LMFDB - Number field search results

Note: Search results may be incomplete due to uncomputed quantities: Class number (222541 objects)

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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	Unit signature rank

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Results (1-50 of 166075 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
2.0.199.1	$x^{2} - x + 50$	$2$	(0, 1)	$-\,199$	$1$	$14.1067359797$	$14.106735979665885$	✓	✓	✓	$C_2$ (as 2T1)	$[9]$	$[9]$	$2$	0	$1$	$0$
2.0.367.1	$x^{2} - x + 92$	$2$	(0, 1)	$-\,367$	$1$	$19.1572440607$	$19.157244060668017$	✓	✓	✓	$C_2$ (as 2T1)	$[9]$	$[9]$	$2$	0	$1$	$0$
2.0.419.1	$x^{2} - x + 105$	$2$	(0, 1)	$-\,419$	$1$	$20.4694894905$	$20.46948949045872$	✓	✓	✓	$C_2$ (as 2T1)	$[9]$	$[9]$	$2$	0	$1$	$0$
2.0.491.1	$x^{2} - x + 123$	$2$	(0, 1)	$-\,491$	$1$	$22.1585198062$	$22.15851980616034$	✓	✓	✓	$C_2$ (as 2T1)	$[9]$	$[9]$	$2$	0	$1$	$0$
2.0.563.1	$x^{2} - x + 141$	$2$	(0, 1)	$-\,563$	$1$	$23.7276210354$	$23.727621035409346$	✓	✓	✓	$C_2$ (as 2T1)	$[9]$	$[9]$	$2$	0	$1$	$0$
2.0.823.1	$x^{2} - x + 206$	$2$	(0, 1)	$-\,823$	$1$	$28.6879765756$	$28.687976575562104$	✓	✓	✓	$C_2$ (as 2T1)	$[9]$	$[9]$	$2$	0	$1$	$0$
2.0.1087.1	$x^{2} - x + 272$	$2$	(0, 1)	$-\,1087$	$1$	$32.9696830437$	$32.96968304366907$	✓	✓	✓	$C_2$ (as 2T1)	$[9]$	$[9]$	$2$	0	$1$	$0$
2.2.1129.1	$x^{2} - x - 282$	$2$	(2, 0)	$1129$	$1$	$33.6005952328$	$33.60059523282288$		✓	✓	$C_2$ (as 2T1)	$[9]$	$[9]$	$2$	$1$	$5.81712001756$	$2$
2.0.1187.1	$x^{2} - x + 297$	$2$	(0, 1)	$-\,1187$	$1$	$34.4528663539$	$34.45286635390443$	✓	✓	✓	$C_2$ (as 2T1)	$[9]$	$[9]$	$2$	0	$1$	$0$
2.0.1291.1	$x^{2} - x + 323$	$2$	(0, 1)	$-\,1291$	$1$	$35.9304884464$	$35.93048844644336$	✓	✓	✓	$C_2$ (as 2T1)	$[9]$	$[9]$	$2$	0	$1$	$0$
2.0.1423.1	$x^{2} - x + 356$	$2$	(0, 1)	$-\,1423$	$1$	$37.7226722277$	$37.72267222772003$	✓	✓	✓	$C_2$ (as 2T1)	$[9]$	$[9]$	$2$	0	$1$	$0$
2.0.1579.1	$x^{2} - x + 395$	$2$	(0, 1)	$-\,1579$	$1$	$39.7366329726$	$39.736632972611055$	✓	✓	✓	$C_2$ (as 2T1)	$[9]$	$[9]$	$2$	0	$1$	$0$
2.0.2003.1	$x^{2} - x + 501$	$2$	(0, 1)	$-\,2003$	$1$	$44.7548880012$	$44.75488800120049$	✓	✓	✓	$C_2$ (as 2T1)	$[9]$	$[9]$	$2$	0	$1$	$0$
2.0.2803.1	$x^{2} - x + 701$	$2$	(0, 1)	$-\,2803$	$1$	$52.9433659678$	$52.94336596779619$	✓	✓	✓	$C_2$ (as 2T1)	$[9]$	$[9]$	$2$	0	$1$	$0$
2.2.3137.1	$x^{2} - x - 784$	$2$	(2, 0)	$3137$	$1$	$56.0089278598$	$56.00892785976178$		✓	✓	$C_2$ (as 2T1)	$[9]$	$[9]$	$2$	$1$	$4.71857858115$	$2$
2.0.3163.1	$x^{2} - x + 791$	$2$	(0, 1)	$-\,3163$	$1$	$56.2405547626$	$56.24055476255546$	✓	✓	✓	$C_2$ (as 2T1)	$[9]$	$[9]$	$2$	0	$1$	$0$
2.0.3259.1	$x^{2} - x + 815$	$2$	(0, 1)	$-\,3259$	$1$	$57.0876519048$	$57.087651904768336$	✓	✓	✓	$C_2$ (as 2T1)	$[9]$	$[9]$	$2$	0	$1$	$0$
2.0.3307.1	$x^{2} - x + 827$	$2$	(0, 1)	$-\,3307$	$1$	$57.5065213693$	$57.5065213693195$	✓	✓	✓	$C_2$ (as 2T1)	$[9]$	$[9]$	$2$	0	$1$	$0$
2.0.3547.1	$x^{2} - x + 887$	$2$	(0, 1)	$-\,3547$	$1$	$59.5566956773$	$59.55669567731239$	✓	✓	✓	$C_2$ (as 2T1)	$[9]$	$[9]$	$2$	0	$1$	$0$
2.0.3643.1	$x^{2} - x + 911$	$2$	(0, 1)	$-\,3643$	$1$	$60.3572696533$	$60.35726965329032$	✓	✓	✓	$C_2$ (as 2T1)	$[9]$	$[9]$	$2$	0	$1$	$0$
2.0.4027.1	$x^{2} - x + 1007$	$2$	(0, 1)	$-\,4027$	$1$	$63.4586479528$	$63.45864795282043$	✓	✓	✓	$C_2$ (as 2T1)	$[3, 3]$	$[3, 3]$	$2$	0	$1$	$0$
2.0.4243.1	$x^{2} - x + 1061$	$2$	(0, 1)	$-\,4243$	$1$	$65.1383143779$	$65.13831437794502$	✓	✓	✓	$C_2$ (as 2T1)	$[9]$	$[9]$	$2$	0	$1$	$0$
2.0.4363.1	$x^{2} - x + 1091$	$2$	(0, 1)	$-\,4363$	$1$	$66.0530090155$	$66.05300901548695$	✓	✓	✓	$C_2$ (as 2T1)	$[9]$	$[9]$	$2$	0	$1$	$0$
2.2.4409.1	$x^{2} - x - 1102$	$2$	(2, 0)	$4409$	$1$	$66.4003012041$	$66.40030120413611$		✓	✓	$C_2$ (as 2T1)	$[9]$	$[9]$	$2$	$1$	$6.49828441758$	$2$
2.0.4483.1	$x^{2} - x + 1121$	$2$	(0, 1)	$-\,4483$	$1$	$66.9552089086$	$66.9552089086428$	✓	✓	✓	$C_2$ (as 2T1)	$[9]$	$[9]$	$2$	0	$1$	$0$
2.0.4723.1	$x^{2} - x + 1181$	$2$	(0, 1)	$-\,4723$	$1$	$68.7240860252$	$68.72408602520662$	✓	✓	✓	$C_2$ (as 2T1)	$[9]$	$[9]$	$2$	0	$1$	$0$
2.0.4987.1	$x^{2} - x + 1247$	$2$	(0, 1)	$-\,4987$	$1$	$70.6186944088$	$70.61869440877535$	✓	✓	✓	$C_2$ (as 2T1)	$[9]$	$[9]$	$2$	0	$1$	$0$
2.0.5443.1	$x^{2} - x + 1361$	$2$	(0, 1)	$-\,5443$	$1$	$73.7766900857$	$73.77669008569035$	✓	✓	✓	$C_2$ (as 2T1)	$[9]$	$[9]$	$2$	0	$1$	$0$
2.2.5521.1	$x^{2} - x - 1380$	$2$	(2, 0)	$5521$	$1$	$74.303431953$	$74.30343195303969$		✓	✓	$C_2$ (as 2T1)	$[9]$	$[9]$	$2$	$1$	$13.3500788615$	$2$
2.0.6043.1	$x^{2} - x + 1511$	$2$	(0, 1)	$-\,6043$	$1$	$77.7367352029$	$77.73673520286275$	✓	✓	✓	$C_2$ (as 2T1)	$[9]$	$[9]$	$2$	0	$1$	$0$
2.0.6427.1	$x^{2} - x + 1607$	$2$	(0, 1)	$-\,6427$	$1$	$80.1685723959$	$80.16857239592083$	✓	✓	✓	$C_2$ (as 2T1)	$[9]$	$[9]$	$2$	0	$1$	$0$
2.2.6616.1	$x^{2} - 1654$	$2$	(2, 0)	$2^{3}\cdot 827$	$2$	$81.3387976307$	$81.33879763065102$		✓	✓	$C_2$ (as 2T1)	$[9]$	$[18]$	$2$	$1$	$10.3012564529$	$1$
2.0.6763.1	$x^{2} - x + 1691$	$2$	(0, 1)	$-\,6763$	$1$	$82.2374610503$	$82.23746105030237$	✓	✓	✓	$C_2$ (as 2T1)	$[9]$	$[9]$	$2$	0	$1$	$0$
2.2.6809.1	$x^{2} - x - 1702$	$2$	(2, 0)	$11\cdot 619$	$2$	$82.5166649835$	$82.516664983505$		✓	✓	$C_2$ (as 2T1)	$[9]$	$[18]$	$2$	$1$	$9.20049202572$	$1$
2.0.6883.1	$x^{2} - x + 1721$	$2$	(0, 1)	$-\,6883$	$1$	$82.9638475482$	$82.96384754819415$	✓	✓	✓	$C_2$ (as 2T1)	$[9]$	$[9]$	$2$	0	$1$	$0$
2.2.7573.1	$x^{2} - x - 1893$	$2$	(2, 0)	$7573$	$1$	$87.0229854694$	$87.02298546935747$		✓	✓	$C_2$ (as 2T1)	$[9]$	$[9]$	$2$	$1$	$4.46604021033$	$2$
2.0.7723.1	$x^{2} - x + 1931$	$2$	(0, 1)	$-\,7723$	$1$	$87.8806008172$	$87.88060081724521$	✓	✓	✓	$C_2$ (as 2T1)	$[9]$	$[9]$	$2$	0	$1$	$0$
2.2.7873.1	$x^{2} - x - 1968$	$2$	(2, 0)	$7873$	$1$	$88.7299273075$	$88.72992730753249$		✓	✓	$C_2$ (as 2T1)	$[9]$	$[9]$	$2$	$1$	$10.0987253363$	$2$
2.0.8563.1	$x^{2} - x + 2141$	$2$	(0, 1)	$-\,8563$	$1$	$92.5364792933$	$92.53647929330357$	✓	✓	✓	$C_2$ (as 2T1)	$[9]$	$[9]$	$2$	0	$1$	$0$
2.0.8803.1	$x^{2} - x + 2201$	$2$	(0, 1)	$-\,8803$	$1$	$93.8243038876$	$93.82430388763883$	✓	✓	✓	$C_2$ (as 2T1)	$[9]$	$[9]$	$2$	0	$1$	$0$
2.0.9067.1	$x^{2} - x + 2267$	$2$	(0, 1)	$-\,9067$	$1$	$95.2207960479$	$95.22079604792222$	✓	✓	✓	$C_2$ (as 2T1)	$[9]$	$[9]$	$2$	0	$1$	$0$
2.2.10273.1	$x^{2} - x - 2568$	$2$	(2, 0)	$10273$	$1$	$101.355808911$	$101.35580891098448$		✓	✓	$C_2$ (as 2T1)	$[9]$	$[9]$	$2$	$1$	$14.8795893712$	$2$
2.0.10627.1	$x^{2} - x + 2657$	$2$	(0, 1)	$-\,10627$	$1$	$103.087341609$	$103.08734160894828$	✓	✓	✓	$C_2$ (as 2T1)	$[9]$	$[9]$	$2$	0	$1$	$0$
2.2.10721.1	$x^{2} - x - 2680$	$2$	(2, 0)	$71\cdot 151$	$2$	$103.542261903$	$103.54226190305097$		✓	✓	$C_2$ (as 2T1)	$[9]$	$[18]$	$2$	$1$	$12.7596761099$	$1$
2.2.11641.1	$x^{2} - x - 2910$	$2$	(2, 0)	$7\cdot 1663$	$2$	$107.893465975$	$107.89346597454362$		✓	✓	$C_2$ (as 2T1)	$[9]$	$[18]$	$2$	$1$	$21.916229552$	$1$
2.2.12409.1	$x^{2} - x - 3102$	$2$	(2, 0)	$12409$	$1$	$111.39569112$	$111.39569111954016$		✓	✓	$C_2$ (as 2T1)	$[9]$	$[9]$	$2$	$1$	$20.7031993244$	$2$
2.2.12657.1	$x^{2} - x - 3164$	$2$	(2, 0)	$3\cdot 4219$	$2$	$112.503333284$	$112.50333328395207$		✓	✓	$C_2$ (as 2T1)	$[9]$	$[18]$	$2$	$1$	$11.1199125058$	$1$
2.2.13069.1	$x^{2} - x - 3267$	$2$	(2, 0)	$7\cdot 1867$	$2$	$114.319727082$	$114.31972708154967$		✓	✓	$C_2$ (as 2T1)	$[9]$	$[18]$	$2$	$1$	$9.72943173662$	$1$
2.2.14876.1	$x^{2} - 3719$	$2$	(2, 0)	$2^{2}\cdot 3719$	$2$	$121.967208708$	$121.96720870791461$		✓	✓	$C_2$ (as 2T1)	$[9]$	$[18]$	$2$	$1$	$8.91462610976$	$1$
2.2.15629.1	$x^{2} - x - 3907$	$2$	(2, 0)	$15629$	$1$	$125.015998976$	$125.01599897613104$		✓	✓	$C_2$ (as 2T1)	$[9]$	$[9]$	$2$	$1$	$4.82837773116$	$2$

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