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 11548 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	Narrow class group	Unit group torsion	Unit group rank	Regulator	Unit signature rank	Max $p$
10.0.433422227.1	$x^{10} - x^{8} - x^{6} - x^{5} + x^{2} + x + 1$	$10$	(0, 5)	$-\,7\cdot 61917461$	$2$	$7.30619262319$	$20818.795041980695$			✓	$S_{10}$ (as 10T45)	trivial	trivial	$2$	$4$	$0.9377049135220212$	$0$	$61917461$
10.0.437865967.1	$x^{10} - x^{9} - x^{8} + 2 x^{7} + 2 x^{6} - 5 x^{5} + 2 x^{4} + 2 x^{3} - x^{2} - x + 1$	$10$	(0, 5)	$-\,7\cdot 11^{2}\cdot 719^{2}$	$3$	$7.31364909208$	$235.29343382253572$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	trivial	$2$	$4$	$0.935373385345$	$0$	$719$
10.0.476322007.1	$x^{10} - x^{9} - 2 x^{8} + 4 x^{7} + x^{6} - 5 x^{5} + x^{4} + 4 x^{3} - x^{2} - 2 x + 1$	$10$	(0, 5)	$-\,7\cdot 73^{2}\cdot 113^{2}$	$3$	$7.37547617968$	$240.29773199096158$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	trivial	$2$	$4$	$1.00383062843$	$0$	$113$
10.0.495413891.1	$x^{10} - x^{9} + 2 x^{8} - 3 x^{7} + 3 x^{6} - 2 x^{5} + 3 x^{4} + 2 x^{2} + x + 1$	$10$	(0, 5)	$-\,7\cdot 70773413$	$2$	$7.40451842215$	$22257.895026259783$			✓	$S_{10}$ (as 10T45)	trivial	trivial	$2$	$4$	$1.015238077698333$	$0$	$70773413$
10.0.568700839.1	$x^{10} - x^{8} - 2 x^{7} + 2 x^{6} - 2 x^{3} + x^{2} + x + 1$	$10$	(0, 5)	$-\,7\cdot 727\cdot 111751$	$3$	$7.50737978998$	$23847.449318533$			✓	$S_{10}$ (as 10T45)	trivial	trivial	$2$	$4$	$1.1287213620180079$	$0$	$111751$
10.0.641018987.1	$x^{10} - x^{9} + x^{8} - 2 x^{7} + 3 x^{6} - 4 x^{5} + 4 x^{4} - 2 x^{3} + 3 x^{2} - 3 x + 1$	$10$	(0, 5)	$-\,7\cdot 29\cdot 1777^{2}$	$3$	$7.59778656583$	$600.60885774354$			?	$C_2 \wr S_5$ (as 10T39)	trivial	trivial	$2$	$4$	$1.18271928937$	$0$	$1777$
10.0.646302475.1	$x^{10} - 2 x^{9} + 3 x^{8} - 4 x^{7} + 6 x^{6} - 6 x^{5} + 5 x^{4} - 5 x^{3} + 3 x^{2} - x + 1$	$10$	(0, 5)	$-\,5^{2}\cdot 7\cdot 13^{3}\cdot 41^{2}$	$4$	$7.60402580304$	$259.34833534029235$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	trivial	$2$	$4$	$1.18911359487$	$0$	$41$
10.0.785499827.1	$x^{10} - x^{9} + 2 x^{8} - 2 x^{7} + 3 x^{6} - 2 x^{5} + 2 x^{4} - 2 x^{3} - x + 1$	$10$	(0, 5)	$-\,7\cdot 112214261$	$2$	$7.75380026181$	$28026.76982814823$			✓	$S_{10}$ (as 10T45)	trivial	trivial	$2$	$4$	$1.3488181427185912$	$0$	$112214261$
10.0.797340467.1	$x^{10} - 3 x^{9} + 5 x^{8} - 8 x^{7} + 11 x^{6} - 12 x^{5} + 12 x^{4} - 10 x^{3} + 7 x^{2} - 3 x + 1$	$10$	(0, 5)	$-\,7\cdot 11\cdot 10355071$	$3$	$7.76540982051$	$28237.217763087072$			✓	$S_{10}$ (as 10T45)	trivial	trivial	$2$	$4$	$1.3816493010134239$	$0$	$10355071$
10.0.814993991.1	$x^{10} - 3 x^{9} + 3 x^{8} + x^{7} - 3 x^{6} + 3 x^{4} - x^{3} - x^{2} + 1$	$10$	(0, 5)	$-\,7\cdot 17\cdot 2617^{2}$	$3$	$7.78243389949$	$558.0528648793052$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	trivial	$2$	$4$	$1.36394459768$	$0$	$2617$
10.0.872757991.1	$x^{10} - 2 x^{9} + 3 x^{8} - 2 x^{7} + x^{5} + x^{4} - 3 x^{3} + 4 x^{2} - 3 x + 1$	$10$	(0, 5)	$-\,7\cdot 2467\cdot 50539$	$3$	$7.8359089926$	$29542.47773968866$			✓	$S_{10}$ (as 10T45)	trivial	trivial	$2$	$4$	$1.4638456820382733$	$0$	$50539$
10.0.897615691.1	$x^{10} - 3 x^{9} + 5 x^{8} - 7 x^{7} + 9 x^{6} - 9 x^{5} + 7 x^{4} - 6 x^{3} + 4 x^{2} - x + 1$	$10$	(0, 5)	$-\,7\cdot 17\cdot 7542989$	$3$	$7.85794606466$	$29960.23516262848$			✓	$S_{10}$ (as 10T45)	trivial	trivial	$2$	$4$	$1.4467331423294614$	$0$	$7542989$
10.0.935128663.1	$x^{10} - x^{9} - 2 x^{8} + 3 x^{7} + 2 x^{6} - 4 x^{5} - x^{4} + 4 x^{3} - 2 x + 1$	$10$	(0, 5)	$-\,7\cdot 1283\cdot 104123$	$3$	$7.8901841048$	$30579.87349548719$			✓	$S_{10}$ (as 10T45)	trivial	trivial	$2$	$4$	$1.4942994756217878$	$0$	$104123$
10.0.1014444235.1	$x^{10} - 2 x^{9} + 2 x^{8} - 2 x^{7} + x^{6} - x^{5} + x^{3} - x^{2} + x + 1$	$10$	(0, 5)	$-\,5\cdot 7\cdot 28984121$	$3$	$7.95468190966$	$31850.341206963545$			✓	$S_{10}$ (as 10T45)	trivial	trivial	$2$	$4$	$1.7047478448355062$	$0$	$28984121$
10.0.1072212827.1	$x^{10} - 2 x^{9} + 5 x^{8} - 8 x^{7} + 12 x^{6} - 16 x^{5} + 17 x^{4} - 15 x^{3} + 10 x^{2} - 4 x + 1$	$10$	(0, 5)	$-\,7\cdot 23\cdot 137\cdot 48611$	$4$	$7.99886007781$	$32744.661045733854$			✓	$S_{10}$ (as 10T45)	trivial	trivial	$2$	$4$	$1.6191941416208484$	$0$	$48611$
10.0.1146484927.1	$x^{10} - 3 x^{7} + x^{6} - x^{5} + 2 x^{4} - 2 x^{3} + 2 x^{2} + 1$	$10$	(0, 5)	$-\,7\cdot 29\cdot 41\cdot 139\cdot 991$	$5$	$8.05261313115$	$33859.78332771786$			✓	$S_{10}$ (as 10T45)	trivial	trivial	$2$	$4$	$1.7479493750775383$	$0$	$991$
10.0.1158178091.1	$x^{10} + 3 x^{6} - x^{5} - 2 x^{4} - 2 x^{3} + 3 x^{2} + 2 x + 1$	$10$	(0, 5)	$-\,7\cdot 17\cdot 509\cdot 19121$	$4$	$8.06078865394$	$34032.01567641858$			?	$S_{10}$ (as 10T45)	trivial	trivial	$2$	$4$	$1.8411290144978567$	$0$	$19121$
10.0.1189402459.1	$x^{10} - 3 x^{9} + 5 x^{8} - 5 x^{7} + 4 x^{6} - 3 x^{5} + 5 x^{4} - 8 x^{3} + 8 x^{2} - 4 x + 1$	$10$	(0, 5)	$-\,7\cdot 169914637$	$2$	$8.08226122747$	$34487.714609698334$			✓	$S_{10}$ (as 10T45)	trivial	trivial	$2$	$4$	$1.76041043142367$	$0$	$169914637$
10.0.1207027759.1	$x^{10} - 3 x^{9} + 5 x^{8} - 9 x^{7} + 13 x^{6} - 13 x^{5} + 12 x^{4} - 9 x^{3} + 5 x^{2} - 2 x + 1$	$10$	(0, 5)	$-\,7\cdot 43\cdot 1523\cdot 2633$	$4$	$8.09415889698$	$34742.305032913406$			✓	$S_{10}$ (as 10T45)	trivial	trivial	$2$	$4$	$1.7809086473683662$	$0$	$2633$
10.0.1215960907.1	$x^{10} - 2 x^{9} + 3 x^{8} - x^{7} - 3 x^{6} + 5 x^{5} - 4 x^{4} + 3 x^{2} - 2 x + 1$	$10$	(0, 5)	$-\,7\cdot 173708701$	$2$	$8.10012948305$	$34870.63100948992$			✓	$S_{10}$ (as 10T45)	trivial	trivial	$2$	$4$	$1.8930399594142264$	$0$	$173708701$
10.2.1295328013.1	$x^{10} - 3 x^{9} + 4 x^{8} - 4 x^{7} + 4 x^{6} - 3 x^{5} + 2 x^{4} - 4 x^{3} + 3 x^{2} - 2 x + 1$	$10$	(2, 4)	$7\cdot 137\cdot 443\cdot 3049$	$4$	$8.15150831286$	$35990.66563707873$			?	$S_{10}$ (as 10T45)	trivial	trivial	$2$	$5$	$2.304641200245765$	$2$	$3049$
10.0.1331681407.1	$x^{10} - x^{9} - 2 x^{8} + 4 x^{7} - 4 x^{5} + 4 x^{4} + 2 x^{3} - 3 x^{2} - x + 1$	$10$	(0, 5)	$-\,7\cdot 190240201$	$2$	$8.17410164032$	$36492.21022355319$			✓	$S_{10}$ (as 10T45)	trivial	trivial	$2$	$4$	$1.9389120561146413$	$0$	$190240201$
10.0.1348350283.1	$x^{10} - 3 x^{9} + 2 x^{8} + 2 x^{7} - 2 x^{6} - 2 x^{5} + 7 x^{4} - 10 x^{3} + 6 x^{2} - x + 1$	$10$	(0, 5)	$-\,7\cdot 61\cdot 1777^{2}$	$3$	$8.18427611894$	$871.0792156859214$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	trivial	$2$	$4$	$1.85292078235$	$0$	$1777$
10.0.1389636451.1	$x^{10} - x^{9} - 2 x^{8} + 3 x^{7} + 2 x^{6} - 4 x^{5} + 2 x^{3} + x^{2} - 2 x + 1$	$10$	(0, 5)	$-\,7\cdot 47\cdot 163\cdot 25913$	$4$	$8.20899743073$	$37277.8278739521$			✓	$S_{10}$ (as 10T45)	trivial	trivial	$2$	$4$	$2.0701842282542615$	$0$	$25913$
10.2.1410887989.1	$x^{10} - x^{9} - x^{8} + 3 x^{6} + 2 x^{5} - x^{4} - 2 x^{3} - x^{2} + 2 x - 1$	$10$	(2, 4)	$7\cdot 97\cdot 2077891$	$3$	$8.22146578286$	$37561.78894834483$			?	$S_{10}$ (as 10T45)	trivial	trivial	$2$	$5$	$2.4318463314187335$	$2$	$2077891$
10.0.1414764827.1	$x^{10} - x^{9} + x^{8} - 3 x^{4} + x^{2} + x + 1$	$10$	(0, 5)	$-\,7\cdot 283\cdot 431\cdot 1657$	$4$	$8.22372208868$	$37613.359687749245$			✓	$S_{10}$ (as 10T45)	trivial	trivial	$2$	$4$	$1.961618210555986$	$0$	$1657$
10.0.1418344627.1	$x^{10} - x^{9} + x^{8} - 3 x^{7} + 4 x^{6} - 3 x^{5} + 5 x^{4} - 4 x^{3} + 2 x^{2} - 2 x + 1$	$10$	(0, 5)	$-\,7\cdot 179\cdot 1131959$	$3$	$8.22580058347$	$37660.91643866357$			✓	$S_{10}$ (as 10T45)	trivial	trivial	$2$	$4$	$2.401227218946458$	$0$	$1131959$
10.0.1451652419.1	$x^{10} - 2 x^{9} + 2 x^{8} - 2 x^{7} + 2 x^{6} - x^{3} + 1$	$10$	(0, 5)	$-\,7\cdot 10631\cdot 19507$	$3$	$8.2449165476$	$38100.55667572326$			✓	$S_{10}$ (as 10T45)	trivial	trivial	$2$	$4$	$1.9740857429548155$	$0$	$19507$
10.0.1473359531.1	$x^{10} - x^{9} - x^{8} + x^{7} + 2 x^{6} - 2 x^{5} + 2 x^{2} - 2 x + 1$	$10$	(0, 5)	$-\,7\cdot 149\cdot 1412617$	$3$	$8.25716330119$	$38384.36571053376$			✓	$S_{10}$ (as 10T45)	trivial	trivial	$2$	$4$	$2.447699225146165$	$0$	$1412617$
10.0.1475880875.1	$x^{10} - x^{9} - 2 x^{8} + x^{7} + 4 x^{6} - 4 x^{4} - 2 x^{3} + x^{2} + 2 x + 1$	$10$	(0, 5)	$-\,5^{3}\cdot 7\cdot 191\cdot 8831$	$4$	$8.25857525352$	$7683.439008673135$			✓	$S_{10}$ (as 10T45)	trivial	trivial	$2$	$4$	$2.1490031704265027$	$0$	$8831$
10.0.1481233663.1	$x^{10} - x^{9} - x^{7} + 2 x^{6} - x^{4} - x^{3} + 4 x^{2} - 3 x + 1$	$10$	(0, 5)	$-\,7\cdot 13\cdot 16277293$	$3$	$8.26156563168$	$38486.79855482916$			?	$S_{10}$ (as 10T45)	trivial	trivial	$2$	$4$	$2.0392980824654137$	$0$	$16277293$
10.0.1501418387.1	$x^{10} - x^{9} + 2 x^{7} + x^{4} + 2 x^{3} - x + 1$	$10$	(0, 5)	$-\,7\cdot 173\cdot 1239817$	$3$	$8.27275519523$	$38748.14043280013$			?	$S_{10}$ (as 10T45)	trivial	trivial	$2$	$4$	$2.1791514809234678$	$0$	$1239817$
10.0.1531001647.1	$x^{10} + x^{8} - 3 x^{5} + x^{2} + 1$	$10$	(0, 5)	$-\,7\cdot 23^{2}\cdot 643^{2}$	$3$	$8.28891270344$	$321.7499028748882$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	trivial	$2$	$4$	$2.32997752673$	$0$	$643$
10.2.1558357997.1	$x^{10} - x^{8} - 4 x^{7} + x^{6} + 4 x^{5} + 4 x^{4} - 2 x^{3} - 2 x^{2} - x + 1$	$10$	(2, 4)	$7\cdot 222622571$	$2$	$8.30360579656$	$39476.04333010085$			✓	$S_{10}$ (as 10T45)	trivial	trivial	$2$	$5$	$2.5841203622505735$	$2$	$222622571$
10.0.1560916259.1	$x^{10} - 3 x^{9} + 4 x^{8} - 3 x^{7} + 2 x^{6} - 2 x^{5} + 4 x^{4} - 5 x^{3} + 4 x^{2} - 2 x + 1$	$10$	(0, 5)	$-\,7\cdot 443\cdot 503359$	$3$	$8.3049679433$	$39508.43275808343$			✓	$S_{10}$ (as 10T45)	trivial	trivial	$2$	$4$	$2.2239325493829813$	$0$	$503359$
10.2.1590103529.1	$x^{10} - 2 x^{8} - 2 x^{7} + 3 x^{6} + 5 x^{5} - x^{4} - 6 x^{3} - 2 x^{2} + 2 x + 1$	$10$	(2, 4)	$7\cdot 227157647$	$2$	$8.32036809768$	$39876.102229280135$			✓	$S_{10}$ (as 10T45)	trivial	trivial	$2$	$5$	$2.610831516100405$	$2$	$227157647$
10.0.1606021907.1	$x^{10} - 2 x^{9} + x^{8} - 2 x^{7} + 4 x^{6} - 5 x^{5} + 8 x^{4} - 8 x^{3} + 6 x^{2} - 3 x + 1$	$10$	(0, 5)	$-\,7\cdot 101\cdot 1061\cdot 2141$	$4$	$8.32866025333$	$40075.203143589926$			?	$S_{10}$ (as 10T45)	trivial	trivial	$2$	$4$	$2.2004658105793613$	$0$	$2141$
10.0.1608802475.1	$x^{10} - 2 x^{9} + x^{8} + x^{7} - 3 x^{5} + 3 x^{4} + x^{3} - 2 x^{2} + 1$	$10$	(0, 5)	$-\,5^{2}\cdot 7\cdot 9193157$	$3$	$8.33010110436$	$23456.400129618945$			✓	$S_{10}$ (as 10T45)	trivial	trivial	$2$	$4$	$2.241704750895131$	$0$	$9193157$
10.0.1626208703.1	$x^{10} - 2 x^{9} + 2 x^{8} - 4 x^{7} + 5 x^{6} - 6 x^{5} + 7 x^{4} - 4 x^{3} + 5 x^{2} - x + 1$	$10$	(0, 5)	$-\,7\cdot 232315529$	$2$	$8.33907016666$	$40326.278070260836$			?	$S_{10}$ (as 10T45)	trivial	trivial	$2$	$4$	$3.342523576103219$	$0$	$232315529$
10.0.1648016384.1	$x^{10} - 2 x^{9} + 2 x^{8} - 4 x^{7} + 3 x^{6} + 2 x^{3} - 2 x^{2} + 1$	$10$	(0, 5)	$-\,2^{10}\cdot 7\cdot 223\cdot 1031$	$4$	$8.35018605803$	$4653.310430464043$			✓	$S_{10}$ (as 10T45)	trivial	trivial	$2$	$4$	$2.6115117238644747$	$0$	$1031$
10.0.1655414264.1	$x^{10} - 2 x^{9} + x^{8} + x^{7} - x^{6} + 2 x^{5} - 2 x^{4} + 2 x^{2} - x + 1$	$10$	(0, 5)	$-\,2^{3}\cdot 7\cdot 5437^{2}$	$3$	$8.35392687298$	$551.7898150564216$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	trivial	$2$	$4$	$3.36860726136$	$0$	$5437$
10.0.1672491331.1	$x^{10} - 2 x^{9} + 2 x^{8} - 2 x^{7} + 3 x^{6} - 3 x^{5} + 2 x^{4} - x + 1$	$10$	(0, 5)	$-\,7\cdot 17\cdot 14054549$	$3$	$8.36250494404$	$40896.10410540349$			✓	$S_{10}$ (as 10T45)	trivial	trivial	$2$	$4$	$2.192634169216176$	$0$	$14054549$
10.2.1676509093.1	$x^{10} - 2 x^{8} - x^{7} + 3 x^{6} + x^{5} - 3 x^{4} - x^{3} + x^{2} + x - 1$	$10$	(2, 4)	$7\cdot 127\cdot 821\cdot 2297$	$4$	$8.36451166829$	$40945.196213963856$			✓	$S_{10}$ (as 10T45)	trivial	trivial	$2$	$5$	$2.710001938272343$	$2$	$2297$
10.2.1745386496.1	$x^{10} - 2 x^{9} + 4 x^{8} - 4 x^{7} + 2 x^{6} + 2 x^{5} - 5 x^{4} + 6 x^{3} - 4 x^{2} + 2 x - 1$	$10$	(2, 4)	$2^{10}\cdot 7\cdot 37\cdot 6581$	$4$	$8.39825701056$	$5000.8225476334665$			✓	$S_{10}$ (as 10T45)	trivial	trivial	$2$	$5$	$2.7778259791298163$	$2$	$6581$
10.0.1754069639.1	$x^{10} - 2 x^{7} + 4 x^{4} + 4 x^{3} + 4 x^{2} + x + 1$	$10$	(0, 5)	$-\,7\cdot 17\cdot 1877\cdot 7853$	$4$	$8.40242574483$	$41881.61457011895$			?	$S_{10}$ (as 10T45)	trivial	trivial	$2$	$4$	$2.2396111233732574$	$0$	$7853$
10.0.1754135551.1	$x^{10} - 2 x^{9} + 2 x^{8} - x^{7} - x^{5} + 3 x^{4} - x^{3} - x^{2} + 1$	$10$	(0, 5)	$-\,7\cdot 47\cdot 5331719$	$3$	$8.40245731777$	$41882.401447385986$			✓	$S_{10}$ (as 10T45)	trivial	trivial	$2$	$4$	$2.266801928876049$	$0$	$5331719$
10.2.1787590973.1	$x^{10} - 2 x^{9} + 4 x^{8} - 5 x^{7} + 5 x^{6} - 4 x^{5} + 2 x^{4} - x^{2} + 2 x - 1$	$10$	(2, 4)	$7\cdot 347\cdot 735937$	$3$	$8.41834684705$	$42279.91216878295$			✓	$S_{10}$ (as 10T45)	trivial	trivial	$2$	$5$	$2.8149955512415046$	$2$	$735937$
10.0.1790248691.1	$x^{10} - 2 x^{9} + 3 x^{8} - 4 x^{7} + 4 x^{6} - 5 x^{5} + 3 x^{4} - 3 x^{3} + 3 x^{2} + 1$	$10$	(0, 5)	$-\,7\cdot 11\cdot 23249983$	$3$	$8.41959761624$	$42311.330527413105$			✓	$S_{10}$ (as 10T45)	trivial	trivial	$2$	$4$	$2.2155629224524542$	$0$	$23249983$
10.0.1806882035.1	$x^{10} - x^{9} + x^{8} + 2 x^{7} + 2 x^{5} + x^{4} + 2 x^{3} + 3 x^{2} + x + 1$	$10$	(0, 5)	$-\,5\cdot 7\cdot 51625201$	$3$	$8.42738781634$	$42507.43505552882$			✓	$S_{10}$ (as 10T45)	trivial	trivial	$2$	$4$	$2.436559040540062$	$0$	$51625201$
10.2.1862687197.1	$x^{10} - x^{9} + x^{8} - 5 x^{7} + x^{6} - 3 x^{5} + 5 x^{4} + 2 x^{3} + 4 x^{2} + x + 1$	$10$	(2, 4)	$7\cdot 29\cdot 193\cdot 47543$	$4$	$8.45306080447$	$43158.860005797185$			✓	$S_{10}$ (as 10T45)	trivial	trivial	$2$	$5$	$2.8867162384699743$	$2$	$47543$

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