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 10161949 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
1.1.1.1	x	$1$	[1,0]	$1$	$$	$1.0$		✓	✓	Trivial (as 1T1)	trivial	$2$	$0$	$1$
2.0.3.1	x^2 - x + 1	$2$	[0,1]	$-\,3$	$$	$1.73205080757$	✓	✓	✓	$C_2$ (as 2T1)	trivial	$6$	$0$	$1$
2.0.4.1	x^2 + 1	$2$	[0,1]	$-\,2^{2}$	$$	$2.0$	✓	✓	✓	$C_2$ (as 2T1)	trivial	$4$	$0$	$1$
2.2.5.1	x^2 - x - 1	$2$	[2,0]	$5$	$$	$2.2360679775$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$0.48121182506$
2.0.7.1	x^2 - x + 2	$2$	[0,1]	$-\,7$	$$	$2.64575131106$	✓	✓	✓	$C_2$ (as 2T1)	trivial	$2$	$0$	$1$
2.0.8.1	x^2 + 2	$2$	[0,1]	$-\,2^{3}$	$$	$2.82842712475$	✓	✓	✓	$C_2$ (as 2T1)	trivial	$2$	$0$	$1$
2.2.8.1	x^2 - 2	$2$	[2,0]	$2^{3}$	$$	$2.82842712475$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$0.88137358702$
2.0.11.1	x^2 - x + 3	$2$	[0,1]	$-\,11$	$$	$3.31662479036$	✓	✓	✓	$C_2$ (as 2T1)	trivial	$2$	$0$	$1$
2.2.12.1	x^2 - 3	$2$	[2,0]	$2^{2}\cdot 3$	$$	$3.46410161514$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$1.31695789692$
2.2.13.1	x^2 - x - 3	$2$	[2,0]	$13$	$$	$3.60555127546$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$1.19476321729$
2.2.17.1	x^2 - x - 4	$2$	[2,0]	$17$	$$	$4.12310562562$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$2.09471254726$
2.0.19.1	x^2 - x + 5	$2$	[0,1]	$-\,19$	$$	$4.35889894354$	✓	✓	✓	$C_2$ (as 2T1)	trivial	$2$	$0$	$1$
2.2.21.1	x^2 - x - 5	$2$	[2,0]	$3\cdot 7$	$$	$4.58257569496$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$1.56679923697$
2.2.24.1	x^2 - 6	$2$	[2,0]	$2^{3}\cdot 3$	$$	$4.89897948557$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$2.29243166956$
2.2.28.1	x^2 - 7	$2$	[2,0]	$2^{2}\cdot 7$	$$	$5.29150262213$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$2.76865938331$
2.2.29.1	x^2 - x - 7	$2$	[2,0]	$29$	$$	$5.38516480713$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$1.64723114637$
2.2.33.1	x^2 - x - 8	$2$	[2,0]	$3\cdot 11$	$$	$5.74456264654$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$3.82816847133$
2.2.37.1	x^2 - x - 9	$2$	[2,0]	$37$	$$	$6.0827625303$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$2.49177985264$
2.2.41.1	x^2 - x - 10	$2$	[2,0]	$41$	$$	$6.40312423743$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$4.15912713463$
2.0.43.1	x^2 - x + 11	$2$	[0,1]	$-\,43$	$$	$6.5574385243$	✓	✓	✓	$C_2$ (as 2T1)	trivial	$2$	$0$	$1$
2.2.44.1	x^2 - 11	$2$	[2,0]	$2^{2}\cdot 11$	$$	$6.63324958071$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$2.99322284613$
2.2.53.1	x^2 - x - 13	$2$	[2,0]	$53$	$$	$7.28010988928$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$1.96572047165$
2.2.56.1	x^2 - 14	$2$	[2,0]	$2^{3}\cdot 7$	$$	$7.48331477355$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$3.40008441411$
2.2.57.1	x^2 - x - 14	$2$	[2,0]	$3\cdot 19$	$$	$7.54983443527$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$5.71041605276$
2.2.61.1	x^2 - x - 15	$2$	[2,0]	$61$	$$	$7.81024967591$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$3.66421846089$
2.0.67.1	x^2 - x + 17	$2$	[0,1]	$-\,67$	$$	$8.18535277187$	✓	✓	✓	$C_2$ (as 2T1)	trivial	$2$	$0$	$1$
2.2.69.1	x^2 - x - 17	$2$	[2,0]	$3\cdot 23$	$$	$8.30662386292$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$3.21727197116$
2.2.73.1	x^2 - x - 18	$2$	[2,0]	$73$	$$	$8.54400374532$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$7.66669041926$
2.2.76.1	x^2 - 19	$2$	[2,0]	$2^{2}\cdot 19$	$$	$8.71779788708$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$5.82893696698$
2.2.77.1	x^2 - x - 19	$2$	[2,0]	$7\cdot 11$	$$	$8.77496438739$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$2.18464379161$
2.2.88.1	x^2 - 22	$2$	[2,0]	$2^{3}\cdot 11$	$$	$9.38083151965$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$5.97634446743$
2.2.89.1	x^2 - x - 22	$2$	[2,0]	$89$	$$	$9.43398113206$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$6.90775627898$
2.2.92.1	x^2 - 23	$2$	[2,0]	$2^{2}\cdot 23$	$$	$9.59166304663$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$3.87076670029$
2.2.93.1	x^2 - x - 23	$2$	[2,0]	$3\cdot 31$	$$	$9.64365076099$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$3.36610464293$
2.2.97.1	x^2 - x - 24	$2$	[2,0]	$97$	$$	$9.8488578018$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$9.32438309598$
2.2.101.1	x^2 - x - 25	$2$	[2,0]	$101$	$$	$10.0498756211$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$2.9982229503$
2.2.109.1	x^2 - x - 27	$2$	[2,0]	$109$	$$	$10.4403065089$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$5.56453508676$
2.2.113.1	x^2 - x - 28	$2$	[2,0]	$113$	$$	$10.6301458127$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$7.3473001159$
2.2.124.1	x^2 - 31	$2$	[2,0]	$2^{2}\cdot 31$	$$	$11.1355287257$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$8.01961268619$
2.2.129.1	x^2 - x - 32	$2$	[2,0]	$3\cdot 43$	$$	$11.3578166916$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$10.4255498073$
2.2.133.1	x^2 - x - 33	$2$	[2,0]	$7\cdot 19$	$$	$11.5325625947$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$5.15325818041$
2.2.137.1	x^2 - x - 34	$2$	[2,0]	$137$	$$	$11.7046999107$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$8.15708386722$
2.2.141.1	x^2 - x - 35	$2$	[2,0]	$3\cdot 47$	$$	$11.874342087$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$5.24699637018$
2.2.149.1	x^2 - x - 37	$2$	[2,0]	$149$	$$	$12.2065556157$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$4.11114250086$
2.2.152.1	x^2 - 38	$2$	[2,0]	$2^{3}\cdot 19$	$$	$12.3288280059$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$4.30388242811$
2.2.157.1	x^2 - x - 39	$2$	[2,0]	$157$	$$	$12.5299640861$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$5.36131420646$
2.2.161.1	x^2 - x - 40	$2$	[2,0]	$7\cdot 23$	$$	$12.6885775404$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$10.0668810976$
2.0.163.1	x^2 - x + 41	$2$	[0,1]	$-\,163$	$$	$12.7671453348$	✓	✓	✓	$C_2$ (as 2T1)	trivial	$2$	$0$	$1$
2.2.172.1	x^2 - 43	$2$	[2,0]	$2^{2}\cdot 43$	$$	$13.1148770486$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$8.84850928027$
2.2.173.1	x^2 - x - 43	$2$	[2,0]	$173$	$$	$13.152946438$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$2.5708146781$

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