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 68750 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
2.0.455.1	$x^{2} - x + 114$	$2$	[0,1]	$-\,5\cdot 7\cdot 13$	$3$	$21.3307290077$	$21.330729007701542$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 10]$	$2$	$1$
2.0.615.1	$x^{2} - x + 154$	$2$	[0,1]	$-\,3\cdot 5\cdot 41$	$3$	$24.7991935353$	$24.79919353527449$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 10]$	$2$	$1$
2.0.776.1	$x^{2} + 194$	$2$	[0,1]	$-\,2^{3}\cdot 97$	$2$	$27.8567765544$	$27.85677655436824$	✓	✓	✓	$C_2$ (as 2T1)	$[20]$	$2$	$1$
2.0.824.1	$x^{2} + 206$	$2$	[0,1]	$-\,2^{3}\cdot 103$	$2$	$28.7054001888$	$28.705400188814647$	✓	✓	✓	$C_2$ (as 2T1)	$[20]$	$2$	$1$
2.0.836.1	$x^{2} + 209$	$2$	[0,1]	$-\,2^{2}\cdot 11\cdot 19$	$3$	$28.9136645896$	$28.91366458960192$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 10]$	$2$	$1$
2.0.920.1	$x^{2} + 230$	$2$	[0,1]	$-\,2^{3}\cdot 5\cdot 23$	$3$	$30.3315017762$	$30.331501776206203$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 10]$	$2$	$1$
2.0.1064.1	$x^{2} + 266$	$2$	[0,1]	$-\,2^{3}\cdot 7\cdot 19$	$3$	$32.6190128606$	$32.61901286060018$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 10]$	$2$	$1$
2.0.1124.1	$x^{2} + 281$	$2$	[0,1]	$-\,2^{2}\cdot 281$	$2$	$33.5261092285$	$33.52610922848042$	✓	✓	✓	$C_2$ (as 2T1)	$[20]$	$2$	$1$
2.0.1160.1	$x^{2} + 290$	$2$	[0,1]	$-\,2^{3}\cdot 5\cdot 29$	$3$	$34.0587727319$	$34.058772731852805$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 10]$	$2$	$1$
2.0.1263.1	$x^{2} - x + 316$	$2$	[0,1]	$-\,3\cdot 421$	$2$	$35.5387112878$	$35.53871128783372$	✓	✓	✓	$C_2$ (as 2T1)	$[20]$	$2$	$1$
2.0.1284.1	$x^{2} + 321$	$2$	[0,1]	$-\,2^{2}\cdot 3\cdot 107$	$3$	$35.8329457343$	$35.832945734337834$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 10]$	$2$	$1$
2.0.1460.1	$x^{2} + 365$	$2$	[0,1]	$-\,2^{2}\cdot 5\cdot 73$	$3$	$38.2099463491$	$38.2099463490856$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 10]$	$2$	$1$
2.0.1495.1	$x^{2} - x + 374$	$2$	[0,1]	$-\,5\cdot 13\cdot 23$	$3$	$38.6652298584$	$38.66522985836241$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 10]$	$2$	$1$
2.0.1524.1	$x^{2} + 381$	$2$	[0,1]	$-\,2^{2}\cdot 3\cdot 127$	$3$	$39.0384425919$	$39.03844259188627$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 10]$	$2$	$1$
2.0.1544.1	$x^{2} + 386$	$2$	[0,1]	$-\,2^{3}\cdot 193$	$2$	$39.2937654088$	$39.293765408777$	✓	✓	✓	$C_2$ (as 2T1)	$[20]$	$2$	$1$
2.0.1592.1	$x^{2} + 398$	$2$	[0,1]	$-\,2^{3}\cdot 199$	$2$	$39.8998746865$	$39.89987468652001$	✓	✓	✓	$C_2$ (as 2T1)	$[20]$	$2$	$1$
2.0.1604.1	$x^{2} + 401$	$2$	[0,1]	$-\,2^{2}\cdot 401$	$2$	$40.049968789$	$40.049968789001575$	✓	✓	✓	$C_2$ (as 2T1)	$[20]$	$2$	$1$
2.0.1652.1	$x^{2} + 413$	$2$	[0,1]	$-\,2^{2}\cdot 7\cdot 59$	$3$	$40.6448028658$	$40.64480286580315$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 10]$	$2$	$1$
2.0.1695.1	$x^{2} - x + 424$	$2$	[0,1]	$-\,3\cdot 5\cdot 113$	$3$	$41.1703777005$	$41.1703777004778$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 10]$	$2$	$1$
2.0.1739.1	$x^{2} - x + 435$	$2$	[0,1]	$-\,37\cdot 47$	$2$	$41.701318924$	$41.701318923986086$	✓	✓	✓	$C_2$ (as 2T1)	$[20]$	$2$	$1$
2.0.1748.1	$x^{2} + 437$	$2$	[0,1]	$-\,2^{2}\cdot 19\cdot 23$	$3$	$41.8090899207$	$41.80908992073375$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 10]$	$2$	$1$
2.0.1796.1	$x^{2} + 449$	$2$	[0,1]	$-\,2^{2}\cdot 449$	$2$	$42.3792402008$	$42.37924020083418$	✓	✓	✓	$C_2$ (as 2T1)	$[20]$	$2$	$1$
2.0.1880.1	$x^{2} + 470$	$2$	[0,1]	$-\,2^{3}\cdot 5\cdot 47$	$3$	$43.3589667774$	$43.3589667773576$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 10]$	$2$	$1$
2.0.1887.1	$x^{2} - x + 472$	$2$	[0,1]	$-\,3\cdot 17\cdot 37$	$3$	$43.4396132579$	$43.439613257946945$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 10]$	$2$	$1$
2.0.1896.1	$x^{2} + 474$	$2$	[0,1]	$-\,2^{3}\cdot 3\cdot 79$	$3$	$43.5430821142$	$43.54308211415448$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 10]$	$2$	$1$
2.0.1928.1	$x^{2} + 482$	$2$	[0,1]	$-\,2^{3}\cdot 241$	$2$	$43.9089968002$	$43.9089968002003$	✓	✓	✓	$C_2$ (as 2T1)	$[20]$	$2$	$1$
2.0.1940.1	$x^{2} + 485$	$2$	[0,1]	$-\,2^{2}\cdot 5\cdot 97$	$3$	$44.0454310911$	$44.04543109109048$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 10]$	$2$	$1$
2.0.1956.1	$x^{2} + 489$	$2$	[0,1]	$-\,2^{2}\cdot 3\cdot 163$	$3$	$44.226688775$	$44.22668877499196$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 10]$	$2$	$1$
2.0.2136.1	$x^{2} + 534$	$2$	[0,1]	$-\,2^{3}\cdot 3\cdot 89$	$3$	$46.2168800332$	$46.216880033165374$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 10]$	$2$	$1$
2.0.2247.1	$x^{2} - x + 562$	$2$	[0,1]	$-\,3\cdot 7\cdot 107$	$3$	$47.402531578$	$47.40253157796533$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 10]$	$2$	$1$
2.0.2360.1	$x^{2} + 590$	$2$	[0,1]	$-\,2^{3}\cdot 5\cdot 59$	$3$	$48.579831206$	$48.579831205964474$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 10]$	$2$	$1$
2.0.2404.1	$x^{2} + 601$	$2$	[0,1]	$-\,2^{2}\cdot 601$	$2$	$49.0306026885$	$49.03060268852505$	✓	✓	✓	$C_2$ (as 2T1)	$[20]$	$2$	$1$
2.0.2407.1	$x^{2} - x + 602$	$2$	[0,1]	$-\,29\cdot 83$	$2$	$49.0611862881$	$49.06118628814432$	✓	✓	✓	$C_2$ (as 2T1)	$[20]$	$2$	$1$
2.0.2483.1	$x^{2} - x + 621$	$2$	[0,1]	$-\,13\cdot 191$	$2$	$49.8297100132$	$49.82971001320397$	✓	✓	✓	$C_2$ (as 2T1)	$[20]$	$2$	$1$
2.0.2487.1	$x^{2} - x + 622$	$2$	[0,1]	$-\,3\cdot 829$	$2$	$49.8698305592$	$49.86983055916673$	✓	✓	✓	$C_2$ (as 2T1)	$[20]$	$2$	$1$
2.0.2532.1	$x^{2} + 633$	$2$	[0,1]	$-\,2^{2}\cdot 3\cdot 211$	$3$	$50.3189825016$	$50.3189825016365$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 10]$	$2$	$1$
2.0.2552.1	$x^{2} + 638$	$2$	[0,1]	$-\,2^{3}\cdot 11\cdot 29$	$3$	$50.5173237613$	$50.51732376126036$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 10]$	$2$	$1$
2.0.2596.1	$x^{2} + 649$	$2$	[0,1]	$-\,2^{2}\cdot 11\cdot 59$	$3$	$50.9509568114$	$50.950956811427986$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 10]$	$2$	$1$
2.0.2603.1	$x^{2} - x + 651$	$2$	[0,1]	$-\,19\cdot 137$	$2$	$51.0196040753$	$51.01960407529639$	✓	✓	✓	$C_2$ (as 2T1)	$[20]$	$2$	$1$
2.0.2712.1	$x^{2} + 678$	$2$	[0,1]	$-\,2^{3}\cdot 3\cdot 113$	$3$	$52.0768662652$	$52.076866265166146$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 10]$	$2$	$1$
2.0.2724.1	$x^{2} + 681$	$2$	[0,1]	$-\,2^{2}\cdot 3\cdot 227$	$3$	$52.1919534028$	$52.191953402799555$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 10]$	$2$	$1$
2.0.2743.1	$x^{2} - x + 686$	$2$	[0,1]	$-\,13\cdot 211$	$2$	$52.3736575007$	$52.373657500693994$	✓	✓	✓	$C_2$ (as 2T1)	$[20]$	$2$	$1$
2.0.2948.1	$x^{2} + 737$	$2$	[0,1]	$-\,2^{2}\cdot 11\cdot 67$	$3$	$54.295487842$	$54.29548784199291$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 10]$	$2$	$1$
2.0.2983.1	$x^{2} - x + 746$	$2$	[0,1]	$-\,19\cdot 157$	$2$	$54.6168472177$	$54.616847217685496$	✓	✓	✓	$C_2$ (as 2T1)	$[20]$	$2$	$1$
2.0.2987.1	$x^{2} - x + 747$	$2$	[0,1]	$-\,29\cdot 103$	$2$	$54.6534536878$	$54.653453687758834$	✓	✓	✓	$C_2$ (as 2T1)	$[20]$	$2$	$1$
2.0.3007.1	$x^{2} - x + 752$	$2$	[0,1]	$-\,31\cdot 97$	$2$	$54.8361194834$	$54.83611948342078$	✓	✓	✓	$C_2$ (as 2T1)	$[20]$	$2$	$1$
2.0.3016.1	$x^{2} + 754$	$2$	[0,1]	$-\,2^{3}\cdot 13\cdot 29$	$3$	$54.918120871$	$54.91812087098393$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 10]$	$2$	$1$
2.0.3076.1	$x^{2} + 769$	$2$	[0,1]	$-\,2^{2}\cdot 769$	$2$	$55.4616984954$	$55.46169849544819$	✓	✓	✓	$C_2$ (as 2T1)	$[20]$	$2$	$1$
2.0.3099.1	$x^{2} - x + 775$	$2$	[0,1]	$-\,3\cdot 1033$	$2$	$55.6686626389$	$55.66866263886712$	✓	✓	✓	$C_2$ (as 2T1)	$[20]$	$2$	$1$
2.0.3103.1	$x^{2} - x + 776$	$2$	[0,1]	$-\,29\cdot 107$	$2$	$55.7045779088$	$55.70457790882182$	✓	✓	✓	$C_2$ (as 2T1)	$[20]$	$2$	$1$

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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.