LMFDB - Number field search results

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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

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Results (1-50 of 13835 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
2.0.167.1	$x^{2} - x + 42$	$2$	[0,1]	$-\,167$	$1$	$12.9228479833$	$12.922847983320086$	✓	✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	0	$1$
2.0.271.1	$x^{2} - x + 68$	$2$	[0,1]	$-\,271$	$1$	$16.4620776332$	$16.46207763315433$	✓	✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	0	$1$
2.0.659.1	$x^{2} - x + 165$	$2$	[0,1]	$-\,659$	$1$	$25.670995306$	$25.67099530598687$	✓	✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	0	$1$
2.0.967.1	$x^{2} - x + 242$	$2$	[0,1]	$-\,967$	$1$	$31.0966236109$	$31.096623610932426$	✓	✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	0	$1$
2.0.1283.1	$x^{2} - x + 321$	$2$	[0,1]	$-\,1283$	$1$	$35.8189893771$	$35.81898937714463$	✓	✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	0	$1$
2.2.1297.1	$x^{2} - x - 324$	$2$	[2,0]	$1297$	$1$	$36.0138862107$	$36.013886210738214$		✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	$1$	$4.27685896446$
2.0.1303.1	$x^{2} - x + 326$	$2$	[0,1]	$-\,1303$	$1$	$36.0970912956$	$36.09709129556009$	✓	✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	0	$1$
2.0.1307.1	$x^{2} - x + 327$	$2$	[0,1]	$-\,1307$	$1$	$36.1524549651$	$36.15245496505044$	✓	✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	0	$1$
2.0.1459.1	$x^{2} - x + 365$	$2$	[0,1]	$-\,1459$	$1$	$38.1968585096$	$38.19685850956856$	✓	✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	0	$1$
2.0.1531.1	$x^{2} - x + 383$	$2$	[0,1]	$-\,1531$	$1$	$39.127995093$	$39.1279950930277$	✓	✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	0	$1$
2.0.1699.1	$x^{2} - x + 425$	$2$	[0,1]	$-\,1699$	$1$	$41.218927691$	$41.2189276910499$	✓	✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	0	$1$
2.0.2027.1	$x^{2} - x + 507$	$2$	[0,1]	$-\,2027$	$1$	$45.022216738$	$45.02221673796171$	✓	✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	0	$1$
2.0.2267.1	$x^{2} - x + 567$	$2$	[0,1]	$-\,2267$	$1$	$47.6130234285$	$47.61302342846965$	✓	✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	0	$1$
2.0.2539.1	$x^{2} - x + 635$	$2$	[0,1]	$-\,2539$	$1$	$50.3884907494$	$50.38849074937649$	✓	✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	0	$1$
2.0.2731.1	$x^{2} - x + 683$	$2$	[0,1]	$-\,2731$	$1$	$52.2589705218$	$52.25897052181568$	✓	✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	0	$1$
2.0.2851.1	$x^{2} - x + 713$	$2$	[0,1]	$-\,2851$	$1$	$53.3947562968$	$53.39475629684998$	✓	✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	0	$1$
2.0.2971.1	$x^{2} - x + 743$	$2$	[0,1]	$-\,2971$	$1$	$54.5068802996$	$54.506880299646575$	✓	✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	0	$1$
2.0.3203.1	$x^{2} - x + 801$	$2$	[0,1]	$-\,3203$	$1$	$56.5950527873$	$56.595052787324086$	✓	✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	0	$1$
2.0.3347.1	$x^{2} - x + 837$	$2$	[0,1]	$-\,3347$	$1$	$57.8532626565$	$57.85326265648291$	✓	✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	0	$1$
2.0.3499.1	$x^{2} - x + 875$	$2$	[0,1]	$-\,3499$	$1$	$59.1523456847$	$59.15234568468101$	✓	✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	0	$1$
2.0.3739.1	$x^{2} - x + 935$	$2$	[0,1]	$-\,3739$	$1$	$61.1473629848$	$61.14736298484179$	✓	✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	0	$1$
2.0.3931.1	$x^{2} - x + 983$	$2$	[0,1]	$-\,3931$	$1$	$62.6976873577$	$62.69768735766894$	✓	✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	0	$1$
2.2.4009.1	$x^{2} - x - 1002$	$2$	[2,0]	$19\cdot 211$	$2$	$63.3166644731$	$63.31666447310692$		✓	✓	$C_2$ (as 2T1)	$[11]$	$[22]$	$2$	$1$	$8.93564031643$
2.0.4051.1	$x^{2} - x + 1013$	$2$	[0,1]	$-\,4051$	$1$	$63.6474665639$	$63.647466563878254$	✓	✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	0	$1$
2.0.5179.1	$x^{2} - x + 1295$	$2$	[0,1]	$-\,5179$	$1$	$71.9652694013$	$71.96526940128828$	✓	✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	0	$1$
2.0.5683.1	$x^{2} - x + 1421$	$2$	[0,1]	$-\,5683$	$1$	$75.3856750318$	$75.38567503179898$	✓	✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	0	$1$
2.2.6081.1	$x^{2} - x - 1520$	$2$	[2,0]	$3\cdot 2027$	$2$	$77.9807668595$	$77.9807668595276$		✓	✓	$C_2$ (as 2T1)	$[11]$	$[22]$	$2$	$1$	$9.00085313191$
2.0.6163.1	$x^{2} - x + 1541$	$2$	[0,1]	$-\,6163$	$1$	$78.5047769247$	$78.50477692471968$	✓	✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	0	$1$
2.0.6547.1	$x^{2} - x + 1637$	$2$	[0,1]	$-\,6547$	$1$	$80.9135340966$	$80.9135340965898$	✓	✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	0	$1$
2.0.7027.1	$x^{2} - x + 1757$	$2$	[0,1]	$-\,7027$	$1$	$83.8272032219$	$83.82720322186587$	✓	✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	0	$1$
2.0.7507.1	$x^{2} - x + 1877$	$2$	[0,1]	$-\,7507$	$1$	$86.6429454716$	$86.64294547163087$	✓	✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	0	$1$
2.0.7603.1	$x^{2} - x + 1901$	$2$	[0,1]	$-\,7603$	$1$	$87.1951833532$	$87.19518335321051$	✓	✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	0	$1$
2.0.7867.1	$x^{2} - x + 1967$	$2$	[0,1]	$-\,7867$	$1$	$88.6961103995$	$88.69611039949835$	✓	✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	0	$1$
2.0.8443.1	$x^{2} - x + 2111$	$2$	[0,1]	$-\,8443$	$1$	$91.8857986851$	$91.88579868510693$	✓	✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	0	$1$
2.0.9283.1	$x^{2} - x + 2321$	$2$	[0,1]	$-\,9283$	$1$	$96.3483263996$	$96.34832639957997$	✓	✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	0	$1$
2.0.9403.1	$x^{2} - x + 2351$	$2$	[0,1]	$-\,9403$	$1$	$96.9690672328$	$96.96906723280368$	✓	✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	0	$1$
2.0.9643.1	$x^{2} - x + 2411$	$2$	[0,1]	$-\,9643$	$1$	$98.1987779965$	$98.19877799647$	✓	✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	0	$1$
2.0.9787.1	$x^{2} - x + 2447$	$2$	[0,1]	$-\,9787$	$1$	$98.9292676613$	$98.92926766129425$	✓	✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	0	$1$
2.2.10401.1	$x^{2} - x - 2600$	$2$	[2,0]	$3\cdot 3467$	$2$	$101.985293057$	$101.98529305738157$		✓	✓	$C_2$ (as 2T1)	$[11]$	$[22]$	$2$	$1$	$9.53748350811$
2.0.10987.1	$x^{2} - x + 2747$	$2$	[0,1]	$-\,10987$	$1$	$104.818891427$	$104.81889142707053$	✓	✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	0	$1$
2.2.12161.1	$x^{2} - x - 3040$	$2$	[2,0]	$12161$	$1$	$110.27692415$	$110.27692415006868$		✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	$1$	$9.57052914008$
2.2.12281.1	$x^{2} - x - 3070$	$2$	[2,0]	$12281$	$1$	$110.819673344$	$110.81967334368028$		✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	$1$	$9.51192535507$
2.2.12589.1	$x^{2} - x - 3147$	$2$	[2,0]	$12589$	$1$	$112.20071301$	$112.2007130102122$		✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	$1$	$6.32972408293$
2.0.13003.1	$x^{2} - x + 3251$	$2$	[0,1]	$-\,13003$	$1$	$114.030697621$	$114.03069762129844$	✓	✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	0	$1$
2.0.13267.1	$x^{2} - x + 3317$	$2$	[0,1]	$-\,13267$	$1$	$115.182463943$	$115.18246394308467$	✓	✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	0	$1$
2.2.14009.1	$x^{2} - x - 3502$	$2$	[2,0]	$14009$	$1$	$118.359621493$	$118.35962149314267$		✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	$1$	$11.2257765839$
2.0.14107.1	$x^{2} - x + 3527$	$2$	[0,1]	$-\,14107$	$1$	$118.77289253$	$118.77289253024026$	✓	✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	0	$1$
2.0.14683.1	$x^{2} - x + 3671$	$2$	[0,1]	$-\,14683$	$1$	$121.173429431$	$121.17342943071307$	✓	✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	0	$1$
2.0.15667.1	$x^{2} - x + 3917$	$2$	[0,1]	$-\,15667$	$1$	$125.167887255$	$125.1678872554778$	✓	✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	0	$1$
2.2.16333.1	$x^{2} - x - 4083$	$2$	[2,0]	$16333$	$1$	$127.800625977$	$127.80062597655773$		✓	✓	$C_2$ (as 2T1)	$[11]$	$[11]$	$2$	$1$	$6.45990690342$

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