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Results (1-50 of 3331 matches)

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Label Polynomial Discriminant Galois group Class group Regulator
6.0.706...744.1 $x^{6} - 84462 x^{4} - 28154 x^{3} + 1809682812 x^{2} - 2430140664 x + 125057534140$ $-\,2^{4}\cdot 3^{8}\cdot 7^{5}\cdot 23^{3}\cdot 2011^{5}$ $S_3\times C_3$ (as 6T5) $[3, 3, 3, 6, 270412464]$ $289.12955934891767$
6.0.157...992.1 $x^{6} - 77226 x^{4} - 25742 x^{3} + 1513899891 x^{2} - 2033592258 x + 100075410073$ $-\,2^{9}\cdot 3^{8}\cdot 11^{3}\cdot 61^{5}\cdot 211^{5}$ $S_3\times C_3$ (as 6T5) $[3, 6, 6, 138560940]$ $285.1255178139885$
6.0.676...728.1 $x^{6} - 660102 x^{4} - 220034 x^{3} + 109503990729 x^{2} - 146383559418 x + 21036679850881$ $-\,2^{6}\cdot 3^{8}\cdot 110017^{5}$ $S_3\times C_3$ (as 6T5) $[3, 5369285196]$ $388.8415933157587$
6.0.115...000.1 $x^{6} + 9042250$ $-\,2^{11}\cdot 3^{6}\cdot 5^{3}\cdot 7^{5}\cdot 5167^{5}$ $D_{6}$ (as 6T3) $[2, 2, 6, 12, 36, 5313384]$ $376.84541505563385$
8.0.914...625.2 $x^{8} - x^{7} + 63506 x^{6} + 86 x^{5} + 1491998473 x^{4} + 247347943 x^{3} + 15311949631364 x^{2} + 16228798468 x + 58002804674614816$ $3^{6}\cdot 5^{4}\cdot 7^{6}\cdot 11^{4}\cdot 13^{6}\cdot 17^{6}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 6692, 20076]$ $1706.950274733737$
8.0.240...664.1 $x^{8} + 426972 x^{6} + 48831720210 x^{4} + 1389985149433608 x^{2} + 1177549085761838244$ $2^{22}\cdot 3^{6}\cdot 7^{6}\cdot 13^{4}\cdot 17^{4}\cdot 23^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 9642, 9642]$ $97.6988467620126$
8.0.279...193.3 $x^{8} - x^{7} + 4711 x^{6} + 653257 x^{5} + 31269320 x^{4} + 1485681448 x^{3} + 62048882160 x^{2} + 1357510184208 x + 31843864896768$ $97^{7}\cdot 389^{6}$ $C_8$ (as 8T1) $[2, 2, 8, 378161320]$ $63308.2675082$
8.0.340...000.6 $x^{8} + 83980 x^{6} + 1763160100 x^{4} + 13408832560500 x^{2} + 33941107418765625$ $2^{24}\cdot 5^{4}\cdot 13^{4}\cdot 17^{6}\cdot 19^{6}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 4972, 19888]$ $1270.5324197061695$
8.0.374...864.2 $x^{8} + 477204 x^{6} + 77263383834 x^{4} + 4527943346207736 x^{2} + 45934368124653836100$ $2^{22}\cdot 3^{6}\cdot 7^{6}\cdot 13^{4}\cdot 19^{4}\cdot 23^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 9242, 9242]$ $97.6988467620126$
8.0.669...384.6 $x^{8} + 99484 x^{6} + 2474266564 x^{4} + 22290667475076 x^{2} + 66839852424062025$ $2^{24}\cdot 7^{4}\cdot 11^{4}\cdot 17^{6}\cdot 19^{6}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 9500, 38000]$ $1270.5324197061695$
8.0.686...000.2 $x^{8} + 251940 x^{6} + 19602191700 x^{4} + 489938112787500 x^{2} + 3781709808078515625$ $2^{24}\cdot 3^{6}\cdot 5^{4}\cdot 13^{4}\cdot 17^{6}\cdot 19^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 6, 6, 3060, 3060]$ $172.36023672349947$
8.0.934...000.2 $x^{8} + 340860 x^{6} + 35972830530 x^{4} + 1370873181740400 x^{2} + 16174932671354979600$ $2^{22}\cdot 3^{4}\cdot 5^{6}\cdot 13^{6}\cdot 19^{4}\cdot 23^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 4, 4, 4, 1132, 2264]$ $186.8030680507958$
8.0.121...544.1 $x^{8} + 361284 x^{6} + 32631532164 x^{4} + 625187524730076 x^{2} + 1527802013559123225$ $2^{24}\cdot 3^{6}\cdot 7^{4}\cdot 11^{6}\cdot 17^{4}\cdot 23^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 7986, 15972]$ $267.19553215080305$
8.0.130...464.1 $x^{8} + 117572 x^{6} + 2728258260 x^{4} + 16667293478108 x^{2} + 7154357106169$ $2^{24}\cdot 7^{4}\cdot 13^{4}\cdot 17^{6}\cdot 19^{6}$ $Q_8$ (as 8T5) $[2, 2, 2, 4, 4, 4, 4, 2460, 9840]$ $1270.5324197061695$
8.0.144...000.1 $x^{8} + 380380 x^{6} + 24764069330 x^{4} + 211679925657200 x^{2} + 309687731236483600$ $2^{22}\cdot 5^{6}\cdot 7^{4}\cdot 11^{4}\cdot 13^{6}\cdot 19^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 2, 4, 2244, 4488]$ $186.8030680507958$
8.0.147...000.1 $x^{8} + 304980 x^{6} + 12310517700 x^{4} + 34763534149500 x^{2} + 12992870888375625$ $2^{24}\cdot 3^{6}\cdot 5^{4}\cdot 13^{4}\cdot 17^{6}\cdot 23^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 13396, 13396]$ $172.36023672349947$
8.0.149...456.2 $x^{8} + 477204 x^{6} + 73196889948 x^{4} + 3557669772020364 x^{2} + 459343681246538361$ $2^{24}\cdot 3^{6}\cdot 7^{6}\cdot 13^{4}\cdot 19^{4}\cdot 23^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 2, 7124, 7124]$ $116.6588945460986$
8.0.189...744.2 $x^{8} + 403788 x^{6} + 55583437140 x^{4} + 2867834850363252 x^{2} + 34423338667622704569$ $2^{24}\cdot 3^{6}\cdot 7^{4}\cdot 11^{6}\cdot 19^{4}\cdot 23^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 2, 7692, 7692]$ $267.19553215080305$
8.0.262...801.1 $x^{8} - 3 x^{7} + 21981 x^{6} - 1506553 x^{5} + 118079394 x^{4} + 985107604 x^{3} + 355307062760 x^{2} - 26402323958592 x + 1918213160448896$ $257^{6}\cdot 457^{6}$ $Q_8$ (as 8T5) $[2, 11738, 457782]$ $13728.847945697138$
8.0.285...609.1 $x^{8} - 3 x^{7} + 22267 x^{6} + 1480071 x^{5} + 192072967 x^{4} + 9542922174 x^{3} + 498102482376 x^{2} + 67067378245728 x + 2198937823749072$ $109^{6}\cdot 1093^{6}$ $Q_8$ (as 8T5) $[2, 7978, 837690]$ $3726.186963165168$
8.0.311...000.1 $x^{8} + 460460 x^{6} + 36288622370 x^{4} + 375493461943600 x^{2} + 664998921102115600$ $2^{22}\cdot 5^{6}\cdot 7^{4}\cdot 11^{4}\cdot 13^{6}\cdot 23^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 2, 2, 2810, 11240]$ $186.8030680507958$
8.0.333...000.1 $x^{8} + 148580 x^{6} + 4357108500 x^{4} + 33638329989500 x^{2} + 18247207305625$ $2^{24}\cdot 5^{4}\cdot 17^{6}\cdot 19^{6}\cdot 23^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 8252, 33008]$ $1270.5324197061695$
8.0.409...896.1 $x^{8} + 249964 x^{6} + 19788025114 x^{4} + 486141211083528 x^{2} + 694730515010581764$ $2^{22}\cdot 11^{6}\cdot 13^{4}\cdot 19^{4}\cdot 23^{6}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 22034, 22034]$ $3884.9926819304123$
8.0.431...089.1 $x^{8} - 3 x^{7} + 23847 x^{6} + 532407 x^{5} + 197582304 x^{4} - 7904851484 x^{3} - 865424215280 x^{2} + 16260831030976 x + 1204643850678016$ $113^{6}\cdot 1129^{6}$ $Q_8$ (as 8T5) $[30, 13650, 40950]$ $16728.476454928634$
8.0.439...761.1 $x^{8} - 3 x^{7} + 23799 x^{6} + 1046123 x^{5} + 226140624 x^{4} + 9336102928 x^{3} - 477385887424 x^{2} + 27296499705552 x + 2242057672443200$ $41^{6}\cdot 3121^{6}$ $Q_8$ (as 8T5) $[2, 16218, 567630]$ $34273.10613739969$
8.0.609...000.2 $x^{8} + 148580 x^{6} + 7160813100 x^{4} + 113995029685500 x^{2} + 181679578561265625$ $2^{24}\cdot 5^{4}\cdot 17^{4}\cdot 19^{6}\cdot 23^{6}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 9236, 27708]$ $4487.275846567552$
8.0.653...121.1 $x^{8} - 3 x^{7} + 25519 x^{6} - 2163893 x^{5} + 332914036 x^{4} - 27627764588 x^{3} + 3187690313664 x^{2} - 178513834233152 x + 5609555648719872$ $73^{6}\cdot 1873^{6}$ $Q_8$ (as 8T5) $[6, 25626, 128130]$ $146361.9407154782$
8.0.672...000.1 $x^{8} + 445740 x^{6} + 26296431300 x^{4} + 108531215626500 x^{2} + 59285176535975625$ $2^{24}\cdot 3^{6}\cdot 5^{4}\cdot 17^{6}\cdot 19^{4}\cdot 23^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 15868, 15868]$ $172.36023672349947$
8.0.701...000.1 $x^{8} + 380380 x^{6} + 23651077450 x^{4} + 432981666117000 x^{2} + 1295697635855122500$ $2^{22}\cdot 5^{4}\cdot 7^{4}\cdot 11^{6}\cdot 13^{6}\cdot 19^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 12378, 12378]$ $1591.6748850822592$
8.0.791...000.4 $x^{8} + 258060 x^{6} + 23308237260 x^{4} + 826726526871300 x^{2} + 8125157813884400025$ $2^{24}\cdot 3^{6}\cdot 5^{6}\cdot 11^{6}\cdot 17^{4}\cdot 23^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 9756, 9756]$ $796.5554198508839$
8.0.796...824.5 $x^{8} + 184756 x^{6} + 9062097044 x^{4} + 147658522577852 x^{2} + 638733854041143289$ $2^{24}\cdot 11^{4}\cdot 13^{4}\cdot 17^{6}\cdot 19^{6}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 5940, 23760]$ $324.03224142238804$
8.0.808...000.3 $x^{8} + 35420 x^{6} + 73425660 x^{4} + 39205512500 x^{2} + 1225172265625$ $2^{24}\cdot 5^{6}\cdot 7^{6}\cdot 11^{6}\cdot 23^{6}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 4, 4, 4, 2600, 7800]$ $5644.537475669447$
8.0.808...000.6 $x^{8} + 35420 x^{6} + 291046140 x^{4} + 127025860500 x^{2} + 12861368375625$ $2^{24}\cdot 5^{6}\cdot 7^{6}\cdot 11^{6}\cdot 23^{6}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 4, 3928, 11784]$ $5644.537475669447$
8.0.808...000.11 $x^{8} + 35420 x^{6} + 361177740 x^{4} + 1143232744500 x^{2} + 1041770838425625$ $2^{24}\cdot 5^{6}\cdot 7^{6}\cdot 11^{6}\cdot 23^{6}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 4, 4, 12, 1848, 1848]$ $5644.537475669447$
8.0.839...976.1 $x^{8} + 352716 x^{6} + 34519962204 x^{4} + 874001353152564 x^{2} + 4563078185370875625$ $2^{24}\cdot 3^{4}\cdot 7^{6}\cdot 13^{6}\cdot 17^{4}\cdot 19^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 7926, 15852]$ $1013.2570710241729$
8.0.100...000.1 $x^{8} + 251940 x^{6} + 2685428460 x^{4} + 5125506410700 x^{2} + 413884642664025$ $2^{24}\cdot 3^{6}\cdot 5^{6}\cdot 13^{6}\cdot 17^{4}\cdot 19^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 868, 1736]$ $380.68772878877894$
8.0.104...384.1 $x^{8} + 223652 x^{6} + 13592450300 x^{4} + 174107870684748 x^{2} + 12367876956855849$ $2^{24}\cdot 11^{6}\cdot 13^{4}\cdot 17^{4}\cdot 23^{6}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 12014, 72084]$ $1162.9100481950197$
8.0.106...000.6 $x^{8} + 213180 x^{6} + 11634831450 x^{4} + 211549791222000 x^{2} + 984764278138410000$ $2^{22}\cdot 3^{6}\cdot 5^{4}\cdot 11^{6}\cdot 17^{6}\cdot 19^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 2, 2, 3812, 7624]$ $957.2936127978904$
8.0.106...000.7 $x^{8} + 213180 x^{6} + 13457520450 x^{4} + 276309931392000 x^{2} + 1679964382863360000$ $2^{22}\cdot 3^{6}\cdot 5^{4}\cdot 11^{6}\cdot 17^{6}\cdot 19^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 2, 2, 3252, 6504]$ $957.2936127978904$
8.0.111...856.1 $x^{8} + 249964 x^{6} + 15620500324 x^{4} + 294243364603188 x^{2} + 254510001690164649$ $2^{24}\cdot 11^{6}\cdot 13^{4}\cdot 19^{6}\cdot 23^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 15522, 31044]$ $3099.8365020414694$
8.0.114...976.2 $x^{8} + 213486 x^{6} + 8278560108 x^{4} + 106921934571816 x^{2} + 395015749495750656$ $2^{12}\cdot 3^{6}\cdot 7^{6}\cdot 13^{6}\cdot 17^{6}\cdot 23^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 4, 4, 1444, 4332]$ $1706.950274733737$
8.0.114...976.3 $x^{8} + 213486 x^{6} + 16380353808 x^{4} + 536706181380096 x^{2} + 6320251991932010496$ $2^{12}\cdot 3^{6}\cdot 7^{6}\cdot 13^{6}\cdot 17^{6}\cdot 23^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 4, 4, 1444, 4332]$ $1706.950274733737$
8.0.119...456.2 $x^{8} + 326876 x^{6} + 31515912978 x^{4} + 1018100399774216 x^{2} + 6691188782492367076$ $2^{22}\cdot 11^{6}\cdot 17^{4}\cdot 19^{4}\cdot 23^{6}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 25394, 25394]$ $3884.9926819304123$
8.0.123...000.2 $x^{8} + 288420 x^{6} + 20040286860 x^{4} + 209025863729100 x^{2} + 48650769782948025$ $2^{24}\cdot 3^{6}\cdot 5^{6}\cdot 11^{6}\cdot 19^{4}\cdot 23^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 4, 4, 4, 8, 568, 1136]$ $796.5554198508839$
8.0.123...000.4 $x^{8} + 288420 x^{6} + 29115133740 x^{4} + 1154186291025900 x^{2} + 12677993456295170025$ $2^{24}\cdot 3^{6}\cdot 5^{6}\cdot 11^{6}\cdot 19^{4}\cdot 23^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 2, 2, 5388, 5388]$ $796.5554198508839$
8.0.123...000.2 $x^{8} + 380380 x^{6} + 43025922940 x^{4} + 1629378375124500 x^{2} + 18348837226870775625$ $2^{24}\cdot 5^{6}\cdot 7^{4}\cdot 11^{4}\cdot 13^{4}\cdot 19^{6}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 11082, 22164]$ $1959.2403433049155$
8.0.128...184.4 $x^{8} + 208012 x^{6} + 7870134020 x^{4} + 85337269756004 x^{2} + 168306430276278889$ $2^{24}\cdot 7^{4}\cdot 17^{6}\cdot 19^{6}\cdot 23^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 4, 4, 1148, 4592]$ $324.03224142238804$
8.0.128...184.5 $x^{8} + 208012 x^{6} + 11487046676 x^{4} + 210730808989316 x^{2} + 1026311722480216249$ $2^{24}\cdot 7^{4}\cdot 17^{6}\cdot 19^{6}\cdot 23^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 4, 4, 1140, 4560]$ $324.03224142238804$
8.0.128...184.6 $x^{8} + 208012 x^{6} + 10817248036 x^{4} + 203764501254132 x^{2} + 1277544644641892025$ $2^{24}\cdot 7^{4}\cdot 17^{6}\cdot 19^{6}\cdot 23^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 7652, 30608]$ $1270.5324197061695$
8.0.141...000.1 $x^{8} + 213180 x^{6} + 8969548500 x^{4} + 99355688734500 x^{2} + 77328720005625$ $2^{24}\cdot 3^{4}\cdot 5^{4}\cdot 11^{4}\cdot 17^{6}\cdot 19^{6}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 680, 1360]$ $1270.5324197061695$
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