Number field search results

Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)

Results (1-50 of 245 matches)

 

Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
7.1.7845011803.1	$x^{7} - 3 x^{6} + 5 x^{5} - 8 x^{4} + 55 x^{3} - 131 x^{2} + 147 x - 18$	$7$	[1,3]	$-\,1987^{3}$	$1$	$25.9127420362$	$44.57577817604534$				$D_{7}$ (as 7T2)	$[13]$	$2$	$3$	$62.2144632168$
7.1.8096384512.1	$x^{7} - 3 x^{6} + 6 x^{5} - 14 x^{4} + 15 x^{3} - x^{2} + 82 x - 134$	$7$	[1,3]	$-\,2^{9}\cdot 251^{3}$	$2$	$26.0297598163$	$44.81071300481616$				$D_{7}$ (as 7T2)	$[13]$	$2$	$3$	$188.290933909$
7.1.56225905191.1	$x^{7} - 2 x^{6} + 7 x^{5} - 20 x^{4} + 103 x^{3} + 112 x^{2} + 111 x + 51$	$7$	[1,3]	$-\,3^{3}\cdot 1277^{3}$	$2$	$34.33248255$	$61.89507250177513$				$D_{7}$ (as 7T2)	$[13]$	$2$	$3$	$100.309169247$
7.1.58575010032.2	$x^{7} - 3 x^{6} + 14 x^{5} - 28 x^{4} + 40 x^{3} - 104 x^{2} + 96 x + 128$	$7$	[1,3]	$-\,2^{4}\cdot 3^{6}\cdot 7^{3}\cdot 11^{4}$	$4$	$34.533820279$	$356.595964631893$			?	$S_7$ (as 7T7)	$[11]$	$2$	$3$	$313.236508718$
7.1.63425726272.1	$x^{7} - x^{6} + 7 x^{5} + x^{4} + 116 x^{3} + 44 x^{2} + 272 x + 96$	$7$	[1,3]	$-\,2^{6}\cdot 997^{3}$	$2$	$34.9285678071$	$63.150613615387776$				$D_{7}$ (as 7T2)	$[13]$	$2$	$3$	$605.69054128$
7.1.207029048256.1	$x^{7} - x^{6} + 15 x^{5} - 17 x^{4} + 23 x^{3} - 9 x^{2} + 5 x + 1$	$7$	[1,3]	$-\,2^{6}\cdot 3^{8}\cdot 79^{3}$	$3$	$41.3595588608$	$69.66280045461589$			✓	$F_7$ (as 7T4)	$[14]$	$2$	$3$	$139.927875569$
7.1.243906324992.1	$x^{7} - 2 x^{6} + 4 x^{5} - 40 x^{4} + 196 x^{3} - 648 x^{2} + 1056 x - 704$	$7$	[1,3]	$-\,2^{9}\cdot 11^{3}\cdot 71^{3}$	$3$	$42.3395416091$	$79.04429138147802$				$D_{7}$ (as 7T2)	$[13]$	$2$	$3$	$980.270503138$
7.1.247200192576.1	$x^{7} - 3 x^{6} + 4 x^{5} + 18 x^{4} - 53 x^{3} + 87 x^{2} - 72 x + 162$	$7$	[1,3]	$-\,2^{6}\cdot 3^{3}\cdot 523^{3}$	$3$	$42.4207556742$	$79.22120928135344$				$D_{7}$ (as 7T2)	$[43]$	$2$	$3$	$745.890002086$
7.1.291698067968.1	$x^{7} - 3 x^{6} - 4 x^{5} + 40 x^{4} - 53 x^{3} - 77 x^{2} + 328 x - 200$	$7$	[1,3]	$-\,2^{9}\cdot 829^{3}$	$2$	$43.4357825597$	$81.43709228600933$				$D_{7}$ (as 7T2)	$[13]$	$2$	$3$	$837.148546529$
7.1.467107946479.1	$x^{7} - 3 x^{6} + 20 x^{5} - 105 x^{4} + 234 x^{3} - 362 x^{2} + 545 x - 425$	$7$	[1,3]	$-\,7759^{3}$	$1$	$46.4579035417$	$88.08518604169488$				$D_{7}$ (as 7T2)	$[29]$	$2$	$3$	$191.142225746$
7.1.489117612439.1	$x^{7} - 3 x^{6} + 3 x^{5} + 16 x^{4} - 80 x^{3} - 15 x^{2} + 90 x - 551$	$7$	[1,3]	$-\,7879^{3}$	$1$	$46.7644882236$	$88.7637313321156$			?	$D_{7}$ (as 7T2)	$[13]$	$2$	$3$	$172.30621252$
7.1.648337611375.1	$x^{7} - x^{6} - 5 x^{5} + 14 x^{4} - 98 x^{3} + 155 x^{2} - 78 x + 417$	$7$	[1,3]	$-\,3^{3}\cdot 5^{3}\cdot 577^{3}$	$3$	$48.6855604498$	$93.03225247192502$				$D_{7}$ (as 7T2)	$[13]$	$2$	$3$	$724.478513887$
7.1.757303595875.1	$x^{7} - 3 x^{6} + 9 x^{5} - 10 x^{4} + 16 x^{3} + 344 x^{2} + 1040 x + 960$	$7$	[1,3]	$-\,5^{3}\cdot 1823^{3}$	$2$	$49.7781296068$	$95.4725091322104$				$D_{7}$ (as 7T2)	$[29]$	$2$	$3$	$560.027438463$
7.1.1722980109375.2	$x^{7} - 3 x^{6} - 9 x^{5} + 120 x^{4} - 480 x^{3} + 1101 x^{2} - 1268 x + 561$	$7$	[1,3]	$-\,3^{8}\cdot 5^{6}\cdot 7^{5}$	$3$	$55.9809208035$	$87.00158931080732$			?	$F_7$ (as 7T4)	$[14]$	$2$	$3$	$234.179096344$
7.3.1865365934656.1	$x^{7} - 2 x^{6} + 10 x^{5} - 2 x^{4} - 16 x^{3} + 16 x^{2} + 4 x - 12$	$7$	[3,2]	$2^{6}\cdot 7^{2}\cdot 29^{6}$	$3$	$56.6195341293$	$85.91296920427573$			?	$\GL(3,2)$ (as 7T5)	$[14]$	$2$	$4$	$751.921635394$
7.1.1962515008000.1	$x^{7} - 2 x^{6} - 15 x^{5} + 8 x^{4} + 258 x^{3} + 768 x^{2} + 400 x - 2560$	$7$	[1,3]	$-\,2^{9}\cdot 5^{3}\cdot 313^{3}$	$3$	$57.0316768515$	$111.89280584559492$				$D_{7}$ (as 7T2)	$[13]$	$2$	$3$	$6316.46962841$
7.1.2843371995463.1	$x^{7} + 13 x^{5} - 71 x^{4} + 25 x^{3} + 192 x^{2} - 50 x - 275$	$7$	[1,3]	$-\,31^{3}\cdot 457^{3}$	$2$	$60.1338621088$	$119.02520741422802$			?	$D_{7}$ (as 7T2)	$[41]$	$2$	$3$	$249.436050594$
7.1.3053042381843.1	$x^{7} + 9 x^{5} - 78 x^{4} - 17 x^{3} + 150 x^{2} + 196 x - 344$	$7$	[1,3]	$-\,89^{3}\cdot 163^{3}$	$2$	$60.7481787082$	$120.44500819876264$				$D_{7}$ (as 7T2)	$[13]$	$2$	$3$	$1108.79168756$
7.1.3372300719936.1	$x^{7} - 3 x^{6} + 10 x^{5} - 50 x^{4} + 89 x^{3} + 189 x^{2} - 868 x + 1144$	$7$	[1,3]	$-\,2^{6}\cdot 23^{3}\cdot 163^{3}$	$3$	$61.6174549827$	$122.45815611873306$				$D_{7}$ (as 7T2)	$[29]$	$2$	$3$	$1224.29784805$
7.1.3437481658688.1	$x^{7} - 14 x^{5} - 42 x^{4} + 329 x^{3} + 854 x^{2} + 336 x - 464$	$7$	[1,3]	$-\,2^{6}\cdot 7^{9}\cdot 11^{3}$	$3$	$61.7861997648$	$93.03473112474836$				$D_{7}$ (as 7T2)	$[43]$	$2$	$3$	$1221.70890946$
7.3.3543369523456.4	$x^{7} - 21 x^{5} - 70 x^{4} + 238 x^{3} + 1092 x^{2} - 2240 x + 736$	$7$	[3,2]	$2^{8}\cdot 7^{12}$	$2$	$62.0545710514$	$112.40858695395093$				$\GL(3,2)$ (as 7T5)	$[14]$	$2$	$4$	$6202.55616215$
7.1.6807097609375.1	$x^{7} - 35 x^{4} + 70 x^{3} - 70 x + 35$	$7$	[1,3]	$-\,5^{6}\cdot 7^{7}\cdot 23^{2}$	$3$	$68.1208851696$	$168.14579623815374$			?	$S_7$ (as 7T7)	$[12]$	$2$	$3$	$377.81137324$
7.1.7143337990979.1	$x^{7} - 3 x^{6} - 30 x^{5} + 230 x^{4} - 471 x^{3} + 269 x^{2} - 268 x + 784$	$7$	[1,3]	$-\,19259^{3}$	$1$	$68.5917052489$	$138.77679921370142$				$D_{7}$ (as 7T2)	$[29]$	$2$	$3$	$462.867364656$
7.1.7597737208179.1	$x^{7} - 3 x^{6} + 17 x^{5} - 76 x^{4} + 99 x^{3} - 839 x^{2} + 5355 x - 6858$	$7$	[1,3]	$-\,3^{3}\cdot 6553^{3}$	$2$	$69.1986708267$	$140.2105559506844$				$D_{7}$ (as 7T2)	$[13]$	$2$	$3$	$4355.69420596$
7.1.8202077997463.1	$x^{7} - 2 x^{6} + 8 x^{5} - 50 x^{4} + 99 x^{3} - 105 x^{2} - 61 x - 21$	$7$	[1,3]	$-\,7^{3}\cdot 43^{3}\cdot 67^{3}$	$3$	$69.9594313411$	$142.01056298740596$			?	$D_{7}$ (as 7T2)	$[13]$	$2$	$3$	$1034.2303067$
7.1.8559770978816.1	$x^{7} - 3 x^{6} - 9 x^{5} - 21 x^{4} + 554 x^{3} - 938 x^{2} - 608 x - 328$	$7$	[1,3]	$-\,2^{9}\cdot 2557^{3}$	$2$	$70.3873463226$	$143.024473430249$				$D_{7}$ (as 7T2)	$[71]$	$2$	$3$	$771.794593404$
7.1.8818423496000.1	$x^{7} - x^{6} + 13 x^{5} - 173 x^{4} + 456 x^{3} - 56 x^{2} - 880 x - 1360$	$7$	[1,3]	$-\,2^{6}\cdot 5^{3}\cdot 1033^{3}$	$3$	$70.6873278346$	$143.7358688706476$				$D_{7}$ (as 7T2)	$[29]$	$2$	$3$	$3354.99302337$
7.1.9333955741375.1	$x^{7} - 3 x^{6} - 3 x^{5} + 108 x^{4} - 119 x^{3} - 1435 x^{2} + 3355 x - 761$	$7$	[1,3]	$-\,5^{3}\cdot 4211^{3}$	$2$	$71.2633991886$	$145.10341140028376$			?	$D_{7}$ (as 7T2)	$[13]$	$2$	$3$	$1059.10373816$
7.1.9397938459727.1	$x^{7} - 32 x^{5} - 70 x^{4} + 532 x^{3} + 750 x^{2} - 1727 x - 5149$	$7$	[1,3]	$-\,47^{3}\cdot 449^{3}$	$2$	$71.3329805795$	$145.26871652217486$			?	$D_{7}$ (as 7T2)	$[43]$	$2$	$3$	$257.907860129$
7.1.9760921523136.1	$x^{7} + 14 x^{5} + 56 x^{3} + 56 x - 286$	$7$	[1,3]	$-\,2^{6}\cdot 3^{3}\cdot 7^{7}\cdot 19^{3}$	$4$	$71.7202089011$	$120.6891109082962$			?	$F_7$ (as 7T4)	$[21]$	$2$	$3$	$976.742858905$
7.1.10354530166336.1	$x^{7} - 3 x^{6} + 38 x^{5} + 30 x^{4} + 33 x^{3} + 1957 x^{2} - 2116 x + 5956$	$7$	[1,3]	$-\,2^{6}\cdot 5449^{3}$	$2$	$72.3276479811$	$147.63468427168462$				$D_{7}$ (as 7T2)	$[29]$	$2$	$3$	$3704.51217264$
7.1.10927746713871.1	$x^{7} - 5 x^{5} - 54 x^{4} - 20 x^{3} - 483 x^{2} - 2259 x - 2187$	$7$	[1,3]	$-\,3^{3}\cdot 13^{3}\cdot 569^{3}$	$3$	$72.8865227406$	$148.96643917339233$				$D_{7}$ (as 7T2)	$[13]$	$2$	$3$	$1842.87873676$
7.1.11328469648579.1	$x^{7} - 3 x^{6} - 26 x^{5} - 64 x^{4} - 170 x^{3} - 222 x^{2} - 41 x - 331$	$7$	[1,3]	$-\,37^{3}\cdot 607^{3}$	$2$	$73.2624784241$	$149.8632710172843$				$D_{7}$ (as 7T2)	$[13]$	$2$	$3$	$2981.13289046$
7.1.12135287592000.1	$x^{7} - 2 x^{6} - 11 x^{5} + 52 x^{4} - 236 x^{3} + 712 x^{2} - 1644 x + 2928$	$7$	[1,3]	$-\,2^{6}\cdot 3^{3}\cdot 5^{3}\cdot 383^{3}$	$4$	$73.986078757$	$151.59155649309758$				$D_{7}$ (as 7T2)	$[13]$	$2$	$3$	$34777.2709499$
7.1.12184465350331.1	$x^{7} - 2 x^{6} - 4 x^{5} - 78 x^{4} - 146 x^{3} - 408 x^{2} - 375 x - 512$	$7$	[1,3]	$-\,23011^{3}$	$1$	$74.0288367775$	$151.69377047196105$				$D_{7}$ (as 7T2)	$[3, 3, 3]$	$2$	$3$	$1175.5942743$
7.1.12280025186911.1	$x^{7} - 2 x^{6} - 18 x^{5} + 81 x^{4} - 233 x^{3} + 523 x^{2} - 462 x + 657$	$7$	[1,3]	$-\,23071^{3}$	$1$	$74.1115008269$	$151.89140857862895$			?	$D_{7}$ (as 7T2)	$[13]$	$2$	$3$	$537.674540048$
7.3.13519130324569.2	$x^{7} - 8 x^{5} - 25 x^{4} - 17 x^{3} + 32 x^{2} + 96 x + 64$	$7$	[3,2]	$631^{2}\cdot 5827^{2}$	$2$	$75.1363029705$	$1917.508018236169$			?	$\GL(3,2)$ (as 7T5)	$[2, 10]$	$2$	$4$	$1257.94702272$
7.1.16253878339691.1	$x^{7} - 3 x^{6} + 2 x^{5} + 65 x^{4} - 61 x^{3} + 216 x^{2} - 616 x + 472$	$7$	[1,3]	$-\,73^{3}\cdot 347^{3}$	$2$	$77.139988912$	$159.15715503865982$				$D_{7}$ (as 7T2)	$[29]$	$2$	$3$	$698.002718806$
7.1.17347830539103.1	$x^{7} - 3 x^{6} + 25 x^{5} + 36 x^{4} + 4 x^{3} + 387 x^{2} - 222 x + 459$	$7$	[1,3]	$-\,3^{3}\cdot 8629^{3}$	$2$	$77.8611365224$	$160.89437529012628$				$D_{7}$ (as 7T2)	$[29]$	$2$	$3$	$1418.87432388$
7.1.23568314355711.1	$x^{7} - x^{6} - 26 x^{5} - 17 x^{4} + 188 x^{3} + 145 x^{2} + 1638 x + 621$	$7$	[1,3]	$-\,3^{3}\cdot 19^{3}\cdot 503^{3}$	$3$	$81.3453338763$	$169.32513103494117$				$D_{7}$ (as 7T2)	$[13]$	$2$	$3$	$1989.77848621$
7.3.23792932840000.4	$x^{7} - 2 x^{6} + 10 x^{5} - 2 x^{4} - 45 x^{3} - 564 x^{2} + 236 x + 1496$	$7$	[3,2]	$2^{6}\cdot 5^{4}\cdot 29^{6}$	$3$	$81.4556361589$	$148.25487895981033$			?	$\GL(3,2)$ (as 7T5)	$[14]$	$2$	$4$	$5038.66055906$
7.1.23917744283328.3	$x^{7} - 196 x^{4} + 196 x^{3} - 784$	$7$	[1,3]	$-\,2^{6}\cdot 3^{3}\cdot 7^{12}$	$3$	$81.5165414782$	$255.12574654918237$				$S_7$ (as 7T7)	$[21]$	$2$	$3$	$3381.37320812$
7.1.24054977590363.1	$x^{7} - 26 x^{5} - x^{4} + 562 x^{3} - 1776 x^{2} + 3256 x - 5680$	$7$	[1,3]	$-\,28867^{3}$	$1$	$81.5831947616$	$169.90291345353674$				$D_{7}$ (as 7T2)	$[13]$	$2$	$3$	$4620.44717595$
7.1.24097501111104.1	$x^{7} - 2 x^{6} + 25 x^{5} - 110 x^{4} - 596 x^{3} - 920 x^{2} - 732 x - 504$	$7$	[1,3]	$-\,2^{6}\cdot 3^{3}\cdot 29^{3}\cdot 83^{3}$	$4$	$81.6037820019$	$169.95293466133498$				$D_{7}$ (as 7T2)	$[13]$	$2$	$3$	$30394.0669288$
7.1.25503049887875.1	$x^{7} - 2 x^{6} + 10 x^{5} - 118 x^{4} + 42 x^{3} + 770 x^{2} - 1127 x - 3724$	$7$	[1,3]	$-\,5^{3}\cdot 7^{3}\cdot 29^{6}$	$3$	$82.2673382104$	$106.05179420024018$				$D_{7}$ (as 7T2)	$[91]$	$2$	$3$	$1093.55124254$
7.1.30755498437691.1	$x^{7} - 3 x^{6} - 8 x^{5} - 52 x^{4} - 68 x^{3} - 136 x^{2} + 4335 x + 19363$	$7$	[1,3]	$-\,17^{3}\cdot 19^{3}\cdot 97^{3}$	$3$	$84.4979377983$	$177.00564962734947$				$D_{7}$ (as 7T2)	$[13]$	$2$	$3$	$2492.41466606$
7.1.31360177055375.1	$x^{7} - 3 x^{6} - 16 x^{5} - 18 x^{4} + 330 x^{3} - 354 x^{2} - 630 x - 185$	$7$	[1,3]	$-\,5^{3}\cdot 7^{3}\cdot 17^{3}\cdot 53^{3}$	$4$	$84.7332905634$	$177.58096744865423$			?	$D_{7}$ (as 7T2)	$[29]$	$2$	$3$	$976.978041323$
7.1.31915344448000.1	$x^{7} - x^{6} - 8 x^{5} - 72 x^{4} + 351 x^{3} - 91 x^{2} - 3380$	$7$	[1,3]	$-\,2^{9}\cdot 5^{3}\cdot 13^{3}\cdot 61^{3}$	$4$	$84.9459721357$	$178.10109488714548$				$D_{7}$ (as 7T2)	$[13]$	$2$	$3$	$30028.7443415$
7.1.35427446793216.3	$x^{7} - 2 x^{6} - 12 x^{5} + 35 x^{4} - 4 x^{3} + 60 x^{2} - 416 x + 484$	$7$	[1,3]	$-\,2^{10}\cdot 3^{6}\cdot 83^{4}$	$3$	$86.2223745754$	$328.23051824779236$			?	$S_7$ (as 7T7)	$[20]$	$2$	$3$	$2146.92826629$
7.3.36299468209216.1	$x^{7} - 2 x^{6} + 22 x^{5} - 48 x^{4} + 136 x^{3} - 236 x^{2} + 130 x - 2$	$7$	[3,2]	$2^{6}\cdot 191^{2}\cdot 3943^{2}$	$3$	$86.5224102288$	$1572.0117314689228$			✓	$\GL(3,2)$ (as 7T5)	$[12]$	$2$	$4$	$1305.75813892$