\cdot 17^{2}\cdot 73^{2} \)	16T1086	$[2, 2, 2, 1446]$ (GRH)
16.0.879975068812771568896884765625.1	x^16 - 6x^15 + 95x^14 - 420x^13 + 3516x^12 - 12135x^11 + 67230x^10 - 183922x^9 + 717275x^8 - 1612435x^7 + 4288394x^6 - 8562175x^5 + 14806730x^4 - 25438633x^3 + 37525970x^2 - 24641603x + 61523369	\( 5^{10}\cdot 547889^{4} \)	16T1496	$[15795]$ (GRH)
16.0.894321072475734016000000000000.5	x^16 - 8x^15 + 76x^14 - 392x^13 + 2324x^12 - 9212x^11 + 41682x^10 - 132356x^9 + 487381x^8 - 1242420x^7 + 3826142x^6 - 7599516x^5 + 19732124x^4 - 28026260x^3 + 60832030x^2 - 47911596x + 84589601	\( 2^{32}\cdot 5^{12}\cdot 31^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[2, 4, 20, 240]$ (GRH)
16.0.901159687005577446635674386849.4	x^16 - 6x^15 + 80x^14 - 362x^13 + 2875x^12 - 10382x^11 + 61600x^10 - 179463x^9 + 864452x^8 - 2002980x^7 + 8155895x^6 - 14377568x^5 + 50660274x^4 - 61397739x^3 + 190235724x^2 - 120478059x + 333123229	\( 3^{8}\cdot 13^{8}\cdot 17^{14} \)	$C_8\times C_2$ (as 16T5)	$[4, 4, 12, 192]$ (GRH)
16.0.905469581514181342527129976832.1	x^16 + 136x^14 + 7174x^12 + 186524x^10 + 2536859x^8 + 18002218x^6 + 66518569x^4 + 119927639x^2 + 82055753	\( 2^{16}\cdot 13^{6}\cdot 17^{15} \)	$(C_2\times C_8).D_4$ (as 16T306)	$[2, 2, 2, 6, 870]$ (GRH)
16.0.914677666726224826965234765625.1	x^16 - 5x^15 + 79x^14 - 319x^13 + 2147x^12 - 7204x^11 + 33080x^10 - 97972x^9 + 322152x^8 - 825737x^7 + 2256940x^6 - 4470224x^5 + 9705318x^4 - 15875277x^3 + 21559104x^2 - 23181663x + 20355859	\( 5^{8}\cdot 29^{6}\cdot 89^{8} \)	$C_2^2.C_2^2:D_4$ (as 16T225)	$[2, 2, 2692]$ (GRH)
16.0.923833726039318399509778661376.5	x^16 + 36x^14 + 854x^12 - 24x^11 + 14660x^10 + 1512x^9 + 185223x^8 + 22368x^7 + 1694252x^6 + 74400x^5 + 10592826x^4 - 847320x^3 + 41438996x^2 - 6189912x + 74638654	\( 2^{48}\cdot 3^{8}\cdot 29^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[3, 3, 5304]$ (GRH)
16.0.1002674797153076232861572265625.1	x^16 - 3x^15 + 110x^14 - 205x^13 + 4689x^12 - 3878x^11 + 101693x^10 + 19015x^9 + 1258001x^8 + 1498347x^7 + 9604628x^6 + 19095936x^5 + 49007769x^4 + 100830379x^3 + 159770709x^2 + 203130409x + 194676821	\( 5^{12}\cdot 29^{6}\cdot 1621^{4} \)	16T1276	$[2, 2, 6906]$ (GRH)
16.0.1009760059176512400000000000000.1	x^16 + 105x^14 + 4470x^12 + 99540x^10 + 1245555x^8 + 8710200x^6 + 31353750x^4 + 45082575x^2 + 3404025	\( 2^{16}\cdot 3^{12}\cdot 5^{14}\cdot 41^{6} \)	$(C_2\times Q_8).C_2^3$ (as 16T226)	$[2, 2, 2, 2, 1070]$ (GRH)
16.0.1029440097875216457264684597248.2	x^16 + 72x^14 + 1800x^12 + 21488x^10 + 137666x^8 + 487832x^6 + 919020x^4 + 786080x^2 + 167042	\( 2^{67}\cdot 17^{8} \)	$C_4:D_4.D_4$ (as 16T681)	$[2, 2, 2706]$ (GRH)
16.0.1081429148943439468514652520448.1	x^16 + 119x^14 + 5831x^12 + 151606x^10 + 2244935x^8 + 18857454x^6 + 84001386x^4 + 168002772x^2 + 98001617	\( 2^{16}\cdot 7^{8}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[2, 2, 13666]$ (GRH)
16.0.1103480924139689928294400000000.4	x^16 - 2x^15 + 67x^14 - 114x^13 + 2237x^12 - 3254x^11 + 47186x^10 - 57752x^9 + 679239x^8 - 678478x^7 + 6785394x^6 - 5234808x^5 + 45778750x^4 - 24484700x^3 + 190527196x^2 - 53576192x + 375033361	\( 2^{24}\cdot 5^{8}\cdot 17^{14} \)	$C_8\times C_2$ (as 16T5)	$[16, 1968]$ (GRH)
16.0.1219275257885198999941650390625.1	x^16 - 6x^15 - 4x^14 + 76x^13 + 61x^12 - 892x^11 + 2683x^10 - 1492x^9 + 7277x^8 - 27084x^7 + 144027x^6 - 247816x^5 + 668076x^4 - 1011818x^3 + 2445759x^2 - 2485508x + 2784016	\( 5^{12}\cdot 11^{8}\cdot 13^{12} \)	$C_4\times C_2^2$ (as 16T2)	$[10, 1160]$ (GRH)

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