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 86)

Label	Polynomial	Discriminant	Galois group	Class group
16.8.28455852688538757001.1	x^16 - 7x^14 + 31x^12 - 67x^10 + 94x^8 - 144x^6 + 165x^4 - 88x^2 + 16	\( 13^{2}\cdot 17^{14} \)	$C_2^5.C_2.C_2$ (as 16T258)	Trivial
16.4.43104723599206637824.1	x^16 + 8x^14 + 11x^12 - 46x^10 - 117x^8 - 46x^6 + 11x^4 + 8x^2 + 1	\( 2^{8}\cdot 17^{14} \)	$C_2^5.C_2.C_2$ (as 16T258)	Trivial
16.4.371946618869716652161.1	x^16 - 7x^15 + 22x^14 - 48x^13 + 70x^12 - 65x^11 - 9x^10 + 180x^9 - 304x^8 + 180x^7 - 9x^6 - 65x^5 + 70x^4 - 48x^3 + 22x^2 - 7x + 1	\( 17^{14}\cdot 47^{2} \)	$C_2^5.C_2.C_2$ (as 16T258)	Trivial
16.4.755848063425150770281.1	x^16 - 9x^14 - 6x^12 - 12x^10 - 15x^8 - 12x^6 - 6x^4 - 9x^2 + 1	\( 17^{14}\cdot 67^{2} \)	$C_2^5.C_2.C_2$ (as 16T258)	Trivial
16.12.1180591620717411303424.1	x^16 - 16x^14 + 76x^12 - 32x^11 - 160x^10 + 144x^9 + 130x^8 - 208x^7 + 16x^6 + 112x^5 - 60x^4 - 16x^3 + 16x^2 - 1	\( 2^{70} \)	$C_2^5.C_2.C_2$ (as 16T258)	Trivial (GRH)
16.0.1180591620717411303424.6	x^16 + 20x^12 - 16x^11 + 64x^10 - 16x^9 + 110x^8 - 16x^7 + 128x^6 + 48x^5 + 172x^4 + 128x^3 + 96x^2 + 64x + 79	\( 2^{70} \)	$C_2^5.C_2.C_2$ (as 16T258)	Trivial
16.0.1180591620717411303424.7	x^16 + 8x^14 + 16x^12 - 32x^11 - 64x^10 - 48x^9 + 100x^8 + 176x^7 + 16x^6 - 128x^5 - 48x^4 + 32x^3 + 16x^2 + 2	\( 2^{70} \)	$C_2^5.C_2.C_2$ (as 16T258)	Trivial
16.0.1332777259325515104256.1	x^16 + 8x^14 + 28x^12 + 64x^10 + 110x^8 + 128x^6 + 88x^4 + 32x^2 + 4	\( 2^{62}\cdot 17^{2} \)	$C_2^5.C_2.C_2$ (as 16T258)	Trivial
16.8.1332777259325515104256.1	x^16 - 8x^14 + 28x^12 - 64x^10 + 110x^8 - 128x^6 + 88x^4 - 32x^2 + 4	\( 2^{62}\cdot 17^{2} \)	$C_2^5.C_2.C_2$ (as 16T258)	Trivial (GRH)
16.8.1333720764177014758609.1	x^16 - 3x^15 - 3x^14 + 13x^13 + 6x^12 - 39x^11 + 58x^10 - 36x^9 - 329x^8 + 920x^7 - 486x^6 - 1185x^5 + 1842x^4 - 625x^3 - 411x^2 + 343x - 67	\( 17^{14}\cdot 89^{2} \)	$C_2^5.C_2.C_2$ (as 16T258)	Trivial (GRH)
16.12.11034809241396899282944.3	x^16 - 8x^14 + 11x^12 + 46x^10 - 117x^8 + 46x^6 + 11x^4 - 8x^2 + 1	\( 2^{16}\cdot 17^{14} \)	$C_2^5.C_2.C_2$ (as 16T258)	Trivial (GRH)
16.0.43391353747383292788736.1	x^16 + 8x^14 + 20x^12 + 48x^10 + 162x^8 + 352x^6 + 416x^4 + 256x^2 + 64	\( 2^{62}\cdot 97^{2} \)	$C_2^5.C_2.C_2$ (as 16T258)	Trivial
16.16.85297744596832966672384.1	x^16 - 24x^14 - 16x^13 + 180x^12 + 176x^11 - 560x^10 - 608x^9 + 842x^8 + 864x^7 - 696x^6 - 512x^5 + 340x^4 + 80x^3 - 80x^2 + 16x - 1	\( 2^{68}\cdot 17^{2} \)	$C_2^5.C_2.C_2$ (as 16T258)	Trivial (GRH)
16.0.85297744596832966672384.2	x^16 + 8x^14 + 4x^12 + 72x^10 + 38x^8 + 248x^6 + 324x^4 + 56x^2 + 1	\( 2^{68}\cdot 17^{2} \)	$C_2^5.C_2.C_2$ (as 16T258)	$[2]$
16.0.85297744596832966672384.3	x^16 - 8x^14 - 16x^13 + 20x^12 + 48x^11 + 192x^10 + 170x^8 - 160x^7 + 728x^6 + 832x^5 + 1876x^4 + 1360x^3 + 1248x^2 + 432x + 191	\( 2^{68}\cdot 17^{2} \)	$C_2^5.C_2.C_2$ (as 16T258)	$[6]$
16.8.85297744596832966672384.3	x^16 - 8x^14 + 4x^12 - 72x^10 + 38x^8 - 248x^6 + 324x^4 - 56x^2 + 1	\( 2^{68}\cdot 17^{2} \)	$C_2^5.C_2.C_2$ (as 16T258)	Trivial (GRH)
16.0.85297744596832966672384.4	x^16 - 8x^14 - 16x^13 + 52x^12 + 16x^11 + 80x^10 - 112x^9 - 522x^8 - 32x^7 + 952x^6 + 480x^5 - 156x^4 - 80x^3 + 224x^2 - 64x + 47	\( 2^{68}\cdot 17^{2} \)	$C_2^5.C_2.C_2$ (as 16T258)	$[2]$
16.8.85297744596832966672384.4	x^16 - 8x^14 + 28x^12 - 136x^10 + 322x^8 + 184x^6 + 36x^4 - 40x^2 + 1	\( 2^{68}\cdot 17^{2} \)	$C_2^5.C_2.C_2$ (as 16T258)	Trivial (GRH)
16.0.85297744596832966672384.5	x^16 + 8x^14 + 28x^12 + 136x^10 + 322x^8 - 184x^6 + 36x^4 + 40x^2 + 1	\( 2^{68}\cdot 17^{2} \)	$C_2^5.C_2.C_2$ (as 16T258)	$[2]$
16.0.85297744596832966672384.6	x^16 + 24x^14 + 220x^12 + 984x^10 + 2242x^8 + 2392x^6 + 868x^4 + 56x^2 + 1	\( 2^{68}\cdot 17^{2} \)	$C_2^5.C_2.C_2$ (as 16T258)	$[6]$
16.16.193497104236838597191936.1	x^16 - 3x^15 - 24x^14 + 49x^13 + 247x^12 - 255x^11 - 1285x^10 + 318x^9 + 3296x^8 + 934x^7 - 3567x^6 - 2210x^5 + 1005x^4 + 964x^3 + 107x^2 - 19x - 1	\( 2^{8}\cdot 17^{14}\cdot 67^{2} \)	$C_2^5.C_2.C_2$ (as 16T258)	Trivial (GRH)
16.8.812727608637355438705561.1	x^16 - 2x^15 - 7x^14 + 41x^13 - 75x^12 - 117x^11 + 439x^10 - 116x^9 - 130x^8 + 384x^7 - 651x^6 - 5138x^5 + 5719x^4 + 10205x^3 - 11469x^2 - 1177x + 1021	\( 13^{6}\cdot 17^{14} \)	$C_2^5.C_2.C_2$ (as 16T258)	Trivial (GRH)
16.0.1864882761796075978817536.1	x^16 + 28x^14 + 326x^12 + 2044x^10 + 7455x^8 + 15842x^6 + 18229x^4 + 8879x^2 + 169	\( 2^{16}\cdot 13^{2}\cdot 17^{14} \)	$C_2^5.C_2.C_2$ (as 16T258)	$[4, 12]$ (GRH)
16.0.20064561186110330606343169.1	x^16 - 5x^15 + 23x^14 - 61x^13 + 174x^12 - 241x^11 + 76x^10 + 442x^9 - 1071x^8 + 202x^7 + 1571x^6 - 3090x^5 + 3803x^4 + 1100x^3 + 4840x^2 + 477x + 1231	\( 23^{2}\cdot 41^{14} \)	$C_2^5.C_2.C_2$ (as 16T258)	Trivial (GRH)
16.0.36449987334313852008876721.1	x^16 - 8x^15 + 40x^14 - 140x^13 + 426x^12 - 1100x^11 + 2730x^10 - 5950x^9 + 13140x^8 - 24956x^7 + 44006x^6 - 61748x^5 + 74947x^4 - 68134x^3 + 42824x^2 - 16078x + 2579	\( 31^{2}\cdot 41^{14} \)	$C_2^5.C_2.C_2$ (as 16T258)	Trivial (GRH)
16.0.51925112029839400000158409.1	x^16 - 7x^15 + 34x^14 - 93x^13 + 180x^12 - 90x^11 - 387x^10 + 1784x^9 - 3124x^8 + 3665x^7 + 756x^6 - 7452x^5 + 16785x^4 - 19048x^3 + 15546x^2 - 8386x + 2789	\( 37^{2}\cdot 41^{14} \)	$C_2^5.C_2.C_2$ (as 16T258)	Trivial (GRH)
16.0.132031639865501060190322441.1	x^16 - x^15 - 15x^14 - 26x^13 + 94x^12 + 237x^11 + 108x^10 - 240x^9 + 1381x^8 + 2754x^7 - 1616x^6 - 2025x^5 + 4790x^4 + 3456x^3 - 1121x^2 + 777x + 1369	\( 41^{14}\cdot 59^{2} \)	$C_2^5.C_2.C_2$ (as 16T258)	Trivial (GRH)
16.8.137350965859713069141239809.3	x^16 - 24x^14 + 14x^12 + 1310x^10 + 1879x^8 - 5346x^6 - 9049x^4 - 275x^2 + 2209	\( 13^{8}\cdot 17^{14} \)	$C_2^5.C_2.C_2$ (as 16T258)	$[2]$ (GRH)
16.8.137350965859713069141239809.5	x^16 - x^15 - 28x^14 + 18x^13 + 230x^12 - 281x^11 - 817x^10 + 2854x^9 + 1579x^8 - 13429x^7 - 81x^6 + 30021x^5 - 6231x^4 - 33566x^3 + 4716x^2 + 14248x + 2704	\( 13^{8}\cdot 17^{14} \)	$C_2^5.C_2.C_2$ (as 16T258)	$[2]$ (GRH)
16.0.261294446145773284588087129.1	x^16 - 8x^15 + 58x^14 - 266x^13 + 1063x^12 - 3284x^11 + 8897x^10 - 19768x^9 + 38797x^8 - 63552x^7 + 91635x^6 - 108966x^5 + 110621x^4 - 87460x^3 + 53248x^2 - 21016x + 3568	\( 41^{14}\cdot 83^{2} \)	$C_2^5.C_2.C_2$ (as 16T258)	Trivial (GRH)
16.12.1814980849112797822933640641.1	x^16 - 5x^15 - 4x^14 - 98x^13 + 44x^12 + 3687x^11 + x^10 - 18873x^9 - 21082x^8 - 39383x^7 + 187327x^6 + 245190x^5 - 351468x^4 - 378293x^3 + 169642x^2 + 202124x + 28561	\( 17^{14}\cdot 47^{6} \)	$C_2^5.C_2.C_2$ (as 16T258)	Trivial (GRH)
16.12.15231185783695887615175635001.1	x^16 - 59x^14 + 1167x^12 - 10273x^10 + 41550x^8 - 79531x^6 + 226485x^4 - 936062x^2 + 1181569	\( 17^{14}\cdot 67^{6} \)	$C_2^5.C_2.C_2$ (as 16T258)	$[2]$ (GRH)
16.8.83680629612698426645202702769.1	x^16 - 2x^15 + 44x^14 - 146x^13 - 143x^12 - 2446x^11 - 22188x^10 + 11597x^9 - 13152x^8 - 120622x^7 + 704747x^6 - 283428x^5 + 1781862x^4 + 3176965x^3 - 13000438x^2 + 10197497x - 2299691	\( 17^{14}\cdot 89^{6} \)	$C_2^5.C_2.C_2$ (as 16T258)	Trivial (GRH)
16.0.167079624220413079894289014921.1	x^16 + 23x^14 + 90x^12 + 919x^10 + 26122x^8 + 210227x^6 + 530997x^4 + 462636x^2 + 87616	\( 37^{2}\cdot 73^{14} \)	$C_2^5.C_2.C_2$ (as 16T258)	$[89]$ (GRH)
16.0.205157668600814015560481982529.1	x^16 - 5x^15 - x^14 + 30x^13 + 91x^12 - 909x^11 + 552x^10 + 7077x^9 - 9503x^8 - 20450x^7 + 76085x^6 - 137199x^5 + 669739x^4 - 1785584x^3 + 2665644x^2 - 1825008x + 741392	\( 41^{2}\cdot 73^{14} \)	$C_2^5.C_2.C_2$ (as 16T258)	$[89]$ (GRH)
16.0.236725729383493411014646970761.1	x^16 - 4x^15 + 63x^14 - 203x^13 + 1548x^12 - 4029x^11 + 18563x^10 - 38020x^9 + 106997x^8 - 164769x^7 + 254636x^6 - 308607x^5 + 268176x^4 - 207376x^3 + 291264x^2 + 60416x + 99328	\( 11^{2}\cdot 89^{14} \)	$C_2^5.C_2.C_2$ (as 16T258)	$[113]$ (GRH)
16.0.615228915774362553504098556769.1	x^16 + 27x^14 + 360x^12 + 3306x^10 + 13094x^8 + 59400x^6 + 131445x^4 + 115167x^2 + 126736	\( 71^{2}\cdot 73^{14} \)	$C_2^5.C_2.C_2$ (as 16T258)	$[89]$ (GRH)
16.0.4009292695690170390860412175969.10	x^16 - 44x^14 + 1034x^12 - 10558x^10 + 108435x^8 - 452838x^6 + 1250039x^4 + 1349021x^2 + 1723969	\( 17^{14}\cdot 47^{8} \)	$C_2^5.C_2.C_2$ (as 16T258)	$[2, 2, 164]$ (GRH)
16.0.4009292695690170390860412175969.20	x^16 - 31x^14 + 311x^12 + 450x^10 - 47337x^8 + 496586x^6 + 1184138x^4 - 21153144x^2 + 176172529	\( 17^{14}\cdot 47^{8} \)	$C_2^5.C_2.C_2$ (as 16T258)	$[2, 2, 164]$ (GRH)
16.0.5614886866882301027209678756129.3	x^16 - 3x^15 + 49x^14 - 37x^13 + 357x^12 + 1172x^11 - 3371x^10 + 3679x^9 - 7306x^8 - 78822x^7 + 259075x^6 - 811880x^5 + 2060975x^4 - 1675190x^3 - 504530x^2 + 752231x + 364951	\( 23^{6}\cdot 41^{14} \)	$C_2^5.C_2.C_2$ (as 16T258)	$[4, 4]$ (GRH)
16.0.8782328919028941504502068196249.1	x^16 - 5x^15 - 4x^14 + 19x^13 + 263x^12 - 722x^11 + 3439x^10 - 12743x^9 + 43024x^8 - 142003x^7 + 290653x^6 - 578058x^5 + 1271664x^4 - 1898648x^3 + 1821584x^2 - 1194368x + 472832	\( 67^{2}\cdot 89^{14} \)	$C_2^5.C_2.C_2$ (as 16T258)	$[339]$ (GRH)
16.12.12070942770246634791690899381881.1	x^16 - 2x^15 - 73x^14 + 136x^13 + 2119x^12 - 3558x^11 - 31582x^10 + 45135x^9 + 258825x^8 - 279513x^7 - 1159099x^6 + 677252x^5 + 2696351x^4 + 147768x^3 - 2970765x^2 - 1286813x + 252041	\( 43^{2}\cdot 97^{14} \)	$C_2^5.C_2.C_2$ (as 16T258)	$[3]$ (GRH)
16.12.14421153369104822203810274058721.1	x^16 - 8x^15 - 12x^14 + 224x^13 - 361x^12 - 1110x^11 + 964x^10 + 11647x^9 + 75830x^8 - 396280x^7 - 423555x^6 + 2730202x^5 - 776294x^4 - 3495249x^3 + 1402136x^2 + 871865x + 89731	\( 47^{2}\cdot 97^{14} \)	$C_2^5.C_2.C_2$ (as 16T258)	Trivial (GRH)
16.8.24292037884309209334711647701449.3	x^16 - 3x^15 - 28x^14 + 262x^13 - 1567x^12 + 4490x^11 + 5157x^10 - 58674x^9 + 104278x^8 + 14231x^7 - 215949x^6 + 229296x^5 - 206741x^4 + 300039x^3 - 191691x^2 - 37137x + 40067	\( 61^{2}\cdot 97^{14} \)	$C_2^5.C_2.C_2$ (as 16T258)	Trivial (GRH)
16.0.33662328752972862921089838254641.5	x^16 - 8x^15 + 34x^14 - 98x^13 + 58x^12 + 562x^11 + 1282x^10 - 12944x^9 + 129638x^8 - 432418x^7 + 1479504x^6 - 2987980x^5 + 5724119x^4 - 6942578x^3 + 7076656x^2 - 4035828x + 835063	\( 31^{6}\cdot 41^{14} \)	$C_2^5.C_2.C_2$ (as 16T258)	$[2, 2]$ (GRH)
16.0.68372792983010839504523425519489.17	x^16 - 2x^15 - 38x^14 + 6x^13 + 753x^12 - 488x^11 - 5264x^10 + 10007x^9 + 58610x^8 - 5118x^7 - 124811x^6 + 359124x^5 + 1612872x^4 + 2547293x^3 + 4896552x^2 + 6638631x + 11810851	\( 17^{14}\cdot 67^{8} \)	$C_2^5.C_2.C_2$ (as 16T258)	$[2, 4, 12, 12]$ (GRH)
16.0.68372792983010839504523425519489.26	x^16 - 6x^15 - 58x^14 + 150x^13 + 434x^12 + 5860x^11 + 46774x^10 - 30432x^9 - 212804x^8 - 4397396x^7 - 40985220x^6 - 22418086x^5 + 574526983x^4 + 1738422858x^3 + 1971691906x^2 + 1453238270x + 1651813193	\( 17^{14}\cdot 67^{8} \)	$C_2^5.C_2.C_2$ (as 16T258)	$[2, 4, 12, 24]$ (GRH)
16.0.97316019886955839743696883969849.4	x^16 - 4x^15 - 46x^14 + 158x^13 + 973x^12 - 2506x^11 - 5306x^10 + 37333x^9 - 36006x^8 - 509316x^7 + 632479x^6 + 5169794x^5 + 1248320x^4 - 16647515x^3 + 43882564x^2 + 194830937x + 170589721	\( 37^{6}\cdot 41^{14} \)	$C_2^5.C_2.C_2$ (as 16T258)	$[2, 2]$ (GRH)
16.8.662834267162184237456650608633249.1	x^16 - 2x^15 + 44x^14 - 282x^13 - 245x^12 - 2378x^11 - 3624x^10 + 91361x^9 - 38278x^8 + 456426x^7 - 376487x^6 - 2399112x^5 + 2640940x^4 - 6092523x^3 + 10371672x^2 + 487097x - 5309473	\( 17^{14}\cdot 89^{8} \)	$C_2^5.C_2.C_2$ (as 16T258)	$[2]$ (GRH)
16.8.662834267162184237456650608633249.5	x^16 - 4x^15 - 55x^14 + 142x^13 - 520x^12 - 1176x^11 + 39923x^10 + 32681x^9 + 230388x^8 + 68341x^7 - 5271253x^6 - 182955x^5 - 41026485x^4 - 88479221x^3 - 12814472x^2 - 292118775x + 1640683769	\( 17^{14}\cdot 89^{8} \)	$C_2^5.C_2.C_2$ (as 16T258)	$[2]$ (GRH)