Number field search results

Note: Search results may be incomplete. Given $p$-adic completions contain an unramified field and completions are only searched for ramified primes.

Results (1-50 of 1192 matches)

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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
10.0.1236938287.1	$x^{10} - x^{9} + 2 x^{8} + x^{7} + x^{6} + 3 x^{5} + 2 x^{4} + 2 x^{3} + 2 x^{2} + 2 x + 1$	$10$	[0,5]	$-\,13\cdot 89\cdot 131\cdot 8161$	$4$	$8.11399626109$	$35170.13345155233$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$2.7269076221085293$
10.2.1377579113.1	$x^{10} - x^{9} + x^{8} + x^{7} - 2 x^{6} - x^{4} - 3 x^{3} + x^{2} + 3 x + 1$	$10$	[2,4]	$89\cdot 251\cdot 61667$	$3$	$8.20184683724$	$37115.75289550247$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$2.316987364606681$
10.0.1460182327.1	$x^{10} - x^{9} + 2 x^{8} - 2 x^{7} + 2 x^{6} - 2 x^{5} + 2 x^{4} - 2 x^{3} + x^{2} + 1$	$10$	[0,5]	$-\,59\cdot 89\cdot 487\cdot 571$	$4$	$8.24974849673$	$38212.332132441225$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$3.03230340984159$
10.2.1467445261.1	$x^{10} - x^{9} + 2 x^{8} - 2 x^{7} + 2 x^{6} - x^{5} + x^{4} - x^{2} - x - 1$	$10$	[2,4]	$89\cdot 101\cdot 163249$	$3$	$8.25384275852$	$38307.24815227531$			?	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$2.4486828467857595$
10.2.1494784993.1	$x^{10} - 2 x^{9} + 3 x^{7} - 4 x^{6} + x^{5} + 3 x^{4} - x^{3} - x - 1$	$10$	[2,4]	$13\cdot 17\cdot 89\cdot 75997$	$4$	$8.2690929347$	$38662.44939214276$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$2.4508662630659335$
10.2.1791395293.1	$x^{10} - x^{9} - x^{8} + 3 x^{7} + x^{6} - 3 x^{5} + x^{4} + 2 x^{3} - x - 1$	$10$	[2,4]	$37\cdot 89\cdot 544001$	$3$	$8.42013671152$	$42324.87794430127$			?	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$2.831850455461943$
10.0.1913608936.1	$x^{10} + x^{8} + x^{6} - x^{5} - x^{4} + 3 x^{2} + 3 x + 1$	$10$	[0,5]	$-\,2^{3}\cdot 89\cdot 2687653$	$3$	$8.47589014106$	$43744.81610431115$			?	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$3.8483144252652295$
10.2.1982289613.1	$x^{10} - x^{8} - x^{7} + 2 x^{5} + 2 x^{4} + 2 x^{3} - x^{2} - 2 x - 1$	$10$	[2,4]	$89\cdot 22272917$	$2$	$8.50583023508$	$44522.91110203824$			?	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$3.0173566592714693$
10.0.2004910832.1	$x^{10} - x^{9} + 2 x^{8} - x^{7} + x^{6} + 2 x^{5} - 3 x^{4} + 4 x^{3} - 2 x + 2$	$10$	[0,5]	$-\,2^{4}\cdot 89\cdot 787\cdot 1789$	$4$	$8.51548731271$	$25129.80979036174$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$3.9690436919094463$
10.2.2041086217.1	$x^{10} - 3 x^{7} + x^{6} + x^{5} + 5 x^{4} - 2 x^{3} - x^{2} - 2 x + 1$	$10$	[2,4]	$23\cdot 89\cdot 997111$	$3$	$8.53072878944$	$45178.38218661664$			?	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$2.970660401018618$
10.0.2260206175.1	$x^{10} - x^{9} + 3 x^{8} - 3 x^{7} + 3 x^{6} - 4 x^{5} + 3 x^{4} - 2 x^{3} + 3 x^{2} + x + 1$	$10$	[0,5]	$-\,5^{2}\cdot 89\cdot 1015823$	$3$	$8.61816502078$	$27802.511374982445$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$2.733540004004307$
10.2.2405914661.1	$x^{10} - 3 x^{9} + 2 x^{8} + 4 x^{7} - 8 x^{6} + 3 x^{5} + 6 x^{4} - 6 x^{3} - 2 x^{2} + 3 x + 1$	$10$	[2,4]	$89\cdot 227\cdot 119087$	$3$	$8.67217477521$	$49050.12396518484$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$3.3474475908407824$
10.0.2547692907.1	$x^{10} - 3 x^{9} + 7 x^{8} - 11 x^{7} + 15 x^{6} - 15 x^{5} + 15 x^{4} - 11 x^{3} + 7 x^{2} - 3 x + 1$	$10$	[0,5]	$-\,3\cdot 89\cdot 3089^{2}$	$3$	$8.72197239494$	$908.1646326520319$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$3.24686884473$
10.2.2639387293.1	$x^{10} - 4 x^{9} + 8 x^{8} - 9 x^{7} + 5 x^{6} + 4 x^{5} - 11 x^{4} + 10 x^{3} - 3 x^{2} - x + 1$	$10$	[2,4]	$89\cdot 1429\cdot 20753$	$3$	$8.75286665228$	$51374.96757176592$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$3.505779117636424$
10.0.2725400987.1	$x^{10} - 3 x^{9} + 5 x^{8} - 4 x^{7} + 2 x^{6} + x^{4} - x^{3} + x^{2} + 1$	$10$	[0,5]	$-\,89\cdot 30622483$	$2$	$8.78098106963$	$52205.3731621564$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$3.4595698951756733$
10.2.2854517381.1	$x^{10} - x^{9} + 3 x^{7} - 7 x^{5} + 10 x^{4} - 5 x^{3} - x^{2} + 2 x - 1$	$10$	[2,4]	$89\cdot 32073229$	$2$	$8.82171999902$	$53427.68365744485$			?	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$3.7468652847862187$
10.2.2862439093.1	$x^{10} - x^{9} - x^{7} - x^{6} + 2 x^{5} + x^{4} - x - 1$	$10$	[2,4]	$43\cdot 89\cdot 139\cdot 5381$	$4$	$8.82416510611$	$53501.76719511235$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$3.6641063144013115$
10.2.2969199221.1	$x^{10} - 3 x^{8} - x^{7} + 5 x^{6} + 2 x^{5} - 4 x^{4} - 2 x^{3} + 3 x^{2} + x - 1$	$10$	[2,4]	$89\cdot 151\cdot 220939$	$3$	$8.85653684643$	$54490.358972941256$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$4.032791829788733$
10.0.2976232179.1	$x^{10} - x^{9} + x^{8} + 2 x^{7} - x^{6} - x^{5} + 3 x^{4} - x^{3} - 2 x^{2} + x + 1$	$10$	[0,5]	$-\,3\cdot 89\cdot 11146937$	$3$	$8.85863240671$	$54554.85477022187$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$4.5620433066747195$
10.0.3024769219.1	$x^{10} - 2 x^{9} + 2 x^{8} + x^{7} - 3 x^{6} + x^{5} + 2 x^{4} - 2 x^{3} - x^{2} + x + 1$	$10$	[0,5]	$-\,41\cdot 89\cdot 359\cdot 2309$	$4$	$8.8729743178$	$54997.901950892636$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$4.038735187533842$
10.0.3039896816.1	$x^{10} - x^{9} - x^{8} + 2 x^{7} - x^{5} + 2 x^{3} + x^{2} - 2 x + 1$	$10$	[0,5]	$-\,2^{4}\cdot 11\cdot 89\cdot 194069$	$4$	$8.87740194974$	$30943.618033395844$			?	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$4.956867406769164$
10.0.3042995707.1	$x^{10} - 2 x^{9} + x^{8} + x^{7} - 2 x^{6} + x^{5} + 1$	$10$	[0,5]	$-\,79\cdot 89\cdot 432797$	$3$	$8.87830650312$	$55163.35474751332$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$2.735477482470533$
10.2.3140714681.1	$x^{10} - x^{9} + 2 x^{8} + 2 x^{7} - 3 x^{6} + 6 x^{5} - 2 x^{4} + x^{3} + x^{2} + 1$	$10$	[2,4]	$13\cdot 89\cdot 409\cdot 6637$	$4$	$8.90641337926$	$56042.07955634766$			?	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$3.9465849729207885$
10.4.3412809931.1	$x^{10} - x^{9} - 2 x^{8} + 5 x^{7} + x^{6} - 8 x^{5} + x^{4} + 7 x^{3} - 3 x^{2} - 3 x + 1$	$10$	[4,3]	$-\,89\cdot 103\cdot 372293$	$3$	$8.98072111618$	$58419.25993197791$			?	$S_{10}$ (as 10T45)	trivial	$2$	$6$	$5.099985297480563$
10.2.3435256621.1	$x^{10} - 2 x^{9} + 2 x^{8} - x^{7} - 3 x^{6} + 4 x^{5} - 2 x^{4} - x^{3} + 2 x^{2} + 2 x - 1$	$10$	[2,4]	$89\cdot 38598389$	$2$	$8.98661049459$	$58611.06227496649$			?	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$5.047283288089158$
10.2.3726609157.1	$x^{10} - 2 x^{9} + 3 x^{8} - x^{7} - 4 x^{6} + 8 x^{5} - 9 x^{4} + 6 x^{3} - 3 x^{2} + 3 x - 1$	$10$	[2,4]	$89\cdot 2297\cdot 18229$	$3$	$9.06006648561$	$61045.95938307465$			?	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$5.28391871382183$
10.2.3779323501.1	$x^{10} - x^{9} + 3 x^{8} - x^{7} + 2 x^{6} + 4 x^{5} + 6 x^{3} + 2 x + 1$	$10$	[2,4]	$89\cdot 42464309$	$2$	$9.07280144927$	$61476.20272105296$			?	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$5.331681681422647$
10.2.3819701377.1	$x^{10} - 2 x^{9} + x^{8} + x^{6} - 5 x^{5} + 3 x^{4} + x^{3} + x^{2} - 3 x + 1$	$10$	[2,4]	$89\cdot 3467\cdot 12379$	$3$	$9.08244844044$	$61803.732710897$			?	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$4.662683071350745$
10.2.3880593397.1	$x^{10} - 3 x^{9} + x^{8} + 6 x^{7} - 8 x^{6} + 2 x^{5} + x^{4} + 1$	$10$	[2,4]	$89\cdot 3727\cdot 11699$	$3$	$9.09682445494$	$62294.409034840355$			?	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$4.598612187387434$
10.2.3887902433.1	$x^{10} + x^{8} - 2 x^{7} - 2 x^{6} + 4 x^{3} + x - 1$	$10$	[2,4]	$89\cdot 43684297$	$2$	$9.0985363769$	$62353.046701825246$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$6.964863020735921$
10.4.6121452307.1	$x^{10} - x^{9} - 5 x^{8} + 6 x^{7} + 6 x^{6} - 10 x^{5} + x^{4} + 4 x^{3} - x^{2} + x - 1$	$10$	[4,3]	$-\,89\cdot 4049\cdot 16987$	$3$	$9.52106317904$	$78239.71055033371$			?	$S_{10}$ (as 10T45)	trivial	$2$	$6$	$7.461116842582305$
10.4.6734591819.1	$x^{10} - x^{9} - x^{8} + 4 x^{7} - 5 x^{6} + x^{5} - x^{4} + x^{3} - 2 x^{2} + x + 1$	$10$	[4,3]	$-\,19^{2}\cdot 89\cdot 263\cdot 797$	$4$	$9.6123843534$	$18826.90099299404$			?	$S_{10}$ (as 10T45)	trivial	$2$	$6$	$7.879352960587293$
10.4.7306488019.1	$x^{10} - x^{9} - 2 x^{8} + 3 x^{7} - 2 x^{6} + x^{5} - x^{4} - 2 x^{3} + 5 x^{2} - 4 x + 1$	$10$	[4,3]	$-\,19^{3}\cdot 89\cdot 11969$	$3$	$9.69105074471$	$4498.841962105359$			?	$S_{10}$ (as 10T45)	trivial	$2$	$6$	$8.84630035400866$
10.4.10339269107.1	$x^{10} - 2 x^{9} - x^{8} + 8 x^{7} - 6 x^{6} - 10 x^{5} + 10 x^{4} + 5 x^{3} - 5 x^{2} - 2 x + 1$	$10$	[4,3]	$-\,89\cdot 227\cdot 307\cdot 1667$	$4$	$10.0334198077$	$101682.19660786248$			?	$S_{10}$ (as 10T45)	trivial	$2$	$6$	$10.133964984855343$
10.2.11100455936.1	$x^{10} - 2 x^{9} + 6 x^{6} - 8 x^{5} - 2 x^{3} + 12 x^{2} - 10 x + 2$	$10$	[2,4]	$2^{10}\cdot 89\cdot 349^{2}$	$3$	$10.1049479707$	$397.94033545326164$			?	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$5$	$13.3352624222$
10.4.11404512599.1	$x^{10} - 2 x^{9} - 2 x^{8} + 7 x^{7} - 5 x^{6} + 5 x^{4} - 5 x^{3} + x^{2} - 1$	$10$	[4,3]	$-\,53\cdot 89\cdot 2417747$	$3$	$10.1322914356$	$106791.91261045942$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$6$	$12.165531580178735$
10.4.11713776563.1	$x^{10} - 3 x^{9} + 2 x^{8} + x^{6} - 6 x^{5} + 5 x^{4} + x^{3} - 4 x^{2} + x + 1$	$10$	[4,3]	$-\,89\cdot 131615467$	$2$	$10.1594382169$	$108230.20171375456$			?	$S_{10}$ (as 10T45)	trivial	$2$	$6$	$11.00419334580777$
10.4.13415366851.1	$x^{10} - 4 x^{9} + 6 x^{8} - 11 x^{6} + 9 x^{5} + 4 x^{4} - 9 x^{3} + x^{2} + 3 x - 1$	$10$	[4,3]	$-\,89\cdot 150734459$	$2$	$10.2981747076$	$115824.72469641358$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$6$	$12.053836915812875$
10.0.14270992648.1	$x^{10} + 2 x^{8} - 5 x^{7} + 5 x^{6} - 7 x^{5} + 11 x^{4} - 8 x^{3} + 6 x^{2} - 4 x + 1$	$10$	[0,5]	$-\,2^{3}\cdot 11^{4}\cdot 37^{2}\cdot 89$	$4$	$10.3620436697$	$802.7912845600272$			?	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$10.8801145261$
10.2.15046275208.1	$x^{10} - 3 x^{9} + x^{8} + 6 x^{7} - 3 x^{6} - 8 x^{5} + 3 x^{4} + 6 x^{3} - x^{2} - 3 x - 1$	$10$	[2,4]	$2^{3}\cdot 89\cdot 4597^{2}$	$3$	$10.4170056596$	$1809.1611315745206$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$5$	$16.0833130426$
10.4.15193488239.1	$x^{10} - x^{8} - 4 x^{7} - 6 x^{6} - 5 x^{5} + x^{4} + 11 x^{3} + 12 x^{2} + 7 x + 1$	$10$	[4,3]	$-\,89\cdot 170713351$	$2$	$10.4271530795$	$123261.86855228181$			?	$S_{10}$ (as 10T45)	trivial	$2$	$6$	$13.173297862933424$
10.4.15382321408.1	$x^{10} - x^{9} - x^{8} - 3 x^{6} - x^{5} + 7 x^{4} - 3 x^{2} + 3 x - 1$	$10$	[4,3]	$-\,2^{8}\cdot 59\cdot 89\cdot 11443$	$4$	$10.4400406137$	$28432.968243602874$			?	$S_{10}$ (as 10T45)	trivial	$2$	$6$	$14.634461215941819$
10.0.17401278843.1	$x^{10} - 3 x^{9} + 3 x^{8} + x^{7} - 2 x^{6} - 6 x^{5} + 16 x^{4} - 14 x^{3} + 6 x^{2} + 1$	$10$	[0,5]	$-\,3^{7}\cdot 13^{2}\cdot 23^{2}\cdot 89$	$4$	$10.569589404$	$587.7221536058123$			?	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$9.80527029428$
10.2.17925744896.1	$x^{10} - 3 x^{9} + 5 x^{8} - 3 x^{7} - 4 x^{6} + 10 x^{5} + 4 x^{4} - 3 x^{3} - 5 x^{2} - 3 x - 1$	$10$	[2,4]	$2^{8}\cdot 89\cdot 887^{2}$	$3$	$10.6010216429$	$1123.8718788189337$			?	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$5$	$18.8028929429$
10.6.19299535813.1	$x^{10} - x^{9} - 5 x^{8} + 4 x^{7} + 9 x^{6} - 8 x^{5} - 5 x^{4} + 9 x^{3} - 4 x - 1$	$10$	[6,2]	$61^{2}\cdot 89\cdot 101\cdot 577$	$4$	$10.679592615$	$35290.961171069495$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$7$	$18.781741633198425$
10.0.21200543684.1	$x^{10} - x^{9} + 2 x^{8} + 2 x^{6} - 3 x^{5} + 3 x^{4} - 2 x^{3} + 5 x^{2} + 2 x + 2$	$10$	[0,5]	$-\,2^{2}\cdot 89\cdot 7717^{2}$	$3$	$10.7803956429$	$1657.4836349116692$			?	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$14.1931146954$
10.2.21951585225.1	$x^{10} - x^{9} - 2 x^{8} + x^{7} + x^{6} + 9 x^{5} - x^{4} + x^{3} + 2 x^{2} - x - 1$	$10$	[2,4]	$3^{4}\cdot 5^{2}\cdot 89\cdot 349^{2}$	$4$	$10.8179903278$	$682.5796656801315$			?	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$5$	$12.3796743856$
10.2.22553895929.1	$x^{10} - 5 x^{9} + 10 x^{8} - 10 x^{7} + 3 x^{6} + 5 x^{5} - 3 x^{4} - 4 x^{3} + 3 x^{2} - 1$	$10$	[2,4]	$89\cdot 15919^{2}$	$2$	$10.8473126323$	$1190.2903007249954$			?	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$5$	$19.4217627898$
10.4.25428567627.1	$x^{10} - 3 x^{8} - x^{7} + x^{6} - x^{5} + 3 x^{4} - 2 x^{3} - 5 x^{2} + 3 x + 1$	$10$	[4,3]	$-\,3^{3}\cdot 89\cdot 3253^{2}$	$3$	$10.9782265744$	$1226.529437463592$			?	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$6$	$21.5918248637$
10.2.29232506125.1	$x^{10} - 3 x^{9} + 4 x^{7} - 7 x^{5} + 4 x^{3} - 3 x - 1$	$10$	[2,4]	$5^{3}\cdot 89\cdot 1621^{2}$	$3$	$11.1323436656$	$849.320316488426$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$5$	$19.459542359$

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