LMFDB - Number field search results

Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)

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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 314179 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
2.0.87.1	x² - x + 22	$2$	[0,1]	$-\,3\cdot 29$	$2$	$9.32737905309$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.0.104.1	x² + 26	$2$	[0,1]	$-\,2^{3}\cdot 13$	$2$	$10.1980390272$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.0.116.1	x² + 29	$2$	[0,1]	$-\,2^{2}\cdot 29$	$2$	$10.7703296143$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.0.152.1	x² + 38	$2$	[0,1]	$-\,2^{3}\cdot 19$	$2$	$12.3288280059$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.0.212.1	x² + 53	$2$	[0,1]	$-\,2^{2}\cdot 53$	$2$	$14.5602197786$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.0.244.1	x² + 61	$2$	[0,1]	$-\,2^{2}\cdot 61$	$2$	$15.6204993518$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.0.247.1	x² - x + 62	$2$	[0,1]	$-\,13\cdot 19$	$2$	$15.7162336455$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.0.339.1	x² - x + 85	$2$	[0,1]	$-\,3\cdot 113$	$2$	$18.4119526395$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.0.411.1	x² - x + 103	$2$	[0,1]	$-\,3\cdot 137$	$2$	$20.2731349327$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.0.424.1	x² + 106	$2$	[0,1]	$-\,2^{3}\cdot 53$	$2$	$20.591260282$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.0.436.1	x² + 109	$2$	[0,1]	$-\,2^{2}\cdot 109$	$2$	$20.8806130178$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.0.451.1	x² - x + 113	$2$	[0,1]	$-\,11\cdot 41$	$2$	$21.2367605816$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.0.472.1	x² + 118	$2$	[0,1]	$-\,2^{3}\cdot 59$	$2$	$21.7255609824$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.0.515.1	x² - x + 129	$2$	[0,1]	$-\,5\cdot 103$	$2$	$22.6936114358$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.0.628.1	x² + 157	$2$	[0,1]	$-\,2^{2}\cdot 157$	$2$	$25.0599281723$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.2.697.1	x² - x - 174	$2$	[2,0]	$17\cdot 41$	$2$	$26.4007575649$		✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$1$	$5.57596345086$
2.0.707.1	x² - x + 177	$2$	[0,1]	$-\,7\cdot 101$	$2$	$26.5894716006$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.0.771.1	x² - x + 193	$2$	[0,1]	$-\,3\cdot 257$	$2$	$27.7668867538$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.2.785.1	x² - x - 196	$2$	[2,0]	$5\cdot 157$	$2$	$28.0178514522$		✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$1$	$4.02567041587$
2.0.808.1	x² + 202	$2$	[0,1]	$-\,2^{3}\cdot 101$	$2$	$28.4253408071$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.0.835.1	x² - x + 209	$2$	[0,1]	$-\,5\cdot 167$	$2$	$28.8963665536$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.0.843.1	x² - x + 211	$2$	[0,1]	$-\,3\cdot 281$	$2$	$29.0344622819$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.0.856.1	x² + 214	$2$	[0,1]	$-\,2^{3}\cdot 107$	$2$	$29.2574776767$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.2.940.1	x² - 235	$2$	[2,0]	$2^{2}\cdot 5\cdot 47$	$3$	$30.6594194335$		✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$1$	$4.52167040866$
2.2.985.1	x² - x - 246	$2$	[2,0]	$5\cdot 197$	$2$	$31.384709653$		✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$1$	$6.70441585679$
2.0.1048.1	x² + 262	$2$	[0,1]	$-\,2^{3}\cdot 131$	$2$	$32.3728281125$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.0.1059.1	x² - x + 265	$2$	[0,1]	$-\,3\cdot 353$	$2$	$32.5422801905$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.0.1099.1	x² - x + 275	$2$	[0,1]	$-\,7\cdot 157$	$2$	$33.1511689085$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.0.1108.1	x² + 277	$2$	[0,1]	$-\,2^{2}\cdot 277$	$2$	$33.2866339542$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.0.1147.1	x² - x + 287	$2$	[0,1]	$-\,31\cdot 37$	$2$	$33.8673884438$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.0.1192.1	x² + 298	$2$	[0,1]	$-\,2^{3}\cdot 149$	$2$	$34.5253530033$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.0.1203.1	x² - x + 301	$2$	[0,1]	$-\,3\cdot 401$	$2$	$34.684290392$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.0.1219.1	x² - x + 305	$2$	[0,1]	$-\,23\cdot 53$	$2$	$34.9141805002$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.0.1267.1	x² - x + 317	$2$	[0,1]	$-\,7\cdot 181$	$2$	$35.5949434611$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.0.1315.1	x² - x + 329	$2$	[0,1]	$-\,5\cdot 263$	$2$	$36.2629287289$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.2.1345.1	x² - x - 336	$2$	[2,0]	$5\cdot 269$	$2$	$36.6742416418$		✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$1$	$9.17802375983$
2.0.1347.1	x² - x + 337	$2$	[0,1]	$-\,3\cdot 449$	$2$	$36.701498607$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.0.1363.1	x² - x + 341	$2$	[0,1]	$-\,29\cdot 47$	$2$	$36.9188298839$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.2.1384.1	x² - 346	$2$	[2,0]	$2^{3}\cdot 173$	$2$	$37.2021504755$		✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$1$	$5.22577557754$
2.0.1432.1	x² + 358	$2$	[0,1]	$-\,2^{3}\cdot 179$	$2$	$37.8417758568$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.0.1563.1	x² - x + 391	$2$	[0,1]	$-\,3\cdot 521$	$2$	$39.5347948015$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.0.1588.1	x² + 397	$2$	[0,1]	$-\,2^{2}\cdot 397$	$2$	$39.8497176903$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.0.1603.1	x² - x + 401	$2$	[0,1]	$-\,7\cdot 229$	$2$	$40.0374824383$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.2.1708.1	x² - 427	$2$	[2,0]	$2^{2}\cdot 7\cdot 61$	$3$	$41.3279566395$		✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$1$	$4.82021652284$
2.2.1765.1	x² - x - 441	$2$	[2,0]	$5\cdot 353$	$2$	$42.0119030752$		✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$1$	$4.43095849208$
2.0.1843.1	x² - x + 461	$2$	[0,1]	$-\,19\cdot 97$	$2$	$42.9301758673$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.0.1915.1	x² - x + 479	$2$	[0,1]	$-\,5\cdot 383$	$2$	$43.7607129741$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.2.1937.1	x² - x - 484	$2$	[2,0]	$13\cdot 149$	$2$	$44.0113621693$		✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$1$	$4.4774659217$
2.0.1963.1	x² - x + 491	$2$	[0,1]	$-\,13\cdot 151$	$2$	$44.3057558338$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.2.2024.1	x² - 506	$2$	[2,0]	$2^{3}\cdot 11\cdot 23$	$3$	$44.9888875168$		✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$1$	$4.49968619067$

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