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 868379 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
2.0.95.1	x^2 - x + 24	$2$	[0,1]	$-\,5\cdot 19$	$$	$9.74679434481$	✓	✓	✓	$C_2$ (as 2T1)	$[8]$	$2$	$0$	$1$
2.0.111.1	x^2 - x + 28	$2$	[0,1]	$-\,3\cdot 37$	$$	$10.5356537529$	✓	✓	✓	$C_2$ (as 2T1)	$[8]$	$2$	$0$	$1$
2.0.164.1	x^2 + 41	$2$	[0,1]	$-\,2^{2}\cdot 41$	$$	$12.8062484749$	✓	✓	✓	$C_2$ (as 2T1)	$[8]$	$2$	$0$	$1$
2.0.183.1	x^2 - x + 46	$2$	[0,1]	$-\,3\cdot 61$	$$	$13.5277492585$	✓	✓	✓	$C_2$ (as 2T1)	$[8]$	$2$	$0$	$1$
2.0.248.1	x^2 + 62	$2$	[0,1]	$-\,2^{3}\cdot 31$	$$	$15.748015748$	✓	✓	✓	$C_2$ (as 2T1)	$[8]$	$2$	$0$	$1$
2.0.260.1	x^2 + 65	$2$	[0,1]	$-\,2^{2}\cdot 5\cdot 13$	$$	$16.1245154966$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 4]$	$2$	$0$	$1$
2.0.264.1	x^2 + 66	$2$	[0,1]	$-\,2^{3}\cdot 3\cdot 11$	$$	$16.2480768093$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 4]$	$2$	$0$	$1$
2.0.276.1	x^2 + 69	$2$	[0,1]	$-\,2^{2}\cdot 3\cdot 23$	$$	$16.6132477258$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 4]$	$2$	$0$	$1$
2.0.295.1	x^2 - x + 74	$2$	[0,1]	$-\,5\cdot 59$	$$	$17.1755640373$	✓	✓	✓	$C_2$ (as 2T1)	$[8]$	$2$	$0$	$1$
2.0.299.1	x^2 - x + 75	$2$	[0,1]	$-\,13\cdot 23$	$$	$17.2916164658$	✓	✓	✓	$C_2$ (as 2T1)	$[8]$	$2$	$0$	$1$
2.0.308.1	x^2 + 77	$2$	[0,1]	$-\,2^{2}\cdot 7\cdot 11$	$$	$17.5499287748$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 4]$	$2$	$0$	$1$
2.0.371.1	x^2 - x + 93	$2$	[0,1]	$-\,7\cdot 53$	$$	$19.2613602843$	✓	✓	✓	$C_2$ (as 2T1)	$[8]$	$2$	$0$	$1$
2.0.376.1	x^2 + 94	$2$	[0,1]	$-\,2^{3}\cdot 47$	$$	$19.3907194297$	✓	✓	✓	$C_2$ (as 2T1)	$[8]$	$2$	$0$	$1$
2.0.395.1	x^2 - x + 99	$2$	[0,1]	$-\,5\cdot 79$	$$	$19.8746069144$	✓	✓	✓	$C_2$ (as 2T1)	$[8]$	$2$	$0$	$1$
2.0.420.1	x^2 + 105	$2$	[0,1]	$-\,2^{2}\cdot 3\cdot 5\cdot 7$	$$	$20.4939015319$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 2, 2]$	$2$	$0$	$1$
2.0.452.1	x^2 + 113	$2$	[0,1]	$-\,2^{2}\cdot 113$	$$	$21.2602916255$	✓	✓	✓	$C_2$ (as 2T1)	$[8]$	$2$	$0$	$1$
2.0.456.1	x^2 + 114	$2$	[0,1]	$-\,2^{3}\cdot 3\cdot 19$	$$	$21.3541565041$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 4]$	$2$	$0$	$1$
2.0.548.1	x^2 + 137	$2$	[0,1]	$-\,2^{2}\cdot 137$	$$	$23.4093998214$	✓	✓	✓	$C_2$ (as 2T1)	$[8]$	$2$	$0$	$1$
2.0.552.1	x^2 + 138	$2$	[0,1]	$-\,2^{3}\cdot 3\cdot 23$	$$	$23.4946802489$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 4]$	$2$	$0$	$1$
2.0.564.1	x^2 + 141	$2$	[0,1]	$-\,2^{2}\cdot 3\cdot 47$	$$	$23.7486841741$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 4]$	$2$	$0$	$1$
2.0.579.1	x^2 - x + 145	$2$	[0,1]	$-\,3\cdot 193$	$$	$24.062418831$	✓	✓	✓	$C_2$ (as 2T1)	$[8]$	$2$	$0$	$1$
2.0.580.1	x^2 + 145	$2$	[0,1]	$-\,2^{2}\cdot 5\cdot 29$	$$	$24.0831891576$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 4]$	$2$	$0$	$1$
2.0.583.1	x^2 - x + 146	$2$	[0,1]	$-\,11\cdot 53$	$$	$24.1453929353$	✓	✓	✓	$C_2$ (as 2T1)	$[8]$	$2$	$0$	$1$
2.0.616.1	x^2 + 154	$2$	[0,1]	$-\,2^{3}\cdot 7\cdot 11$	$$	$24.819347292$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 4]$	$2$	$0$	$1$
2.0.632.1	x^2 + 158	$2$	[0,1]	$-\,2^{3}\cdot 79$	$$	$25.13961018$	✓	✓	✓	$C_2$ (as 2T1)	$[8]$	$2$	$0$	$1$
2.0.651.1	x^2 - x + 163	$2$	[0,1]	$-\,3\cdot 7\cdot 31$	$$	$25.5147016443$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 4]$	$2$	$0$	$1$
2.0.660.1	x^2 + 165	$2$	[0,1]	$-\,2^{2}\cdot 3\cdot 5\cdot 11$	$$	$25.6904651573$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 2, 2]$	$2$	$0$	$1$
2.0.712.1	x^2 + 178	$2$	[0,1]	$-\,2^{3}\cdot 89$	$$	$26.6833281283$	✓	✓	✓	$C_2$ (as 2T1)	$[8]$	$2$	$0$	$1$
2.0.820.1	x^2 + 205	$2$	[0,1]	$-\,2^{2}\cdot 5\cdot 41$	$$	$28.6356421266$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 4]$	$2$	$0$	$1$
2.0.840.1	x^2 + 210	$2$	[0,1]	$-\,2^{3}\cdot 3\cdot 5\cdot 7$	$$	$28.9827534924$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 2, 2]$	$2$	$0$	$1$
2.0.852.1	x^2 + 213	$2$	[0,1]	$-\,2^{2}\cdot 3\cdot 71$	$$	$29.1890390387$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 4]$	$2$	$0$	$1$
2.0.868.1	x^2 + 217	$2$	[0,1]	$-\,2^{2}\cdot 7\cdot 31$	$$	$29.4618397253$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 4]$	$2$	$0$	$1$
2.0.904.1	x^2 + 226	$2$	[0,1]	$-\,2^{3}\cdot 113$	$$	$30.0665927567$	✓	✓	✓	$C_2$ (as 2T1)	$[8]$	$2$	$0$	$1$
2.2.904.1	x^2 - 226	$2$	[2,0]	$2^{3}\cdot 113$	$$	$30.0665927567$		✓	✓	$C_2$ (as 2T1)	$[8]$	$2$	$1$	$3.40230664548$
2.0.915.1	x^2 - x + 229	$2$	[0,1]	$-\,3\cdot 5\cdot 61$	$$	$30.2489669245$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 4]$	$2$	$0$	$1$
2.0.939.1	x^2 - x + 235	$2$	[0,1]	$-\,3\cdot 313$	$$	$30.6431068921$	✓	✓	✓	$C_2$ (as 2T1)	$[8]$	$2$	$0$	$1$
2.0.952.1	x^2 + 238	$2$	[0,1]	$-\,2^{3}\cdot 7\cdot 17$	$$	$30.8544972411$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 4]$	$2$	$0$	$1$
2.0.979.1	x^2 - x + 245	$2$	[0,1]	$-\,11\cdot 89$	$$	$31.2889756943$	✓	✓	✓	$C_2$ (as 2T1)	$[8]$	$2$	$0$	$1$
2.0.987.1	x^2 - x + 247	$2$	[0,1]	$-\,3\cdot 7\cdot 47$	$$	$31.4165561448$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 4]$	$2$	$0$	$1$
2.0.995.1	x^2 - x + 249	$2$	[0,1]	$-\,5\cdot 199$	$$	$31.5436205912$	✓	✓	✓	$C_2$ (as 2T1)	$[8]$	$2$	$0$	$1$
2.0.1032.1	x^2 + 258	$2$	[0,1]	$-\,2^{3}\cdot 3\cdot 43$	$$	$32.1247568084$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 4]$	$2$	$0$	$1$
2.0.1043.1	x^2 - x + 261	$2$	[0,1]	$-\,7\cdot 149$	$$	$32.2955105239$	✓	✓	✓	$C_2$ (as 2T1)	$[8]$	$2$	$0$	$1$
2.0.1060.1	x^2 + 265	$2$	[0,1]	$-\,2^{2}\cdot 5\cdot 53$	$$	$32.5576411922$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 4]$	$2$	$0$	$1$
2.0.1092.1	x^2 + 273	$2$	[0,1]	$-\,2^{2}\cdot 3\cdot 7\cdot 13$	$$	$33.0454232837$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 2, 2]$	$2$	$0$	$1$
2.0.1128.1	x^2 + 282	$2$	[0,1]	$-\,2^{3}\cdot 3\cdot 47$	$$	$33.5857112475$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 4]$	$2$	$0$	$1$
2.0.1131.1	x^2 - x + 283	$2$	[0,1]	$-\,3\cdot 13\cdot 29$	$$	$33.6303434416$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 4]$	$2$	$0$	$1$
2.0.1155.1	x^2 - x + 289	$2$	[0,1]	$-\,3\cdot 5\cdot 7\cdot 11$	$$	$33.9852909359$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 2, 2]$	$2$	$0$	$1$
2.0.1195.1	x^2 - x + 299	$2$	[0,1]	$-\,5\cdot 239$	$$	$34.5687720349$	✓	✓	✓	$C_2$ (as 2T1)	$[8]$	$2$	$0$	$1$
2.0.1204.1	x^2 + 301	$2$	[0,1]	$-\,2^{2}\cdot 7\cdot 43$	$$	$34.6987031458$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 4]$	$2$	$0$	$1$
2.0.1240.1	x^2 + 310	$2$	[0,1]	$-\,2^{3}\cdot 5\cdot 31$	$$	$35.2136337233$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 4]$	$2$	$0$	$1$

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