LMFDB - Number field search results

Refine search

Degree	Signature	Ramified prime count	Ramified	Unramified primes

Galois group	Field is	Intermediate field	Class group structure	Class number

Discriminant	Root discriminant	Galois root discriminant	Narrow class group	Narrow class number

CM field	Relative class number	Regulator	$p$ -adic completions	Monogenic

Index	Ines. $p$	Minimal sibling

		Sort order	Select

Results (1-50 of 1008 matches)

Next Download displayed columns for results to

Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	Galois	Monogenic	Galois group	Class group	Narrow class group	Unit group torsion	Unit group rank	Regulator
5.5.14641.1	$x^{5} - x^{4} - 4 x^{3} + 3 x^{2} + 3 x - 1$	$5$	[5,0]	$11^{4}$	$1$	$6.80948312752$	$6.809483127522301$	✓	✓	$C_5$ (as 5T1)	trivial	trivial	$2$	$4$	$1.63569412559$
5.5.390625.1	$x^{5} - 10 x^{3} - 5 x^{2} + 10 x - 1$	$5$	[5,0]	$5^{8}$	$1$	$13.132639022$	$13.132639022018836$	✓		$C_5$ (as 5T1)	trivial	trivial	$2$	$4$	$16.0696118231$
5.5.923521.1	$x^{5} - x^{4} - 12 x^{3} + 21 x^{2} + x - 5$	$5$	[5,0]	$31^{4}$	$1$	$15.598734101$	$15.59873410095393$	✓		$C_5$ (as 5T1)	trivial	trivial	$2$	$4$	$30.3695765133$
5.5.2825761.1	$x^{5} - x^{4} - 16 x^{3} - 5 x^{2} + 21 x + 9$	$5$	[5,0]	$41^{4}$	$1$	$19.5086440773$	$19.50864407731132$	✓		$C_5$ (as 5T1)	trivial	trivial	$2$	$4$	$123.329982692$
5.5.13845841.1	$x^{5} - x^{4} - 24 x^{3} + 17 x^{2} + 41 x + 13$	$5$	[5,0]	$61^{4}$	$1$	$26.8079662462$	$26.807966246166025$	✓		$C_5$ (as 5T1)	trivial	trivial	$2$	$4$	$93.7680714453$
5.5.25411681.1	$x^{5} - x^{4} - 28 x^{3} - 37 x^{2} + 25 x - 1$	$5$	[5,0]	$71^{4}$	$1$	$30.2695997909$	$30.269599790850265$	✓		$C_5$ (as 5T1)	trivial	trivial	$2$	$4$	$70.6106756434$
5.5.104060401.1	$x^{5} - x^{4} - 40 x^{3} - 93 x^{2} - 21 x + 17$	$5$	[5,0]	$101^{4}$	$1$	$40.128885573$	$40.12888557303687$	✓		$C_5$ (as 5T1)	trivial	trivial	$2$	$4$	$119.525694644$
5.5.294499921.1	$x^{5} - x^{4} - 52 x^{3} + 89 x^{2} + 109 x - 193$	$5$	[5,0]	$131^{4}$	$1$	$49.4102483206$	$49.410248320622195$	✓		$C_5$ (as 5T1)	trivial	trivial	$2$	$4$	$247.953961572$
5.5.519885601.1	$x^{5} - x^{4} - 60 x^{3} + 12 x^{2} + 784 x - 128$	$5$	[5,0]	$151^{4}$	$1$	$55.3581486897$	$55.358148689726$	✓		$C_5$ (as 5T1)	trivial	trivial	$2$	$4$	$9575.16761977$
5.5.1073283121.1	$x^{5} - x^{4} - 72 x^{3} + 123 x^{2} + 223 x + 49$	$5$	[5,0]	$181^{4}$	$1$	$63.9945308995$	$63.99453089948475$	✓		$C_5$ (as 5T1)	trivial	trivial	$2$	$4$	$1245.95724225$
5.5.1330863361.1	$x^{5} - x^{4} - 76 x^{3} + 359 x^{2} - 437 x + 155$	$5$	[5,0]	$191^{4}$	$1$	$66.8077266614$	$66.80772666139775$	✓		$C_5$ (as 5T1)	$[11]$	$[11]$	$2$	$4$	$185.439033921$
5.5.1982119441.1	$x^{5} - x^{4} - 84 x^{3} + 59 x^{2} + 1661 x - 269$	$5$	[5,0]	$211^{4}$	$1$	$72.3479057657$	$72.34790576574842$	✓		$C_5$ (as 5T1)	trivial	trivial	$2$	$4$	$577.507733173$
5.5.3373402561.1	$x^{5} - x^{4} - 96 x^{3} + 212 x^{2} + 1232 x - 512$	$5$	[5,0]	$241^{4}$	$1$	$80.4662262575$	$80.4662262574868$	✓		$C_5$ (as 5T1)	trivial	trivial	$2$	$4$	$30917.0186222$
5.5.3969126001.1	$x^{5} - x^{4} - 100 x^{3} + 20 x^{2} + 1504 x - 1024$	$5$	[5,0]	$251^{4}$	$1$	$83.1264008617$	$83.12640086168598$	✓		$C_5$ (as 5T1)	trivial	trivial	$2$	$4$	$52885.8852389$
5.5.5393580481.1	$x^{5} - x^{4} - 108 x^{3} + 401 x^{2} - 13 x - 845$	$5$	[5,0]	$271^{4}$	$1$	$88.3843622794$	$88.38436227941675$	✓		$C_5$ (as 5T1)	trivial	trivial	$2$	$4$	$4098.90045327$
5.5.5719140625.1	$x^{5} - 110 x^{3} - 605 x^{2} - 990 x - 451$	$5$	[5,0]	$5^{8}\cdot 11^{4}$	$2$	$89.4264838403$	$89.42648384027824$	✓		$C_5$ (as 5T1)	$[5]$	$[5]$	$2$	$4$	$272.480237494$
5.5.5719140625.2	$x^{5} - 110 x^{3} - 495 x^{2} - 440 x - 99$	$5$	[5,0]	$5^{8}\cdot 11^{4}$	$2$	$89.4264838403$	$89.42648384027824$	✓		$C_5$ (as 5T1)	$[5]$	$[5]$	$2$	$4$	$2302.76208389$
5.5.5719140625.3	$x^{5} - 110 x^{3} - 55 x^{2} + 660 x + 649$	$5$	[5,0]	$5^{8}\cdot 11^{4}$	$2$	$89.4264838403$	$89.42648384027824$	✓		$C_5$ (as 5T1)	$[5]$	$[5]$	$2$	$4$	$382.646168029$
5.5.5719140625.4	$x^{5} - 110 x^{3} - 220 x^{2} + 1485 x + 1276$	$5$	[5,0]	$5^{8}\cdot 11^{4}$	$2$	$89.4264838403$	$89.42648384027824$	✓		$C_5$ (as 5T1)	$[5]$	$[5]$	$2$	$4$	$8475.85345405$
5.5.6234839521.1	$x^{5} - x^{4} - 112 x^{3} + 191 x^{2} + 2257 x - 967$	$5$	[5,0]	$281^{4}$	$1$	$90.9840062401$	$90.9840062401245$	✓		$C_5$ (as 5T1)	trivial	trivial	$2$	$4$	$1165.65240048$
5.5.9354951841.1	$x^{5} - x^{4} - 124 x^{3} - 535 x^{2} - 413 x + 539$	$5$	[5,0]	$311^{4}$	$1$	$98.6752672315$	$98.67526723145183$	✓		$C_5$ (as 5T1)	trivial	trivial	$2$	$4$	$5087.72088405$
5.5.12003612721.1	$x^{5} - x^{4} - 132 x^{3} + 887 x^{2} - 1843 x + 1027$	$5$	[5,0]	$331^{4}$	$1$	$103.719972995$	$103.7199729945502$	✓		$C_5$ (as 5T1)	trivial	trivial	$2$	$4$	$2582.67345578$
5.5.13521270961.1	$x^{5} - x^{4} - 136 x^{3} + 300 x^{2} + 2016 x - 3136$	$5$	[5,0]	$11^{4}\cdot 31^{4}$	$2$	$106.219316671$	$106.21931667115254$	✓		$C_5$ (as 5T1)	$[5]$	$[5]$	$2$	$4$	$15927.8863443$
5.5.13521270961.2	$x^{5} - x^{4} - 136 x^{3} - 41 x^{2} + 3039 x - 1431$	$5$	[5,0]	$11^{4}\cdot 31^{4}$	$2$	$106.219316671$	$106.21931667115254$	✓		$C_5$ (as 5T1)	$[5]$	$[5]$	$2$	$4$	$2564.52443732$
5.5.13521270961.3	$x^{5} - x^{4} - 136 x^{3} - 723 x^{2} - 1053 x - 67$	$5$	[5,0]	$11^{4}\cdot 31^{4}$	$2$	$106.219316671$	$106.21931667115254$	✓		$C_5$ (as 5T1)	$[5]$	$[5]$	$2$	$4$	$489.762552216$
5.5.13521270961.4	$x^{5} - x^{4} - 136 x^{3} + 641 x^{2} - 371 x - 67$	$5$	[5,0]	$11^{4}\cdot 31^{4}$	$2$	$106.219316671$	$106.21931667115254$	✓		$C_5$ (as 5T1)	$[5]$	$[5]$	$2$	$4$	$383.707630684$
5.5.25856961601.1	$x^{5} - x^{4} - 160 x^{3} - 369 x^{2} + 879 x + 29$	$5$	[5,0]	$401^{4}$	$1$	$120.924833503$	$120.92483350286062$	✓		$C_5$ (as 5T1)	trivial	trivial	$2$	$4$	$1555.36216125$
5.5.31414372081.1	$x^{5} - x^{4} - 168 x^{3} - 219 x^{2} + 3853 x + 3517$	$5$	[5,0]	$421^{4}$	$1$	$125.726167348$	$125.72616734794764$	✓		$C_5$ (as 5T1)	trivial	trivial	$2$	$4$	$1697.49706573$
5.5.34507149121.1	$x^{5} - x^{4} - 172 x^{3} + 724 x^{2} + 1824 x - 1728$	$5$	[5,0]	$431^{4}$	$1$	$128.109641576$	$128.10964157622095$	✓		$C_5$ (as 5T1)	trivial	trivial	$2$	$4$	$391579.04227$
5.5.41371966801.1	$x^{5} - x^{4} - 180 x^{3} + 1389 x^{2} - 3341 x + 2551$	$5$	[5,0]	$11^{4}\cdot 41^{4}$	$2$	$132.843782685$	$132.8437826852893$	✓		$C_5$ (as 5T1)	$[5]$	$[5]$	$2$	$4$	$358.821278588$
5.5.41371966801.2	$x^{5} - x^{4} - 180 x^{3} - 415 x^{2} + 1169 x + 2551$	$5$	[5,0]	$11^{4}\cdot 41^{4}$	$2$	$132.843782685$	$132.8437826852893$	✓		$C_5$ (as 5T1)	$[5]$	$[5]$	$2$	$4$	$2009.77128675$
5.5.41371966801.3	$x^{5} - x^{4} - 180 x^{3} - 415 x^{2} + 3875 x + 2551$	$5$	[5,0]	$11^{4}\cdot 41^{4}$	$2$	$132.843782685$	$132.8437826852893$	✓		$C_5$ (as 5T1)	$[5]$	$[5]$	$2$	$4$	$1485.1344106$
5.5.41371966801.4	$x^{5} - x^{4} - 180 x^{3} + 36 x^{2} + 3424 x + 3904$	$5$	[5,0]	$11^{4}\cdot 41^{4}$	$2$	$132.843782685$	$132.8437826852893$	✓		$C_5$ (as 5T1)	$[5]$	$[5]$	$2$	$4$	$23210.5470603$
5.5.45165175441.1	$x^{5} - x^{4} - 184 x^{3} + 129 x^{2} + 4551 x - 5419$	$5$	[5,0]	$461^{4}$	$1$	$135.195034302$	$135.1950343017928$	✓		$C_5$ (as 5T1)	trivial	trivial	$2$	$4$	$4946.7233313$
5.5.58120048561.1	$x^{5} - x^{4} - 196 x^{3} - 59 x^{2} + 2019 x - 1377$	$5$	[5,0]	$491^{4}$	$1$	$142.188736054$	$142.18873605415627$	✓		$C_5$ (as 5T1)	trivial	trivial	$2$	$4$	$28434.7104177$
5.5.73680216481.1	$x^{5} - x^{4} - 208 x^{3} + 771 x^{2} + 4143 x - 2083$	$5$	[5,0]	$521^{4}$	$1$	$149.097437236$	$149.09743723635626$	✓		$C_5$ (as 5T1)	trivial	trivial	$2$	$4$	$3171.44786999$
5.5.85662167761.1	$x^{5} - x^{4} - 216 x^{3} - 1147 x^{2} - 805 x + 2629$	$5$	[5,0]	$541^{4}$	$1$	$153.658932626$	$153.65893262567562$	✓		$C_5$ (as 5T1)	trivial	trivial	$2$	$4$	$5591.83636552$
5.5.106302733681.1	$x^{5} - x^{4} - 228 x^{3} - 868 x^{2} + 3056 x + 7552$	$5$	[5,0]	$571^{4}$	$1$	$160.438608482$	$160.43860848150953$	✓		$C_5$ (as 5T1)	trivial	trivial	$2$	$4$	$148439.26957$
5.5.130466162401.1	$x^{5} - x^{4} - 240 x^{3} - 1755 x^{2} - 3731 x - 2399$	$5$	[5,0]	$601^{4}$	$1$	$167.147381576$	$167.14738157598725$	✓		$C_5$ (as 5T1)	trivial	trivial	$2$	$4$	$23153.4060852$
5.5.158532181921.1	$x^{5} - x^{4} - 252 x^{3} - 2095 x^{2} - 5785 x - 5069$	$5$	[5,0]	$631^{4}$	$1$	$173.789481456$	$173.78948145596087$	✓		$C_5$ (as 5T1)	$[11]$	$[11]$	$2$	$4$	$478.383345376$
5.5.168823196161.1	$x^{5} - x^{4} - 256 x^{3} + 564 x^{2} + 5328 x + 5120$	$5$	[5,0]	$641^{4}$	$1$	$175.989364729$	$175.98936472906092$	✓		$C_5$ (as 5T1)	$[11]$	$[11]$	$2$	$4$	$39805.8132601$
5.5.190899960241.1	$x^{5} - x^{4} - 264 x^{3} + 185 x^{2} + 16837 x - 4851$	$5$	[5,0]	$661^{4}$	$1$	$180.368696867$	$180.36869686739456$	✓		$C_5$ (as 5T1)	trivial	trivial	$2$	$4$	$107708.333686$
5.5.202716958081.1	$x^{5} - x^{4} - 268 x^{3} - 1020 x^{2} + 4128 x - 1024$	$5$	[5,0]	$11^{4}\cdot 61^{4}$	$2$	$182.548393836$	$182.5483938364549$	✓		$C_5$ (as 5T1)	$[5]$	$[5]$	$2$	$4$	$25011.6652454$
5.5.202716958081.2	$x^{5} - x^{4} - 268 x^{3} + 2335 x^{2} - 5937 x + 2331$	$5$	[5,0]	$11^{4}\cdot 61^{4}$	$2$	$182.548393836$	$182.5483938364549$	✓		$C_5$ (as 5T1)	$[5]$	$[5]$	$2$	$4$	$19885.4936643$
5.5.202716958081.3	$x^{5} - x^{4} - 268 x^{3} - 349 x^{2} + 3457 x + 5015$	$5$	[5,0]	$11^{4}\cdot 61^{4}$	$2$	$182.548393836$	$182.5483938364549$	✓		$C_5$ (as 5T1)	$[5]$	$[5]$	$2$	$4$	$4572.95146181$
5.5.202716958081.4	$x^{5} - x^{4} - 268 x^{3} - 349 x^{2} + 7483 x + 13067$	$5$	[5,0]	$11^{4}\cdot 61^{4}$	$2$	$182.548393836$	$182.5483938364549$	✓		$C_5$ (as 5T1)	$[5]$	$[5]$	$2$	$4$	$1293.31076803$
5.5.227988105361.1	$x^{5} - x^{4} - 276 x^{3} + 1299 x^{2} + 5329 x - 15581$	$5$	[5,0]	$691^{4}$	$1$	$186.888439574$	$186.88843957442577$	✓		$C_5$ (as 5T1)	trivial	trivial	$2$	$4$	$11543.7370825$
5.5.241474942801.1	$x^{5} - x^{4} - 280 x^{3} - 2047 x^{2} - 3791 x - 1699$	$5$	[5,0]	$701^{4}$	$1$	$189.049013027$	$189.04901302748888$	✓		$C_5$ (as 5T1)	trivial	trivial	$2$	$4$	$11580.5925324$
5.5.318097128001.1	$x^{5} - x^{4} - 300 x^{3} + 2313 x^{2} - 3761 x + 571$	$5$	[5,0]	$751^{4}$	$1$	$199.761573204$	$199.7615732040473$	✓		$C_5$ (as 5T1)	trivial	trivial	$2$	$4$	$11903.3361639$
5.5.335381132641.1	$x^{5} - x^{4} - 304 x^{3} - 2831 x^{2} - 8925 x - 8775$	$5$	[5,0]	$761^{4}$	$1$	$201.886707538$	$201.88670753754164$	✓		$C_5$ (as 5T1)	trivial	trivial	$2$	$4$	$193371.740026$

Next Download displayed columns for results to

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (1-50 of 1008 matches)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.