Number field search results

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

Results (1-50 of )

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Label	Polynomial	Discriminant	Galois group	Class group
2.0.39.1	x^2 - x + 10	\( -\,3\cdot 13 \)	$C_2$ (as 2T1)	$[4]$
2.0.55.1	x^2 - x + 14	\( -\,5\cdot 11 \)	$C_2$ (as 2T1)	$[4]$
2.0.56.1	x^2 + 14	\( -\,2^{3}\cdot 7 \)	$C_2$ (as 2T1)	$[4]$
2.0.68.1	x^2 + 17	\( -\,2^{2}\cdot 17 \)	$C_2$ (as 2T1)	$[4]$
2.0.84.1	x^2 + 21	\( -\,2^{2}\cdot 3\cdot 7 \)	$C_2$ (as 2T1)	$[2, 2]$
2.0.120.1	x^2 + 30	\( -\,2^{3}\cdot 3\cdot 5 \)	$C_2$ (as 2T1)	$[2, 2]$
2.0.132.1	x^2 + 33	\( -\,2^{2}\cdot 3\cdot 11 \)	$C_2$ (as 2T1)	$[2, 2]$
2.0.136.1	x^2 + 34	\( -\,2^{3}\cdot 17 \)	$C_2$ (as 2T1)	$[4]$
2.2.145.1	x^2 - x - 36	\( 5\cdot 29 \)	$C_2$ (as 2T1)	$[4]$
2.0.155.1	x^2 - x + 39	\( -\,5\cdot 31 \)	$C_2$ (as 2T1)	$[4]$
2.0.168.1	x^2 + 42	\( -\,2^{3}\cdot 3\cdot 7 \)	$C_2$ (as 2T1)	$[2, 2]$
2.0.184.1	x^2 + 46	\( -\,2^{3}\cdot 23 \)	$C_2$ (as 2T1)	$[4]$
2.0.195.1	x^2 - x + 49	\( -\,3\cdot 5\cdot 13 \)	$C_2$ (as 2T1)	$[2, 2]$
2.0.203.1	x^2 - x + 51	\( -\,7\cdot 29 \)	$C_2$ (as 2T1)	$[4]$
2.0.219.1	x^2 - x + 55	\( -\,3\cdot 73 \)	$C_2$ (as 2T1)	$[4]$
2.0.228.1	x^2 + 57	\( -\,2^{2}\cdot 3\cdot 19 \)	$C_2$ (as 2T1)	$[2, 2]$
2.0.259.1	x^2 - x + 65	\( -\,7\cdot 37 \)	$C_2$ (as 2T1)	$[4]$
2.0.280.1	x^2 + 70	\( -\,2^{3}\cdot 5\cdot 7 \)	$C_2$ (as 2T1)	$[2, 2]$
2.0.291.1	x^2 - x + 73	\( -\,3\cdot 97 \)	$C_2$ (as 2T1)	$[4]$
2.0.292.1	x^2 + 73	\( -\,2^{2}\cdot 73 \)	$C_2$ (as 2T1)	$[4]$
2.0.312.1	x^2 + 78	\( -\,2^{3}\cdot 3\cdot 13 \)	$C_2$ (as 2T1)	$[2, 2]$
2.0.323.1	x^2 - x + 81	\( -\,17\cdot 19 \)	$C_2$ (as 2T1)	$[4]$
2.0.328.1	x^2 + 82	\( -\,2^{3}\cdot 41 \)	$C_2$ (as 2T1)	$[4]$
2.2.328.1	x^2 - 82	\( 2^{3}\cdot 41 \)	$C_2$ (as 2T1)	$[4]$
2.0.340.1	x^2 + 85	\( -\,2^{2}\cdot 5\cdot 17 \)	$C_2$ (as 2T1)	$[2, 2]$
2.0.355.1	x^2 - x + 89	\( -\,5\cdot 71 \)	$C_2$ (as 2T1)	$[4]$
2.0.372.1	x^2 + 93	\( -\,2^{2}\cdot 3\cdot 31 \)	$C_2$ (as 2T1)	$[2, 2]$
2.0.388.1	x^2 + 97	\( -\,2^{2}\cdot 97 \)	$C_2$ (as 2T1)	$[4]$
2.0.408.1	x^2 + 102	\( -\,2^{3}\cdot 3\cdot 17 \)	$C_2$ (as 2T1)	$[2, 2]$
2.0.435.1	x^2 - x + 109	\( -\,3\cdot 5\cdot 29 \)	$C_2$ (as 2T1)	$[2, 2]$
2.2.445.1	x^2 - x - 111	\( 5\cdot 89 \)	$C_2$ (as 2T1)	$[4]$
2.0.483.1	x^2 - x + 121	\( -\,3\cdot 7\cdot 23 \)	$C_2$ (as 2T1)	$[2, 2]$
2.2.505.1	x^2 - x - 126	\( 5\cdot 101 \)	$C_2$ (as 2T1)	$[4]$
2.0.520.1	x^2 + 130	\( -\,2^{3}\cdot 5\cdot 13 \)	$C_2$ (as 2T1)	$[2, 2]$
2.2.520.1	x^2 - 130	\( 2^{3}\cdot 5\cdot 13 \)	$C_2$ (as 2T1)	$[2, 2]$
2.0.532.1	x^2 + 133	\( -\,2^{2}\cdot 7\cdot 19 \)	$C_2$ (as 2T1)	$[2, 2]$
2.0.555.1	x^2 - x + 139	\( -\,3\cdot 5\cdot 37 \)	$C_2$ (as 2T1)	$[2, 2]$
2.0.568.1	x^2 + 142	\( -\,2^{3}\cdot 71 \)	$C_2$ (as 2T1)	$[4]$
2.0.595.1	x^2 - x + 149	\( -\,5\cdot 7\cdot 17 \)	$C_2$ (as 2T1)	$[2, 2]$
2.0.627.1	x^2 - x + 157	\( -\,3\cdot 11\cdot 19 \)	$C_2$ (as 2T1)	$[2, 2]$
2.0.667.1	x^2 - x + 167	\( -\,23\cdot 29 \)	$C_2$ (as 2T1)	$[4]$
2.2.680.1	x^2 - 170	\( 2^{3}\cdot 5\cdot 17 \)	$C_2$ (as 2T1)	$[2, 2]$
2.2.689.1	x^2 - x - 172	\( 13\cdot 53 \)	$C_2$ (as 2T1)	$[4]$
2.0.708.1	x^2 + 177	\( -\,2^{2}\cdot 3\cdot 59 \)	$C_2$ (as 2T1)	$[2, 2]$
2.0.715.1	x^2 - x + 179	\( -\,5\cdot 11\cdot 13 \)	$C_2$ (as 2T1)	$[2, 2]$
2.0.723.1	x^2 - x + 181	\( -\,3\cdot 241 \)	$C_2$ (as 2T1)	$[4]$
2.0.760.1	x^2 + 190	\( -\,2^{3}\cdot 5\cdot 19 \)	$C_2$ (as 2T1)	$[2, 2]$
2.0.763.1	x^2 - x + 191	\( -\,7\cdot 109 \)	$C_2$ (as 2T1)	$[4]$
2.0.772.1	x^2 + 193	\( -\,2^{2}\cdot 193 \)	$C_2$ (as 2T1)	$[4]$
2.2.777.1	x^2 - x - 194	\( 3\cdot 7\cdot 37 \)	$C_2$ (as 2T1)	$[4]$

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