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	CM field	Relative class number

Regulator	$p$ -adic completions	Monogenic	Index	Ines. $p$

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Results (1-50 of 129207 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
2.0.47.1	$x^{2} - x + 12$	$2$	[0,1]	$-\,47$	$1$	$6.8556546004$	$6.855654600401044$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	0	$1$
2.0.79.1	$x^{2} - x + 20$	$2$	[0,1]	$-\,79$	$1$	$8.88819441732$	$8.888194417315589$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	0	$1$
2.0.103.1	$x^{2} - x + 26$	$2$	[0,1]	$-\,103$	$1$	$10.1488915651$	$10.14889156509222$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	0	$1$
2.0.127.1	$x^{2} - x + 32$	$2$	[0,1]	$-\,127$	$1$	$11.2694276696$	$11.269427669584644$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	0	$1$
2.0.131.1	$x^{2} - x + 33$	$2$	[0,1]	$-\,131$	$1$	$11.4455231423$	$11.445523142259598$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	0	$1$
2.0.179.1	$x^{2} - x + 45$	$2$	[0,1]	$-\,179$	$1$	$13.3790881603$	$13.379088160259652$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	0	$1$
2.0.227.1	$x^{2} - x + 57$	$2$	[0,1]	$-\,227$	$1$	$15.0665191733$	$15.066519173319364$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	0	$1$
2.0.347.1	$x^{2} - x + 87$	$2$	[0,1]	$-\,347$	$1$	$18.6279360102$	$18.627936010197157$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	0	$1$
2.2.401.1	$x^{2} - x - 100$	$2$	[2,0]	$401$	$1$	$20.0249843945$	$20.024984394500787$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$3.68950386899$
2.0.443.1	$x^{2} - x + 111$	$2$	[0,1]	$-\,443$	$1$	$21.0475651798$	$21.047565179849187$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	0	$1$
2.0.523.1	$x^{2} - x + 131$	$2$	[0,1]	$-\,523$	$1$	$22.8691932521$	$22.869193252058544$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	0	$1$
2.0.571.1	$x^{2} - x + 143$	$2$	[0,1]	$-\,571$	$1$	$23.8956062907$	$23.895606290697042$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	0	$1$
2.0.619.1	$x^{2} - x + 155$	$2$	[0,1]	$-\,619$	$1$	$24.8797106092$	$24.879710609249457$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	0	$1$
2.0.683.1	$x^{2} - x + 171$	$2$	[0,1]	$-\,683$	$1$	$26.1342686907$	$26.13426869074396$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	0	$1$
2.0.691.1	$x^{2} - x + 173$	$2$	[0,1]	$-\,691$	$1$	$26.2868788562$	$26.28687885618983$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	0	$1$
2.0.739.1	$x^{2} - x + 185$	$2$	[0,1]	$-\,739$	$1$	$27.1845544381$	$27.184554438136374$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	0	$1$
2.0.787.1	$x^{2} - x + 197$	$2$	[0,1]	$-\,787$	$1$	$28.0535202782$	$28.053520278211074$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	0	$1$
2.2.817.1	$x^{2} - x - 204$	$2$	[2,0]	$19\cdot 43$	$2$	$28.5832118559$	$28.583211855912904$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$6.53087550275$
2.0.947.1	$x^{2} - x + 237$	$2$	[0,1]	$-\,947$	$1$	$30.7733651069$	$30.773365106858236$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	0	$1$
2.0.1051.1	$x^{2} - x + 263$	$2$	[0,1]	$-\,1051$	$1$	$32.4191301549$	$32.41913015489465$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	0	$1$
2.2.1093.1	$x^{2} - x - 273$	$2$	[2,0]	$1093$	$1$	$33.0605505096$	$33.06055050963308$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$3.49742457285$
2.0.1123.1	$x^{2} - x + 281$	$2$	[0,1]	$-\,1123$	$1$	$33.5111921602$	$33.51119216023208$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	0	$1$
2.2.1393.1	$x^{2} - x - 348$	$2$	[2,0]	$7\cdot 199$	$2$	$37.322915213$	$37.322915213043046$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$8.87710287839$
2.2.1429.1	$x^{2} - x - 357$	$2$	[2,0]	$1429$	$1$	$37.8021163429$	$37.8021163428716$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$5.24177500862$
2.2.1641.1	$x^{2} - x - 410$	$2$	[2,0]	$3\cdot 547$	$2$	$40.5092582011$	$40.50925820105819$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$9.07680896629$
2.0.1723.1	$x^{2} - x + 431$	$2$	[0,1]	$-\,1723$	$1$	$41.509035161$	$41.50903516103452$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	0	$1$
2.0.1747.1	$x^{2} - x + 437$	$2$	[0,1]	$-\,1747$	$1$	$41.797129088$	$41.79712908801273$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	0	$1$
2.2.1756.1	$x^{2} - 439$	$2$	[2,0]	$2^{2}\cdot 439$	$2$	$41.9046536795$	$41.90465367951393$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$6.77992061615$
2.0.1867.1	$x^{2} - x + 467$	$2$	[0,1]	$-\,1867$	$1$	$43.2087954009$	$43.2087954009366$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	0	$1$
2.2.1897.1	$x^{2} - x - 474$	$2$	[2,0]	$7\cdot 271$	$2$	$43.5545634808$	$43.55456348076513$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$11.3828851143$
2.2.1996.1	$x^{2} - 499$	$2$	[2,0]	$2^{2}\cdot 499$	$2$	$44.6766158074$	$44.67661580737735$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$9.1027551489$
2.2.2081.1	$x^{2} - x - 520$	$2$	[2,0]	$2081$	$1$	$45.6179789118$	$45.617978911828175$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$9.00208544832$
2.2.2153.1	$x^{2} - x - 538$	$2$	[2,0]	$2153$	$1$	$46.4004310325$	$46.400431032480725$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$6.13988919696$
2.0.2203.1	$x^{2} - x + 551$	$2$	[0,1]	$-\,2203$	$1$	$46.9361268108$	$46.93612681080534$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	0	$1$
2.0.2347.1	$x^{2} - x + 587$	$2$	[0,1]	$-\,2347$	$1$	$48.4458460552$	$48.4458460551573$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	0	$1$
2.0.2683.1	$x^{2} - x + 671$	$2$	[0,1]	$-\,2683$	$1$	$51.7976833459$	$51.79768334587948$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	0	$1$
2.2.2908.1	$x^{2} - 727$	$2$	[2,0]	$2^{2}\cdot 727$	$2$	$53.9258750509$	$53.925875050851054$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$7.28344775704$
2.2.3121.1	$x^{2} - x - 780$	$2$	[2,0]	$3121$	$1$	$55.8659108939$	$55.86591089385369$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$17.0428020714$
2.2.3181.1	$x^{2} - x - 795$	$2$	[2,0]	$3181$	$1$	$56.4003546088$	$56.4003546088143$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$6.33505739519$
2.2.3253.1	$x^{2} - x - 813$	$2$	[2,0]	$3253$	$1$	$57.0350769264$	$57.0350769263968$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$4.04335891284$
2.2.3928.1	$x^{2} - 982$	$2$	[2,0]	$2^{3}\cdot 491$	$2$	$62.673758464$	$62.67375846396959$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$9.77984990888$
2.2.3997.1	$x^{2} - x - 999$	$2$	[2,0]	$7\cdot 571$	$2$	$63.2218316723$	$63.221831672294975$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$6.34387734541$
2.2.4353.1	$x^{2} - x - 1088$	$2$	[2,0]	$3\cdot 1451$	$2$	$65.9772688128$	$65.97726881282674$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$8.66664711492$
2.2.4357.1	$x^{2} - x - 1089$	$2$	[2,0]	$4357$	$1$	$66.0075753228$	$66.007575322837$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$4.88285930975$
2.2.4441.1	$x^{2} - x - 1110$	$2$	[2,0]	$4441$	$1$	$66.6408283262$	$66.64082832618455$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$19.808541877$
2.2.4504.1	$x^{2} - 1126$	$2$	[2,0]	$2^{3}\cdot 563$	$2$	$67.1118469423$	$67.11184694225007$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$12.1140121797$
2.2.4757.1	$x^{2} - x - 1189$	$2$	[2,0]	$67\cdot 71$	$2$	$68.9710084021$	$68.97100840208152$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$4.23389639848$
2.2.4889.1	$x^{2} - x - 1222$	$2$	[2,0]	$4889$	$1$	$69.9213844257$	$69.92138442565336$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$13.2457555413$
2.2.5241.1	$x^{2} - x - 1310$	$2$	[2,0]	$3\cdot 1747$	$2$	$72.394751191$	$72.39475119095306$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$16.1271217925$
2.2.5269.1	$x^{2} - x - 1317$	$2$	[2,0]	$11\cdot 479$	$2$	$72.5878777758$	$72.58787777583802$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$9.39074341598$

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Elliptic curves over $\Q$
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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.