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
Monogenic	Index	Ines. \(p\)

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Results (1-50 of 410 matches)

 

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
2.0.103.1	x^2 - x + 26	$2$	[0,1]	$-\,103$	$$	$10.1488915651$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$0$	$1$
2.0.104.1	x^2 + 26	$2$	[0,1]	$-\,2^{3}\cdot 13$	$$	$10.1980390272$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.0.107.1	x^2 - x + 27	$2$	[0,1]	$-\,107$	$$	$10.3440804328$	✓	✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	$0$	$1$
2.0.111.1	x^2 - x + 28	$2$	[0,1]	$-\,3\cdot 37$	$$	$10.5356537529$	✓	✓	✓	$C_2$ (as 2T1)	$[8]$	$2$	$0$	$1$
2.0.115.1	x^2 - x + 29	$2$	[0,1]	$-\,5\cdot 23$	$$	$10.7238052948$	✓	✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$0$	$1$
2.0.116.1	x^2 + 29	$2$	[0,1]	$-\,2^{2}\cdot 29$	$$	$10.7703296143$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.0.119.1	x^2 - x + 30	$2$	[0,1]	$-\,7\cdot 17$	$$	$10.9087121146$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	$0$	$1$
2.0.120.1	x^2 + 30	$2$	[0,1]	$-\,2^{3}\cdot 3\cdot 5$	$$	$10.9544511501$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 2]$	$2$	$0$	$1$
2.0.123.1	x^2 - x + 31	$2$	[0,1]	$-\,3\cdot 41$	$$	$11.0905365064$	✓	✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$0$	$1$
2.0.127.1	x^2 - x + 32	$2$	[0,1]	$-\,127$	$$	$11.2694276696$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$0$	$1$
2.0.131.1	x^2 - x + 33	$2$	[0,1]	$-\,131$	$$	$11.4455231423$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$0$	$1$
2.0.132.1	x^2 + 33	$2$	[0,1]	$-\,2^{2}\cdot 3\cdot 11$	$$	$11.4891252931$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 2]$	$2$	$0$	$1$
2.0.136.1	x^2 + 34	$2$	[0,1]	$-\,2^{3}\cdot 17$	$$	$11.6619037897$	✓	✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$0$	$1$
2.0.139.1	x^2 - x + 35	$2$	[0,1]	$-\,139$	$$	$11.7898261226$	✓	✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	$0$	$1$
2.0.143.1	x^2 - x + 36	$2$	[0,1]	$-\,11\cdot 13$	$$	$11.9582607431$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	$0$	$1$
2.0.148.1	x^2 + 37	$2$	[0,1]	$-\,2^{2}\cdot 37$	$$	$12.1655250606$	✓	✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$0$	$1$
2.0.151.1	x^2 - x + 38	$2$	[0,1]	$-\,151$	$$	$12.2882057274$	✓	✓	✓	$C_2$ (as 2T1)	$[7]$	$2$	$0$	$1$
2.0.152.1	x^2 + 38	$2$	[0,1]	$-\,2^{3}\cdot 19$	$$	$12.3288280059$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.0.155.1	x^2 - x + 39	$2$	[0,1]	$-\,5\cdot 31$	$$	$12.449899598$	✓	✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$0$	$1$
2.0.159.1	x^2 - x + 40	$2$	[0,1]	$-\,3\cdot 53$	$$	$12.6095202129$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	$0$	$1$
2.0.163.1	x^2 - x + 41	$2$	[0,1]	$-\,163$	$$	$12.7671453348$	✓	✓	✓	$C_2$ (as 2T1)	trivial	$2$	$0$	$1$
2.0.164.1	x^2 + 41	$2$	[0,1]	$-\,2^{2}\cdot 41$	$$	$12.8062484749$	✓	✓	✓	$C_2$ (as 2T1)	$[8]$	$2$	$0$	$1$
2.0.167.1	x^2 - x + 42	$2$	[0,1]	$-\,167$	$$	$12.9228479833$	✓	✓	✓	$C_2$ (as 2T1)	$[11]$	$2$	$0$	$1$
2.0.168.1	x^2 + 42	$2$	[0,1]	$-\,2^{3}\cdot 3\cdot 7$	$$	$12.9614813968$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 2]$	$2$	$0$	$1$
2.0.179.1	x^2 - x + 45	$2$	[0,1]	$-\,179$	$$	$13.3790881603$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$0$	$1$
2.0.183.1	x^2 - x + 46	$2$	[0,1]	$-\,3\cdot 61$	$$	$13.5277492585$	✓	✓	✓	$C_2$ (as 2T1)	$[8]$	$2$	$0$	$1$
2.0.184.1	x^2 + 46	$2$	[0,1]	$-\,2^{3}\cdot 23$	$$	$13.5646599663$	✓	✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$0$	$1$
2.0.187.1	x^2 - x + 47	$2$	[0,1]	$-\,11\cdot 17$	$$	$13.6747943312$	✓	✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$0$	$1$
2.0.191.1	x^2 - x + 48	$2$	[0,1]	$-\,191$	$$	$13.8202749611$	✓	✓	✓	$C_2$ (as 2T1)	$[13]$	$2$	$0$	$1$
2.0.195.1	x^2 - x + 49	$2$	[0,1]	$-\,3\cdot 5\cdot 13$	$$	$13.9642400438$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 2]$	$2$	$0$	$1$
2.0.199.1	x^2 - x + 50	$2$	[0,1]	$-\,199$	$$	$14.1067359797$	✓	✓	✓	$C_2$ (as 2T1)	$[9]$	$2$	$0$	$1$
2.0.203.1	x^2 - x + 51	$2$	[0,1]	$-\,7\cdot 29$	$$	$14.2478068488$	✓	✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$0$	$1$
2.0.211.1	x^2 - x + 53	$2$	[0,1]	$-\,211$	$$	$14.5258390463$	✓	✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	$0$	$1$
2.0.212.1	x^2 + 53	$2$	[0,1]	$-\,2^{2}\cdot 53$	$$	$14.5602197786$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.0.215.1	x^2 - x + 54	$2$	[0,1]	$-\,5\cdot 43$	$$	$14.6628782986$	✓	✓	✓	$C_2$ (as 2T1)	$[14]$	$2$	$0$	$1$
2.0.219.1	x^2 - x + 55	$2$	[0,1]	$-\,3\cdot 73$	$$	$14.7986485869$	✓	✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$0$	$1$
2.0.223.1	x^2 - x + 56	$2$	[0,1]	$-\,223$	$$	$14.9331845231$	✓	✓	✓	$C_2$ (as 2T1)	$[7]$	$2$	$0$	$1$
2.0.227.1	x^2 - x + 57	$2$	[0,1]	$-\,227$	$$	$15.0665191733$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$0$	$1$
2.0.228.1	x^2 + 57	$2$	[0,1]	$-\,2^{2}\cdot 3\cdot 19$	$$	$15.0996688705$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 2]$	$2$	$0$	$1$
2.0.231.1	x^2 - x + 58	$2$	[0,1]	$-\,3\cdot 7\cdot 11$	$$	$15.1986841536$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 6]$	$2$	$0$	$1$
2.0.232.1	x^2 + 58	$2$	[0,1]	$-\,2^{3}\cdot 29$	$$	$15.2315462117$	✓	✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$0$	$1$
2.0.235.1	x^2 - x + 59	$2$	[0,1]	$-\,5\cdot 47$	$$	$15.3297097168$	✓	✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$0$	$1$
2.0.239.1	x^2 - x + 60	$2$	[0,1]	$-\,239$	$$	$15.4596248337$	✓	✓	✓	$C_2$ (as 2T1)	$[15]$	$2$	$0$	$1$
2.0.244.1	x^2 + 61	$2$	[0,1]	$-\,2^{2}\cdot 61$	$$	$15.6204993518$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.0.247.1	x^2 - x + 62	$2$	[0,1]	$-\,13\cdot 19$	$$	$15.7162336455$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$0$	$1$
2.0.248.1	x^2 + 62	$2$	[0,1]	$-\,2^{3}\cdot 31$	$$	$15.748015748$	✓	✓	✓	$C_2$ (as 2T1)	$[8]$	$2$	$0$	$1$
2.0.251.1	x^2 - x + 63	$2$	[0,1]	$-\,251$	$$	$15.8429795178$	✓	✓	✓	$C_2$ (as 2T1)	$[7]$	$2$	$0$	$1$
2.0.255.1	x^2 - x + 64	$2$	[0,1]	$-\,3\cdot 5\cdot 17$	$$	$15.9687194227$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 6]$	$2$	$0$	$1$
2.0.259.1	x^2 - x + 65	$2$	[0,1]	$-\,7\cdot 37$	$$	$16.0934769394$	✓	✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$0$	$1$
2.0.260.1	x^2 + 65	$2$	[0,1]	$-\,2^{2}\cdot 5\cdot 13$	$$	$16.1245154966$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 4]$	$2$	$0$	$1$