LMFDB - Number field search results

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Degree	Signature	Class number	Class group structure	CM field

Ramified prime count	Ramified	Unramified primes	Galois group	Galois

Discriminant	Root discriminant	Galois root discriminant	Regulator	Intermediate field

$p$-adic completions	Minimal sibling	Monogenic	Index	Ines. $p$

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Results (1-50 of 14248 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	Unit group torsion	Regulator
2.0.591.1	$x^{2} - x + 148$	$2$	[0,1]	$-\,3\cdot 197$	$2$	$24.3104915623$	$24.310491562286437$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.623.1	$x^{2} - x + 156$	$2$	[0,1]	$-\,7\cdot 89$	$2$	$24.9599679487$	$24.95996794869737$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.767.1	$x^{2} - x + 192$	$2$	[0,1]	$-\,13\cdot 59$	$2$	$27.6947648483$	$27.694764848252458$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.871.1	$x^{2} - x + 218$	$2$	[0,1]	$-\,13\cdot 67$	$2$	$29.5127091267$	$29.512709126747414$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.879.1	$x^{2} - x + 220$	$2$	[0,1]	$-\,3\cdot 293$	$2$	$29.6479341607$	$29.647934160747187$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.1076.1	$x^{2} + 269$	$2$	[0,1]	$-\,2^{2}\cdot 269$	$2$	$32.8024389337$	$32.802438933713454$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.1111.1	$x^{2} - x + 278$	$2$	[0,1]	$-\,11\cdot 101$	$2$	$33.331666625$	$33.331666624997915$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.1167.1	$x^{2} - x + 292$	$2$	[0,1]	$-\,3\cdot 389$	$2$	$34.1613817051$	$34.161381705077446$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.1304.1	$x^{2} + 326$	$2$	[0,1]	$-\,2^{3}\cdot 163$	$2$	$36.1109401705$	$36.11094017053558$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.1556.1	$x^{2} + 389$	$2$	[0,1]	$-\,2^{2}\cdot 389$	$2$	$39.4461658466$	$39.44616584663204$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.1591.1	$x^{2} - x + 398$	$2$	[0,1]	$-\,37\cdot 43$	$2$	$39.8873413504$	$39.88734135035826$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.1639.1	$x^{2} - x + 410$	$2$	[0,1]	$-\,11\cdot 149$	$2$	$40.48456496$	$40.48456495999432$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.1903.1	$x^{2} - x + 476$	$2$	[0,1]	$-\,11\cdot 173$	$2$	$43.6233882224$	$43.62338822237447$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.2215.1	$x^{2} - x + 554$	$2$	[0,1]	$-\,5\cdot 443$	$2$	$47.063786503$	$47.06378650300037$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.2216.1	$x^{2} + 554$	$2$	[0,1]	$-\,2^{3}\cdot 277$	$2$	$47.0744091838$	$47.07440918375928$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.2263.1	$x^{2} - x + 566$	$2$	[0,1]	$-\,31\cdot 73$	$2$	$47.5709995691$	$47.57099956906519$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.2435.1	$x^{2} - x + 609$	$2$	[0,1]	$-\,5\cdot 487$	$2$	$49.3457191659$	$49.34571916590131$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.2623.1	$x^{2} - x + 656$	$2$	[0,1]	$-\,43\cdot 61$	$2$	$51.2152321092$	$51.21523210920751$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.2648.1	$x^{2} + 662$	$2$	[0,1]	$-\,2^{3}\cdot 331$	$2$	$51.4587213211$	$51.45872132107443$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.2815.1	$x^{2} - x + 704$	$2$	[0,1]	$-\,5\cdot 563$	$2$	$53.0565735795$	$53.056573579529235$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.2863.1	$x^{2} - x + 716$	$2$	[0,1]	$-\,7\cdot 409$	$2$	$53.5070088867$	$53.50700888668698$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.2935.1	$x^{2} - x + 734$	$2$	[0,1]	$-\,5\cdot 587$	$2$	$54.1756402823$	$54.17564028232615$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.3032.1	$x^{2} + 758$	$2$	[0,1]	$-\,2^{3}\cdot 379$	$2$	$55.0635995917$	$55.06359959174482$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.3151.1	$x^{2} - x + 788$	$2$	[0,1]	$-\,23\cdot 137$	$2$	$56.1337688027$	$56.133768802744754$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.3316.1	$x^{2} + 829$	$2$	[0,1]	$-\,2^{2}\cdot 829$	$2$	$57.5847201956$	$57.584720195551874$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.3563.1	$x^{2} - x + 891$	$2$	[0,1]	$-\,7\cdot 509$	$2$	$59.6908703237$	$59.69087032369355$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.3587.1	$x^{2} - x + 897$	$2$	[0,1]	$-\,17\cdot 211$	$2$	$59.8915686888$	$59.89156868875618$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.3827.1	$x^{2} - x + 957$	$2$	[0,1]	$-\,43\cdot 89$	$2$	$61.8627513129$	$61.862751312886175$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.4084.1	$x^{2} + 1021$	$2$	[0,1]	$-\,2^{2}\cdot 1021$	$2$	$63.9061812347$	$63.90618123468183$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.4115.1	$x^{2} - x + 1029$	$2$	[0,1]	$-\,5\cdot 823$	$2$	$64.1482657599$	$64.1482657598785$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.4163.1	$x^{2} - x + 1041$	$2$	[0,1]	$-\,23\cdot 181$	$2$	$64.5213143078$	$64.52131430775415$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.4328.1	$x^{2} + 1082$	$2$	[0,1]	$-\,2^{3}\cdot 541$	$2$	$65.7875368136$	$65.7875368135941$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.4456.1	$x^{2} + 1114$	$2$	[0,1]	$-\,2^{3}\cdot 557$	$2$	$66.7532770731$	$66.75327707311455$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.4504.1	$x^{2} + 1126$	$2$	[0,1]	$-\,2^{3}\cdot 563$	$2$	$67.1118469423$	$67.11184694225007$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.4667.1	$x^{2} - x + 1167$	$2$	[0,1]	$-\,13\cdot 359$	$2$	$68.315444813$	$68.31544481301428$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.4811.1	$x^{2} - x + 1203$	$2$	[0,1]	$-\,17\cdot 283$	$2$	$69.3613725354$	$69.36137253543934$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.5383.1	$x^{2} - x + 1346$	$2$	[0,1]	$-\,7\cdot 769$	$2$	$73.3689307541$	$73.36893075410055$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.5416.1	$x^{2} + 1354$	$2$	[0,1]	$-\,2^{3}\cdot 677$	$2$	$73.5934779719$	$73.59347797189639$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.5603.1	$x^{2} - x + 1401$	$2$	[0,1]	$-\,13\cdot 431$	$2$	$74.8531896448$	$74.85318964479737$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.5716.1	$x^{2} + 1429$	$2$	[0,1]	$-\,2^{2}\cdot 1429$	$2$	$75.6042326857$	$75.6042326857432$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.5739.1	$x^{2} - x + 1435$	$2$	[0,1]	$-\,3\cdot 1913$	$2$	$75.7561878661$	$75.75618786607468$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.5972.1	$x^{2} + 1493$	$2$	[0,1]	$-\,2^{2}\cdot 1493$	$2$	$77.2787163454$	$77.27871634544663$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.6019.1	$x^{2} - x + 1505$	$2$	[0,1]	$-\,13\cdot 463$	$2$	$77.5822144567$	$77.58221445666526$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.6127.1	$x^{2} - x + 1532$	$2$	[0,1]	$-\,11\cdot 557$	$2$	$78.2751557009$	$78.27515570089912$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.6243.1	$x^{2} - x + 1561$	$2$	[0,1]	$-\,3\cdot 2081$	$2$	$79.0126572139$	$79.012657213892$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.6616.1	$x^{2} + 1654$	$2$	[0,1]	$-\,2^{3}\cdot 827$	$2$	$81.3387976307$	$81.33879763065102$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.6772.1	$x^{2} + 1693$	$2$	[0,1]	$-\,2^{2}\cdot 1693$	$2$	$82.2921624458$	$82.29216244576394$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.6819.1	$x^{2} - x + 1705$	$2$	[0,1]	$-\,3\cdot 2273$	$2$	$82.5772365728$	$82.57723657279892$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.7179.1	$x^{2} - x + 1795$	$2$	[0,1]	$-\,3\cdot 2393$	$2$	$84.7289796941$	$84.72897969408106$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$
2.0.7235.1	$x^{2} - x + 1809$	$2$	[0,1]	$-\,5\cdot 1447$	$2$	$85.0588031893$	$85.05880318932309$	✓	✓	✓	$C_2$ (as 2T1)	$[22]$	$2$	$1$

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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.