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 (33 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
1.1.1.1	x	$1$	[1,0]	$1$	$$	$1.0$		✓	✓	Trivial (as 1T1)	trivial	$2$	$0$	$1$
2.2.5.1	x^2 - x - 1	$2$	[2,0]	$5$	$$	$2.2360679775$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$0.48121182506$
2.2.8.1	x^2 - 2	$2$	[2,0]	$2^{3}$	$$	$2.82842712475$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$0.88137358702$
2.2.12.1	x^2 - 3	$2$	[2,0]	$2^{2}\cdot 3$	$$	$3.46410161514$		✓	✓	$C_2$ (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	$2$	$1$	$2.09471254726$
2.2.21.1	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	$2$	$1$	$2.49177985264$
2.2.40.1	x^2 - 10	$2$	[2,0]	$2^{3}\cdot 5$	$$	$6.32455532034$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$1.81844645923$
2.2.41.1	x^2 - x - 10	$2$	[2,0]	$41$	$$	$6.40312423743$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$4.15912713463$
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	$2$	$1$	$5.71041605276$
2.2.60.1	x^2 - 15	$2$	[2,0]	$2^{2}\cdot 3\cdot 5$	$$	$7.74596669241$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$2.0634370689$
2.2.61.1	x^2 - x - 15	$2$	[2,0]	$61$	$$	$7.81024967591$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$3.66421846089$
2.2.65.1	x^2 - x - 16	$2$	[2,0]	$5\cdot 13$	$$	$8.0622577483$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$2.77647228072$
2.2.69.1	x^2 - x - 17	$2$	[2,0]	$3\cdot 23$	$$	$8.30662386292$		✓	✓	$C_2$ (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]	$7\cdot 11$	$$	$8.77496438739$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$2.18464379161$
2.2.85.1	x^2 - x - 21	$2$	[2,0]	$5\cdot 17$	$$	$9.21954445729$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$2.20934770862$
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]	$97$	$$	$9.8488578018$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$9.32438309598$
3.3.49.1	x^3 - x^2 - 2x + 1	$3$	[3,0]	$7^{2}$	$$	$3.65930571002$		✓	✓	$C_3$ (as 3T1)	trivial	$2$	$2$	$0.525454682123$
3.3.81.1	x^3 - 3x - 1	$3$	[3,0]	$3^{4}$	$$	$4.32674871092$		✓	✓	$C_3$ (as 3T1)	trivial	$2$	$2$	$0.849287450646$