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 596377 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	Unit group rank	Regulator
2.0.23.1	$x^{2} - x + 6$	$2$	[0,1]	$-\,23$	$1$	$4.79583152331$	$4.795831523312719$	✓	✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	0	$1$
2.0.31.1	$x^{2} - x + 8$	$2$	[0,1]	$-\,31$	$1$	$5.56776436283$	$5.5677643628300215$	✓	✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	0	$1$
2.0.59.1	$x^{2} - x + 15$	$2$	[0,1]	$-\,59$	$1$	$7.68114574787$	$7.681145747868608$	✓	✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	0	$1$
2.0.83.1	$x^{2} - x + 21$	$2$	[0,1]	$-\,83$	$1$	$9.11043357914$	$9.1104335791443$	✓	✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	0	$1$
2.0.107.1	$x^{2} - x + 27$	$2$	[0,1]	$-\,107$	$1$	$10.3440804328$	$10.344080432788601$	✓	✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	0	$1$
2.0.139.1	$x^{2} - x + 35$	$2$	[0,1]	$-\,139$	$1$	$11.7898261226$	$11.789826122551595$	✓	✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	0	$1$
2.0.211.1	$x^{2} - x + 53$	$2$	[0,1]	$-\,211$	$1$	$14.5258390463$	$14.52583904633395$	✓	✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	0	$1$
2.2.229.1	$x^{2} - x - 57$	$2$	[2,0]	$229$	$1$	$15.1327459504$	$15.132745950421556$		✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	$1$	$2.71246530518$
2.2.257.1	$x^{2} - x - 64$	$2$	[2,0]	$257$	$1$	$16.0312195419$	$16.0312195418814$		✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	$1$	$3.46671103788$
2.0.283.1	$x^{2} - x + 71$	$2$	[0,1]	$-\,283$	$1$	$16.8226038413$	$16.822603841260722$	✓	✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	0	$1$
2.0.307.1	$x^{2} - x + 77$	$2$	[0,1]	$-\,307$	$1$	$17.5214154679$	$17.52141546793523$	✓	✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	0	$1$
2.2.316.1	$x^{2} - 79$	$2$	[2,0]	$2^{2}\cdot 79$	$2$	$17.7763888346$	$17.776388834631177$		✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	$1$	$5.07513475044$
2.2.321.1	$x^{2} - x - 80$	$2$	[2,0]	$3\cdot 107$	$2$	$17.9164728672$	$17.916472867168917$		✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	$1$	$6.06377980031$
2.0.331.1	$x^{2} - x + 83$	$2$	[0,1]	$-\,331$	$1$	$18.1934053987$	$18.193405398660254$	✓	✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	0	$1$
2.0.379.1	$x^{2} - x + 95$	$2$	[0,1]	$-\,379$	$1$	$19.4679223339$	$19.467922333931785$	✓	✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	0	$1$
2.2.469.1	$x^{2} - x - 117$	$2$	[2,0]	$7\cdot 67$	$2$	$21.6564078277$	$21.656407827707714$		✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	$1$	$4.17415049943$
2.2.473.1	$x^{2} - x - 118$	$2$	[2,0]	$11\cdot 43$	$2$	$21.7485631709$	$21.748563170931547$		✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	$1$	$5.15902226812$
2.0.499.1	$x^{2} - x + 125$	$2$	[0,1]	$-\,499$	$1$	$22.3383079037$	$22.338307903688676$	✓	✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	0	$1$
2.0.547.1	$x^{2} - x + 137$	$2$	[0,1]	$-\,547$	$1$	$23.3880311271$	$23.388031127053$	✓	✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	0	$1$
2.2.568.1	$x^{2} - 142$	$2$	[2,0]	$2^{3}\cdot 71$	$2$	$23.8327505756$	$23.83275057562597$		✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	$1$	$5.65597958506$
2.0.643.1	$x^{2} - x + 161$	$2$	[0,1]	$-\,643$	$1$	$25.3574446662$	$25.357444666211933$	✓	✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	0	$1$
2.2.733.1	$x^{2} - x - 183$	$2$	[2,0]	$733$	$1$	$27.0739727414$	$27.073972741361768$		✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	$1$	$3.29720579418$
2.2.761.1	$x^{2} - x - 190$	$2$	[2,0]	$761$	$1$	$27.5862284483$	$27.586228448267445$		✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	$1$	$7.37775929885$
2.0.883.1	$x^{2} - x + 221$	$2$	[0,1]	$-\,883$	$1$	$29.7153159162$	$29.715315916207253$	✓	✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	0	$1$
2.2.892.1	$x^{2} - 223$	$2$	[2,0]	$2^{2}\cdot 223$	$2$	$29.8663690461$	$29.866369046136157$		✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	$1$	$6.10478824992$
2.0.907.1	$x^{2} - x + 227$	$2$	[0,1]	$-\,907$	$1$	$30.1164406928$	$30.116440692751194$	✓	✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	0	$1$
2.2.993.1	$x^{2} - x - 248$	$2$	[2,0]	$3\cdot 331$	$2$	$31.5119025132$	$31.51190251317746$		✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	$1$	$8.57432934711$
2.2.1016.1	$x^{2} - 254$	$2$	[2,0]	$2^{3}\cdot 127$	$2$	$31.874754901$	$31.874754901018456$		✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	$1$	$6.23440688102$
2.2.1101.1	$x^{2} - x - 275$	$2$	[2,0]	$3\cdot 367$	$2$	$33.1813200461$	$33.18132004607411$		✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	$1$	$5.8998898474$
2.2.1229.1	$x^{2} - x - 307$	$2$	[2,0]	$1229$	$1$	$35.0570962859$	$35.05709628591621$		✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	$1$	$3.55616339025$
2.2.1257.1	$x^{2} - x - 314$	$2$	[2,0]	$3\cdot 419$	$2$	$35.4541958025$	$35.45419580247167$		✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	$1$	$12.2199656887$
2.2.1304.1	$x^{2} - 326$	$2$	[2,0]	$2^{3}\cdot 163$	$2$	$36.1109401705$	$36.11094017053558$		✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	$1$	$6.47696999602$
2.2.1373.1	$x^{2} - x - 343$	$2$	[2,0]	$1373$	$1$	$37.0540146273$	$37.05401462729781$		✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	$1$	$3.61164757377$
2.2.1436.1	$x^{2} - 359$	$2$	[2,0]	$2^{2}\cdot 359$	$2$	$37.894590643$	$37.89459064299283$		✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	$1$	$6.57924928299$
2.2.1489.1	$x^{2} - x - 372$	$2$	[2,0]	$1489$	$1$	$38.5875627631$	$38.58756276314948$		✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	$1$	$19.108657903$
2.2.1509.1	$x^{2} - x - 377$	$2$	[2,0]	$3\cdot 503$	$2$	$38.8458491991$	$38.84584919911006$		✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	$1$	$6.22455450807$
2.2.1772.1	$x^{2} - 443$	$2$	[2,0]	$2^{2}\cdot 443$	$2$	$42.0951303597$	$42.09513035969837$		✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	$1$	$6.78445578297$
2.2.1901.1	$x^{2} - x - 475$	$2$	[2,0]	$1901$	$1$	$43.6004587132$	$43.60045871318328$		✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	$1$	$6.07764750381$
2.2.1929.1	$x^{2} - x - 482$	$2$	[2,0]	$3\cdot 643$	$2$	$43.920382512$	$43.9203825119955$		✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	$1$	$19.3512250493$
2.2.1957.1	$x^{2} - x - 489$	$2$	[2,0]	$19\cdot 103$	$2$	$44.2379927212$	$44.23799272118933$		✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	$1$	$6.83410758012$
2.2.2021.1	$x^{2} - x - 505$	$2$	[2,0]	$43\cdot 47$	$2$	$44.955533586$	$44.955533585978046$		✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	$1$	$3.80616829641$
2.2.2089.1	$x^{2} - x - 522$	$2$	[2,0]	$2089$	$1$	$45.7055795281$	$45.70557952810576$		✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	$1$	$22.8072764595$
2.2.2101.1	$x^{2} - x - 525$	$2$	[2,0]	$11\cdot 191$	$2$	$45.8366665455$	$45.83666654546336$		✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	$1$	$10.222014007$
2.2.2177.1	$x^{2} - x - 544$	$2$	[2,0]	$7\cdot 311$	$2$	$46.6583325892$	$46.65833258915282$		✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	$1$	$9.32349046193$
2.2.2213.1	$x^{2} - x - 553$	$2$	[2,0]	$2213$	$1$	$47.0425339454$	$47.042533945356304$		✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	$1$	$3.85059998815$
2.2.2429.1	$x^{2} - x - 607$	$2$	[2,0]	$7\cdot 347$	$2$	$49.2848861214$	$49.28488612140643$		✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	$1$	$5.84353601533$
2.2.2557.1	$x^{2} - x - 639$	$2$	[2,0]	$2557$	$1$	$50.5667875191$	$50.566787519082126$		✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	$1$	$9.54731248874$
2.2.2589.1	$x^{2} - x - 647$	$2$	[2,0]	$3\cdot 863$	$2$	$50.8822169328$	$50.882216932834204$		✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	$1$	$6.76272817043$
2.2.2636.1	$x^{2} - 659$	$2$	[2,0]	$2^{2}\cdot 659$	$2$	$51.341990612$	$51.34199061197374$		✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	$1$	$9.38092666544$
2.2.2677.1	$x^{2} - x - 669$	$2$	[2,0]	$2677$	$1$	$51.7397332811$	$51.73973328110612$		✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	$1$	$8.23668539281$

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