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 2584161 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
2.0.15.1	x^2 - x + 4	$2$	[0,1]	$-\,3\cdot 5$	$$	$3.87298334621$	✓	✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$0$	$1$
2.0.20.1	x^2 + 5	$2$	[0,1]	$-\,2^{2}\cdot 5$	$$	$4.472135955$	✓	✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$0$	$1$
2.0.24.1	x^2 + 6	$2$	[0,1]	$-\,2^{3}\cdot 3$	$$	$4.89897948557$	✓	✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$0$	$1$
2.0.35.1	x^2 - x + 9	$2$	[0,1]	$-\,5\cdot 7$	$$	$5.9160797831$	✓	✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$0$	$1$
2.0.40.1	x^2 + 10	$2$	[0,1]	$-\,2^{3}\cdot 5$	$$	$6.32455532034$	✓	✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$0$	$1$
2.2.40.1	x^2 - 10	$2$	[2,0]	$2^{3}\cdot 5$	$$	$6.32455532034$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$1.81844645923$
2.0.51.1	x^2 - x + 13	$2$	[0,1]	$-\,3\cdot 17$	$$	$7.14142842854$	✓	✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$0$	$1$
2.0.52.1	x^2 + 13	$2$	[0,1]	$-\,2^{2}\cdot 13$	$$	$7.21110255093$	✓	✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$0$	$1$
2.2.60.1	x^2 - 15	$2$	[2,0]	$2^{2}\cdot 3\cdot 5$	$$	$7.74596669241$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$2.0634370689$
2.2.65.1	x^2 - x - 16	$2$	[2,0]	$5\cdot 13$	$$	$8.0622577483$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$2.77647228072$
2.2.85.1	x^2 - x - 21	$2$	[2,0]	$5\cdot 17$	$$	$9.21954445729$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$2.20934770862$
2.0.88.1	x^2 + 22	$2$	[0,1]	$-\,2^{3}\cdot 11$	$$	$9.38083151965$	✓	✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$0$	$1$
2.0.91.1	x^2 - x + 23	$2$	[0,1]	$-\,7\cdot 13$	$$	$9.53939201417$	✓	✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$0$	$1$
2.2.104.1	x^2 - 26	$2$	[2,0]	$2^{3}\cdot 13$	$$	$10.1980390272$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$2.31243834127$
2.2.105.1	x^2 - x - 26	$2$	[2,0]	$3\cdot 5\cdot 7$	$$	$10.246950766$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$4.40657049308$
2.0.115.1	x^2 - x + 29	$2$	[0,1]	$-\,5\cdot 23$	$$	$10.7238052948$	✓	✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$0$	$1$
2.2.120.1	x^2 - 30	$2$	[2,0]	$2^{3}\cdot 3\cdot 5$	$$	$10.9544511501$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$3.08896990484$
2.0.123.1	x^2 - x + 31	$2$	[0,1]	$-\,3\cdot 41$	$$	$11.0905365064$	✓	✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$0$	$1$
2.2.136.1	x^2 - 34	$2$	[2,0]	$2^{3}\cdot 17$	$$	$11.6619037897$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$4.24829109791$
2.2.140.1	x^2 - 35	$2$	[2,0]	$2^{2}\cdot 5\cdot 7$	$$	$11.8321595662$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$2.47788873029$
2.0.148.1	x^2 + 37	$2$	[0,1]	$-\,2^{2}\cdot 37$	$$	$12.1655250606$	✓	✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$0$	$1$
2.2.156.1	x^2 - 39	$2$	[2,0]	$2^{2}\cdot 3\cdot 13$	$$	$12.4899959968$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$3.91162276521$
2.2.165.1	x^2 - x - 41	$2$	[2,0]	$3\cdot 5\cdot 11$	$$	$12.8452325787$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$2.55897897703$
2.2.168.1	x^2 - 42	$2$	[2,0]	$2^{3}\cdot 3\cdot 7$	$$	$12.9614813968$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$3.2566139548$
2.2.185.1	x^2 - x - 46	$2$	[2,0]	$5\cdot 37$	$$	$13.6014705087$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$4.9127089471$
2.0.187.1	x^2 - x + 47	$2$	[0,1]	$-\,11\cdot 17$	$$	$13.6747943312$	✓	✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$0$	$1$
2.2.204.1	x^2 - 51	$2$	[2,0]	$2^{2}\cdot 3\cdot 17$	$$	$14.2828568571$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$4.60507017098$
2.2.205.1	x^2 - x - 51	$2$	[2,0]	$5\cdot 41$	$$	$14.3178210633$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$3.76065884353$
2.2.220.1	x^2 - 55	$2$	[2,0]	$2^{2}\cdot 5\cdot 11$	$$	$14.8323969742$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$5.18175198713$
2.2.221.1	x^2 - x - 55	$2$	[2,0]	$13\cdot 17$	$$	$14.8660687473$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$2.70357583093$
2.0.232.1	x^2 + 58	$2$	[0,1]	$-\,2^{3}\cdot 29$	$$	$15.2315462117$	✓	✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$0$	$1$
2.2.232.1	x^2 - 58	$2$	[2,0]	$2^{3}\cdot 29$	$$	$15.2315462117$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$5.28829253732$
2.0.235.1	x^2 - x + 59	$2$	[0,1]	$-\,5\cdot 47$	$$	$15.3297097168$	✓	✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$0$	$1$
2.2.264.1	x^2 - 66	$2$	[2,0]	$2^{3}\cdot 3\cdot 11$	$$	$16.2480768093$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$4.86747527361$
2.2.265.1	x^2 - x - 66	$2$	[2,0]	$5\cdot 53$	$$	$16.2788205961$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$9.40459050642$
2.0.267.1	x^2 - x + 67	$2$	[0,1]	$-\,3\cdot 89$	$$	$16.3401346384$	✓	✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$0$	$1$
2.2.273.1	x^2 - x - 68	$2$	[2,0]	$3\cdot 7\cdot 13$	$$	$16.5227116419$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$7.28207318508$
2.2.280.1	x^2 - 70	$2$	[2,0]	$2^{3}\cdot 5\cdot 7$	$$	$16.7332005307$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$6.21859615148$
2.2.285.1	x^2 - x - 71	$2$	[2,0]	$3\cdot 5\cdot 19$	$$	$16.8819430161$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$2.82973503752$
2.2.296.1	x^2 - 74	$2$	[2,0]	$2^{3}\cdot 37$	$$	$17.2046505341$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$4.45448247706$
2.2.305.1	x^2 - x - 76	$2$	[2,0]	$5\cdot 61$	$$	$17.4642491966$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$6.88550862454$
2.2.312.1	x^2 - 78	$2$	[2,0]	$2^{3}\cdot 3\cdot 13$	$$	$17.6635217327$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$4.66335008258$
2.2.345.1	x^2 - x - 86	$2$	[2,0]	$3\cdot 5\cdot 23$	$$	$18.574175621$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$9.51207326218$
2.2.348.1	x^2 - 87	$2$	[2,0]	$2^{2}\cdot 3\cdot 29$	$$	$18.6547581062$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$4.02503266055$
2.2.357.1	x^2 - x - 89	$2$	[2,0]	$3\cdot 7\cdot 17$	$$	$18.8944436277$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$2.94165731465$
2.2.364.1	x^2 - 91	$2$	[2,0]	$2^{2}\cdot 7\cdot 13$	$$	$19.0787840283$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$8.05452250863$
2.2.365.1	x^2 - x - 91	$2$	[2,0]	$5\cdot 73$	$$	$19.1049731745$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$2.94719762257$
2.2.377.1	x^2 - x - 94	$2$	[2,0]	$13\cdot 29$	$$	$19.4164878389$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$6.14418102911$
2.2.380.1	x^2 - 95	$2$	[2,0]	$2^{2}\cdot 5\cdot 19$	$$	$19.4935886896$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$4.3565444206$
2.2.385.1	x^2 - x - 96	$2$	[2,0]	$5\cdot 7\cdot 11$	$$	$19.6214168703$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$12.163488683$

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