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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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
2.0.39.1	x^2 - x + 10	$2$	[0,1]	$-\,3\cdot 13$	$$	$6.2449979984$	✓	✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$0$	$1$
2.0.55.1	x^2 - x + 14	$2$	[0,1]	$-\,5\cdot 11$	$$	$7.4161984871$	✓	✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$0$	$1$
2.0.56.1	x^2 + 14	$2$	[0,1]	$-\,2^{3}\cdot 7$	$$	$7.48331477355$	✓	✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$0$	$1$
2.0.68.1	x^2 + 17	$2$	[0,1]	$-\,2^{2}\cdot 17$	$$	$8.24621125124$	✓	✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$0$	$1$
2.0.84.1	x^2 + 21	$2$	[0,1]	$-\,2^{2}\cdot 3\cdot 7$	$$	$9.16515138991$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 2]$	$2$	$0$	$1$
2.0.120.1	x^2 + 30	$2$	[0,1]	$-\,2^{3}\cdot 3\cdot 5$	$$	$10.9544511501$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 2]$	$2$	$0$	$1$
2.0.132.1	x^2 + 33	$2$	[0,1]	$-\,2^{2}\cdot 3\cdot 11$	$$	$11.4891252931$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 2]$	$2$	$0$	$1$
2.0.136.1	x^2 + 34	$2$	[0,1]	$-\,2^{3}\cdot 17$	$$	$11.6619037897$	✓	✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$0$	$1$
2.2.145.1	x^2 - x - 36	$2$	[2,0]	$5\cdot 29$	$$	$12.0415945788$		✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$1$	$3.1797854377$
2.0.155.1	x^2 - x + 39	$2$	[0,1]	$-\,5\cdot 31$	$$	$12.449899598$	✓	✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$0$	$1$
2.0.168.1	x^2 + 42	$2$	[0,1]	$-\,2^{3}\cdot 3\cdot 7$	$$	$12.9614813968$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 2]$	$2$	$0$	$1$
2.0.184.1	x^2 + 46	$2$	[0,1]	$-\,2^{3}\cdot 23$	$$	$13.5646599663$	✓	✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$0$	$1$
2.0.195.1	x^2 - x + 49	$2$	[0,1]	$-\,3\cdot 5\cdot 13$	$$	$13.9642400438$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 2]$	$2$	$0$	$1$
2.0.203.1	x^2 - x + 51	$2$	[0,1]	$-\,7\cdot 29$	$$	$14.2478068488$	✓	✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$0$	$1$
2.0.219.1	x^2 - x + 55	$2$	[0,1]	$-\,3\cdot 73$	$$	$14.7986485869$	✓	✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$0$	$1$
2.0.228.1	x^2 + 57	$2$	[0,1]	$-\,2^{2}\cdot 3\cdot 19$	$$	$15.0996688705$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 2]$	$2$	$0$	$1$
2.0.259.1	x^2 - x + 65	$2$	[0,1]	$-\,7\cdot 37$	$$	$16.0934769394$	✓	✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$0$	$1$
2.0.280.1	x^2 + 70	$2$	[0,1]	$-\,2^{3}\cdot 5\cdot 7$	$$	$16.7332005307$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 2]$	$2$	$0$	$1$
2.0.291.1	x^2 - x + 73	$2$	[0,1]	$-\,3\cdot 97$	$$	$17.0587221092$	✓	✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$0$	$1$
2.0.292.1	x^2 + 73	$2$	[0,1]	$-\,2^{2}\cdot 73$	$$	$17.0880074906$	✓	✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$0$	$1$
2.0.312.1	x^2 + 78	$2$	[0,1]	$-\,2^{3}\cdot 3\cdot 13$	$$	$17.6635217327$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 2]$	$2$	$0$	$1$
2.0.323.1	x^2 - x + 81	$2$	[0,1]	$-\,17\cdot 19$	$$	$17.9722007556$	✓	✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$0$	$1$
2.0.328.1	x^2 + 82	$2$	[0,1]	$-\,2^{3}\cdot 41$	$$	$18.1107702763$	✓	✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$0$	$1$
2.2.328.1	x^2 - 82	$2$	[2,0]	$2^{3}\cdot 41$	$$	$18.1107702763$		✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$1$	$2.89344398589$
2.0.340.1	x^2 + 85	$2$	[0,1]	$-\,2^{2}\cdot 5\cdot 17$	$$	$18.4390889146$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 2]$	$2$	$0$	$1$
2.0.355.1	x^2 - x + 89	$2$	[0,1]	$-\,5\cdot 71$	$$	$18.8414436814$	✓	✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$0$	$1$
2.0.372.1	x^2 + 93	$2$	[0,1]	$-\,2^{2}\cdot 3\cdot 31$	$$	$19.287301522$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 2]$	$2$	$0$	$1$
2.0.388.1	x^2 + 97	$2$	[0,1]	$-\,2^{2}\cdot 97$	$$	$19.6977156036$	✓	✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$0$	$1$
2.0.408.1	x^2 + 102	$2$	[0,1]	$-\,2^{3}\cdot 3\cdot 17$	$$	$20.1990098767$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 2]$	$2$	$0$	$1$
2.0.435.1	x^2 - x + 109	$2$	[0,1]	$-\,3\cdot 5\cdot 29$	$$	$20.8566536146$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 2]$	$2$	$0$	$1$
2.2.445.1	x^2 - x - 111	$2$	[2,0]	$5\cdot 89$	$$	$21.0950231097$		✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$1$	$3.04678233722$
2.0.483.1	x^2 - x + 121	$2$	[0,1]	$-\,3\cdot 7\cdot 23$	$$	$21.9772609758$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 2]$	$2$	$0$	$1$
2.2.505.1	x^2 - x - 126	$2$	[2,0]	$5\cdot 101$	$$	$22.4722050542$		✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$1$	$7.38894571564$
2.0.520.1	x^2 + 130	$2$	[0,1]	$-\,2^{3}\cdot 5\cdot 13$	$$	$22.803508502$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 2]$	$2$	$0$	$1$
2.2.520.1	x^2 - 130	$2$	[2,0]	$2^{3}\cdot 5\cdot 13$	$$	$22.803508502$		✓	✓	$C_2$ (as 2T1)	$[2, 2]$	$2$	$1$	$4.73627538627$
2.0.532.1	x^2 + 133	$2$	[0,1]	$-\,2^{2}\cdot 7\cdot 19$	$$	$23.0651251893$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 2]$	$2$	$0$	$1$
2.0.555.1	x^2 - x + 139	$2$	[0,1]	$-\,3\cdot 5\cdot 37$	$$	$23.5584379788$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 2]$	$2$	$0$	$1$
2.0.568.1	x^2 + 142	$2$	[0,1]	$-\,2^{3}\cdot 71$	$$	$23.8327505756$	✓	✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$0$	$1$
2.0.595.1	x^2 - x + 149	$2$	[0,1]	$-\,5\cdot 7\cdot 17$	$$	$24.3926218353$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 2]$	$2$	$0$	$1$
2.0.627.1	x^2 - x + 157	$2$	[0,1]	$-\,3\cdot 11\cdot 19$	$$	$25.0399680511$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 2]$	$2$	$0$	$1$
2.0.667.1	x^2 - x + 167	$2$	[0,1]	$-\,23\cdot 29$	$$	$25.8263431403$	✓	✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$0$	$1$
2.2.680.1	x^2 - 170	$2$	[2,0]	$2^{3}\cdot 5\cdot 17$	$$	$26.0768096208$		✓	✓	$C_2$ (as 2T1)	$[2, 2]$	$2$	$1$	$3.25957255626$
2.2.689.1	x^2 - x - 172	$2$	[2,0]	$13\cdot 53$	$$	$26.2488094968$		✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$1$	$5.34708485421$
2.0.708.1	x^2 + 177	$2$	[0,1]	$-\,2^{2}\cdot 3\cdot 59$	$$	$26.6082693913$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 2]$	$2$	$0$	$1$
2.0.715.1	x^2 - x + 179	$2$	[0,1]	$-\,5\cdot 11\cdot 13$	$$	$26.7394839142$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 2]$	$2$	$0$	$1$
2.0.723.1	x^2 - x + 181	$2$	[0,1]	$-\,3\cdot 241$	$$	$26.8886593195$	✓	✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$0$	$1$
2.0.760.1	x^2 + 190	$2$	[0,1]	$-\,2^{3}\cdot 5\cdot 19$	$$	$27.5680975042$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 2]$	$2$	$0$	$1$
2.0.763.1	x^2 - x + 191	$2$	[0,1]	$-\,7\cdot 109$	$$	$27.6224546339$	✓	✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$0$	$1$
2.0.772.1	x^2 + 193	$2$	[0,1]	$-\,2^{2}\cdot 193$	$$	$27.7848879789$	✓	✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$0$	$1$
2.2.777.1	x^2 - x - 194	$2$	[2,0]	$3\cdot 7\cdot 37$	$$	$27.8747197295$		✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$1$	$6.10031392473$

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