Number field search results

Note: Search results may be incomplete due to uncomputed quantities: Class number (199205 objects)

Degree	Signature	Class number	Class group structure	CM field
Ramified prime count	Ramified	Unramified primes	Galois group	Is Galois
Discriminant	Root discriminant	Regulator	Intermediate field	$p$-adic completions
Monogenic	Index	Ines. \(p\)

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Results (1-50 of 129132 matches)

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Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	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]	$-\,47$	$$	$6.8556546004$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$0$	$1$
2.0.79.1	x^2 - x + 20	$2$	[0,1]	$-\,79$	$$	$8.88819441732$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$0$	$1$
2.0.103.1	x^2 - x + 26	$2$	[0,1]	$-\,103$	$$	$10.1488915651$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$0$	$1$
2.0.127.1	x^2 - x + 32	$2$	[0,1]	$-\,127$	$$	$11.2694276696$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$0$	$1$
2.0.131.1	x^2 - x + 33	$2$	[0,1]	$-\,131$	$$	$11.4455231423$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$0$	$1$
2.0.179.1	x^2 - x + 45	$2$	[0,1]	$-\,179$	$$	$13.3790881603$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$0$	$1$
2.0.227.1	x^2 - x + 57	$2$	[0,1]	$-\,227$	$$	$15.0665191733$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$0$	$1$
2.0.347.1	x^2 - x + 87	$2$	[0,1]	$-\,347$	$$	$18.6279360102$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$0$	$1$
2.2.401.1	x^2 - x - 100	$2$	[2,0]	$401$	$$	$20.0249843945$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$3.68950386899$
2.0.443.1	x^2 - x + 111	$2$	[0,1]	$-\,443$	$$	$21.0475651798$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$0$	$1$
2.0.523.1	x^2 - x + 131	$2$	[0,1]	$-\,523$	$$	$22.8691932521$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$0$	$1$
2.0.571.1	x^2 - x + 143	$2$	[0,1]	$-\,571$	$$	$23.8956062907$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$0$	$1$
2.0.619.1	x^2 - x + 155	$2$	[0,1]	$-\,619$	$$	$24.8797106092$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$0$	$1$
2.0.683.1	x^2 - x + 171	$2$	[0,1]	$-\,683$	$$	$26.1342686907$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$0$	$1$
2.0.691.1	x^2 - x + 173	$2$	[0,1]	$-\,691$	$$	$26.2868788562$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$0$	$1$
2.0.739.1	x^2 - x + 185	$2$	[0,1]	$-\,739$	$$	$27.1845544381$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$0$	$1$
2.0.787.1	x^2 - x + 197	$2$	[0,1]	$-\,787$	$$	$28.0535202782$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$0$	$1$
2.2.817.1	x^2 - x - 204	$2$	[2,0]	$19\cdot 43$	$$	$28.5832118559$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$6.53087550275$
2.0.947.1	x^2 - x + 237	$2$	[0,1]	$-\,947$	$$	$30.7733651069$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$0$	$1$
2.0.1051.1	x^2 - x + 263	$2$	[0,1]	$-\,1051$	$$	$32.4191301549$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$0$	$1$
2.2.1093.1	x^2 - x - 273	$2$	[2,0]	$1093$	$$	$33.0605505096$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$3.49742457285$
2.0.1123.1	x^2 - x + 281	$2$	[0,1]	$-\,1123$	$$	$33.5111921602$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$0$	$1$
2.2.1393.1	x^2 - x - 348	$2$	[2,0]	$7\cdot 199$	$$	$37.322915213$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$8.87710287839$
2.2.1429.1	x^2 - x - 357	$2$	[2,0]	$1429$	$$	$37.8021163429$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$5.24177500862$
2.2.1641.1	x^2 - x - 410	$2$	[2,0]	$3\cdot 547$	$$	$40.5092582011$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$9.07680896629$
2.0.1723.1	x^2 - x + 431	$2$	[0,1]	$-\,1723$	$$	$41.509035161$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$0$	$1$
2.0.1747.1	x^2 - x + 437	$2$	[0,1]	$-\,1747$	$$	$41.797129088$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$0$	$1$
2.2.1756.1	x^2 - 439	$2$	[2,0]	$2^{2}\cdot 439$	$$	$41.9046536795$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$6.77992061615$
2.0.1867.1	x^2 - x + 467	$2$	[0,1]	$-\,1867$	$$	$43.2087954009$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$0$	$1$
2.2.1897.1	x^2 - x - 474	$2$	[2,0]	$7\cdot 271$	$$	$43.5545634808$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$11.3828851143$
2.2.1996.1	x^2 - 499	$2$	[2,0]	$2^{2}\cdot 499$	$$	$44.6766158074$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$9.1027551489$
2.2.2081.1	x^2 - x - 520	$2$	[2,0]	$2081$	$$	$45.6179789118$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$9.00208544832$
2.2.2153.1	x^2 - x - 538	$2$	[2,0]	$2153$	$$	$46.4004310325$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$6.13988919696$
2.0.2203.1	x^2 - x + 551	$2$	[0,1]	$-\,2203$	$$	$46.9361268108$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$0$	$1$
2.0.2347.1	x^2 - x + 587	$2$	[0,1]	$-\,2347$	$$	$48.4458460552$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$0$	$1$
2.0.2683.1	x^2 - x + 671	$2$	[0,1]	$-\,2683$	$$	$51.7976833459$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$0$	$1$
2.2.2908.1	x^2 - 727	$2$	[2,0]	$2^{2}\cdot 727$	$$	$53.9258750509$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$7.28344775704$
2.2.3121.1	x^2 - x - 780	$2$	[2,0]	$3121$	$$	$55.8659108939$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$17.0428020714$
2.2.3181.1	x^2 - x - 795	$2$	[2,0]	$3181$	$$	$56.4003546088$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$6.33505739519$
2.2.3253.1	x^2 - x - 813	$2$	[2,0]	$3253$	$$	$57.0350769264$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$4.04335891284$
2.2.3928.1	x^2 - 982	$2$	[2,0]	$2^{3}\cdot 491$	$$	$62.673758464$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$9.77984990888$
2.2.3997.1	x^2 - x - 999	$2$	[2,0]	$7\cdot 571$	$$	$63.2218316723$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$6.34387734541$
2.2.4353.1	x^2 - x - 1088	$2$	[2,0]	$3\cdot 1451$	$$	$65.9772688128$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$8.66664711492$
2.2.4357.1	x^2 - x - 1089	$2$	[2,0]	$4357$	$$	$66.0075753228$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$4.88285930975$
2.2.4441.1	x^2 - x - 1110	$2$	[2,0]	$4441$	$$	$66.6408283262$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$19.808541877$
2.2.4504.1	x^2 - 1126	$2$	[2,0]	$2^{3}\cdot 563$	$$	$67.1118469423$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$12.1140121797$
2.2.4757.1	x^2 - x - 1189	$2$	[2,0]	$67\cdot 71$	$$	$68.9710084021$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$4.23389639848$
2.2.4889.1	x^2 - x - 1222	$2$	[2,0]	$4889$	$$	$69.9213844257$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$13.2457555413$
2.2.5241.1	x^2 - x - 1310	$2$	[2,0]	$3\cdot 1747$	$$	$72.394751191$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$16.1271217925$
2.2.5269.1	x^2 - x - 1317	$2$	[2,0]	$11\cdot 479$	$$	$72.5878777758$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$9.39074341598$

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