LMFDB - Number field search results

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Results (1-50 of 154722 matches)

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Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
5.1.41381.1	$x^{5} - x^{4} - 2 x^{2} + 4 x - 1$	$5$	[1,2]	$41381$	$1$	$8.38224202495$	$203.42320418280704$	✓	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$1.64035423487$
5.1.48917.1	$x^{5} - 2 x^{4} + 2 x^{3} - 4 x^{2} + 5 x - 1$	$5$	[1,2]	$11\cdot 4447$	$2$	$8.66746233186$	$221.17187886347577$	✓	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$1.75453049414$
5.1.52612.1	$x^{5} - 3 x^{3} - 3 x^{2} + 2 x - 1$	$5$	[1,2]	$2^{2}\cdot 7\cdot 1879$	$3$	$8.7946176345$	$182.05351723747205$	?	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$2.37495993605$
5.1.61508.2	$x^{5} - 2 x^{4} + x^{3} + 3 x^{2} + 2 x - 1$	$5$	[1,2]	$2^{2}\cdot 15377$	$2$	$9.07373979848$	$196.84413115068207$	?	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$2.54670721331$
5.1.61877.1	$x^{5} - x^{4} + 4 x^{3} - 4 x^{2} + 1$	$5$	[1,2]	$43\cdot 1439$	$2$	$9.08460083811$	$248.75087939543047$	✓	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$1.92733830844$
5.1.64261.1	$x^{5} - 2 x^{4} + 5 x^{3} - 2 x^{2} + x + 1$	$5$	[1,2]	$179\cdot 359$	$2$	$9.15354868812$	$253.4975345047758$	✓	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$2.5247222789$
5.1.64665.1	$x^{5} - x^{4} + 2 x^{3} - 5 x^{2} + 5 x - 1$	$5$	[1,2]	$3^{3}\cdot 5\cdot 479$	$3$	$9.16502927194$	$176.31701417610324$	✓	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$1.89505399726$
5.1.73156.1	$x^{5} - x^{3} - x^{2} + 4 x + 1$	$5$	[1,2]	$2^{2}\cdot 18289$	$2$	$9.39398776583$	$214.67508510084414$	?	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$2.75994080914$
5.1.78557.1	$x^{5} - x^{4} + 2 x^{3} - 4 x^{2} + 2 x + 1$	$5$	[1,2]	$17\cdot 4621$	$2$	$9.52877293254$	$280.28021692584724$	✓	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$2.09833591754$
5.1.79677.1	$x^{5} - x^{4} + 2 x^{3} + x^{2} + 2 x - 1$	$5$	[1,2]	$3^{3}\cdot 13\cdot 227$	$3$	$9.55578994925$	$195.71588166981866$	✓	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$3.14927271408$
5.1.81417.1	$x^{5} - x^{4} + 3 x^{3} - 6 x^{2} + 3 x - 1$	$5$	[1,2]	$3\cdot 7\cdot 3877$	$3$	$9.59716627372$	$285.3366432829825$	✓	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$2.05641558227$
5.1.81508.1	$x^{5} - 2 x^{4} - x^{3} + 5 x^{2} + 1$	$5$	[1,2]	$2^{2}\cdot 7\cdot 41\cdot 71$	$4$	$9.59931067093$	$226.59837260539993$	?	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$2.97580645711$
5.1.81628.1	$x^{5} - 2 x^{4} - 2 x^{3} - x^{2} + 4 x - 4$	$5$	[1,2]	$2^{2}\cdot 20407$	$2$	$9.60213552129$	$285.70614274110386$	?	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$4.5753856842$
5.1.83269.1	$x^{5} + 2 x^{3} - 4 x^{2} + x + 1$	$5$	[1,2]	$83269$	$1$	$9.64043586687$	$288.5636844788339$	✓	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$2.15997037046$
5.1.83404.1	$x^{5} - x^{4} + x^{3} - 2 x^{2} - 2 x + 4$	$5$	[1,2]	$2^{2}\cdot 29\cdot 719$	$3$	$9.64355975611$	$288.7975069144469$	?	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$4.47961637834$
5.1.87257.1	$x^{5} + 6 x^{3} - x^{2} + 2 x + 1$	$5$	[1,2]	$87257$	$1$	$9.73105787408$	$295.39295861614573$	?	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$3.00496702005$
5.1.89092.1	$x^{5} - 2 x^{4} + 3 x^{3} + x^{2} + 2 x + 1$	$5$	[1,2]	$2^{2}\cdot 22273$	$2$	$9.77164636885$	$236.90597942774053$	✓	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$4.3295350838$
5.1.95461.1	$x^{5} + 2 x^{3} - 4 x^{2} + x - 1$	$5$	[1,2]	$95461$	$1$	$9.90752543394$	$308.9676358455688$	✓	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$2.42365991803$
5.1.97301.1	$x^{5} - x^{4} + 4 x^{3} - 3 x^{2} + 2 x + 1$	$5$	[1,2]	$97301$	$1$	$9.94542761254$	$311.93108213193506$	✓	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$3.01947695375$
5.1.97397.1	$x^{5} - 2 x^{4} + x^{3} + 3 x + 1$	$5$	[1,2]	$97397$	$1$	$9.94738932819$	$312.0849243395137$	✓	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$3.67166902306$
5.1.100708.1	$x^{5} - 2 x^{4} + x^{3} + 5 x^{2} - 2 x + 1$	$5$	[1,2]	$2^{2}\cdot 17\cdot 1481$	$3$	$10.0141200684$	$251.8770822175103$	?	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$3.15442291979$
5.1.103997.1	$x^{5} - 2 x^{4} + 4 x^{3} - 2 x^{2} - x - 1$	$5$	[1,2]	$103997$	$1$	$10.0786917379$	$322.48565859585136$	✓	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$2.36456017214$
5.1.106328.1	$x^{5} - 2 x^{4} + 3 x^{3} - 7 x^{2} + 2 x - 1$	$5$	[1,2]	$2^{3}\cdot 13291$	$2$	$10.1234730022$	$326.07974484779027$	?	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$5.07390197422$
5.1.108421.1	$x^{5} - x^{4} + 4 x^{3} + 4 x + 1$	$5$	[1,2]	$108421$	$1$	$10.1630176946$	$329.27344259748617$	✓	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$3.06589905262$
5.1.108449.1	$x^{5} - x^{4} + x^{3} - 4 x^{2} + 3 x + 1$	$5$	[1,2]	$11\cdot 9859$	$2$	$10.1635425654$	$329.3159577062733$	✓	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$2.38532708183$
5.1.108716.1	$x^{5} - x^{4} - 3 x^{3} + 2 x^{2} + 6 x + 4$	$5$	[1,2]	$2^{2}\cdot 27179$	$2$	$10.1685421457$	$329.7210942599821$	?	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$6.28484192604$
5.1.110029.1	$x^{5} + 2 x^{3} - 2 x^{2} + 4 x - 1$	$5$	[1,2]	$19\cdot 5791$	$2$	$10.1929861283$	$331.70619529939444$	✓	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$3.15011206046$
5.1.111509.1	$x^{5} - 2 x^{4} + 6 x^{3} - 4 x^{2} + 4 x + 1$	$5$	[1,2]	$111509$	$1$	$10.2202609409$	$333.9296333061802$	✓	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$3.70744512622$
5.1.113429.1	$x^{5} - x^{4} + 4 x^{2} + 2 x - 1$	$5$	[1,2]	$31\cdot 3659$	$2$	$10.2552162021$	$336.7922208127735$	✓	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$2.6035528815$
5.1.113717.1	$x^{5} - 4 x^{2} - 1$	$5$	[1,2]	$113717$	$1$	$10.2604185881$	$337.2195130771646$	✓	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$4.20411825733$
5.1.115037.1	$x^{5} - 2 x^{4} + 3 x^{3} - 2 x^{2} - 3 x - 1$	$5$	[1,2]	$13\cdot 8849$	$2$	$10.2841288546$	$339.17104829274564$	✓	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$3.64150590398$
5.1.115256.1	$x^{5} - x^{4} + 3 x^{3} - 2 x^{2} + 8 x + 1$	$5$	[1,2]	$2^{3}\cdot 14407$	$2$	$10.2880415281$	$339.4937407375871$	?	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$3.57846961537$
5.1.116073.1	$x^{5} - 2 x^{4} + 5 x^{3} - 5 x^{2} + x - 1$	$5$	[1,2]	$3^{4}\cdot 1433$	$2$	$10.3025858436$	$163.7890138742535$	✓	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$2.40122150072$
5.1.116317.2	$x^{5} - 2 x^{4} + 4 x^{3} - 7 x^{2} + 7 x - 4$	$5$	[1,2]	$41\cdot 2837$	$2$	$10.3069136715$	$341.0527818388233$	✓	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$3.15590433013$
5.1.116849.1	$x^{5} - x^{4} - x^{3} + 4 x^{2} + 5 x + 1$	$5$	[1,2]	$116849$	$1$	$10.3163246328$	$341.8318299983195$	✓	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$2.45634842358$
5.1.117668.1	$x^{5} - 2 x^{4} - x^{3} + 3 x^{2} + 4 x - 1$	$5$	[1,2]	$2^{2}\cdot 23\cdot 1279$	$3$	$10.3307457764$	$272.26126248424504$	?	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$3.46913662577$
5.1.117749.1	$x^{5} - x^{4} + 2 x^{3} - 3 x^{2} - 2 x - 1$	$5$	[1,2]	$73\cdot 1613$	$2$	$10.3321676755$	$343.14574163174456$	✓	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$3.99538115794$
5.1.119433.1	$x^{5} - 2 x^{4} + 5 x^{3} - 6 x^{2} + 2 x + 1$	$5$	[1,2]	$3\cdot 41\cdot 971$	$3$	$10.3615533695$	$345.59079848861717$	✓	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$2.31713491544$
5.1.120068.1	$x^{5} - x^{4} + 3 x^{3} - 2 x^{2} + 4 x - 4$	$5$	[1,2]	$2^{2}\cdot 13\cdot 2309$	$3$	$10.3725480493$	$275.02381771291886$	?	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$4.47143010282$
5.1.120149.1	$x^{5} - x^{4} - 2 x^{3} + 6 x^{2} - 7 x + 4$	$5$	[1,2]	$137\cdot 877$	$2$	$10.3739471727$	$346.62515777133086$	✓	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$3.21006250466$
5.1.120917.1	$x^{5} - 4 x^{2} + 5 x - 1$	$5$	[1,2]	$120917$	$1$	$10.3871755783$	$347.731218040601$	✓	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$2.26944611483$
5.1.122364.1	$x^{5} - x^{4} + 2 x^{3} - 5 x^{2} + 8 x - 4$	$5$	[1,2]	$2^{2}\cdot 3^{3}\cdot 11\cdot 103$	$4$	$10.4119178548$	$242.54169842255698$	?	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$4.0812078028$
5.1.122581.1	$x^{5} - 2 x^{3} - 2 x^{2} + 5 x - 1$	$5$	[1,2]	$37\cdot 3313$	$2$	$10.4156081316$	$350.11569516375584$	✓	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$2.51326172754$
5.1.124417.1	$x^{5} - 2 x^{4} + 3 x^{3} - 6 x^{2} + 4 x + 1$	$5$	[1,2]	$83\cdot 1499$	$2$	$10.4466235525$	$352.7279404867156$	✓	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$2.60436568014$
5.1.130277.1	$x^{5} - x^{4} + 4 x^{2} + 2 x + 1$	$5$	[1,2]	$7\cdot 37\cdot 503$	$3$	$10.5432268221$	$360.93905302696186$	✓	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$2.49829376491$
5.1.130925.1	$x^{5} - 2 x^{4} + 4 x^{3} - 6 x^{2} + 3 x + 1$	$5$	[1,2]	$5^{2}\cdot 5237$	$2$	$10.5536944539$	$211.60274138991988$	✓	$S_5$ (as 5T5)	$[3]$	$2$	$2$	$2.38203698354$
5.1.135449.1	$x^{5} - x^{3} - 3 x^{2} + 5 x - 1$	$5$	[1,2]	$135449$	$1$	$10.625641537$	$368.03396582380816$	✓	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$2.3969778015$
5.1.139096.1	$x^{5} - x^{4} - x^{3} + 6 x - 4$	$5$	[1,2]	$2^{3}\cdot 17387$	$2$	$10.6822546867$	$372.9557614516767$	?	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$6.12717513646$
5.1.140541.1	$x^{5} - 5 x^{2} - x - 4$	$5$	[1,2]	$3\cdot 79\cdot 593$	$3$	$10.7043575692$	$374.8879832696695$	?	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$5.07603812355$
5.1.142533.1	$x^{5} + x^{3} - 4 x^{2} - 3 x - 1$	$5$	[1,2]	$3^{3}\cdot 5279$	$2$	$10.7345312647$	$261.7684460260161$	✓	$S_5$ (as 5T5)	$[2]$	$2$	$2$	$4.10095020652$

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Elliptic curves over $\Q$
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