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 1370659 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
2.0.3.1	x^2 - x + 1	$2$	[0,1]	$-\,3$	$1$	$1.73205080757$	✓	✓	✓	$C_2$ (as 2T1)	trivial	$6$	$0$	$1$
2.0.4.1	x^2 + 1	$2$	[0,1]	$-\,2^{2}$	$1$	$2.0$	✓	✓	✓	$C_2$ (as 2T1)	trivial	$4$	$0$	$1$
2.2.5.1	x^2 - x - 1	$2$	[2,0]	$5$	$1$	$2.2360679775$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$0.48121182506$
2.0.7.1	x^2 - x + 2	$2$	[0,1]	$-\,7$	$1$	$2.64575131106$	✓	✓	✓	$C_2$ (as 2T1)	trivial	$2$	$0$	$1$
2.0.8.1	x^2 + 2	$2$	[0,1]	$-\,2^{3}$	$1$	$2.82842712475$	✓	✓	✓	$C_2$ (as 2T1)	trivial	$2$	$0$	$1$
2.2.8.1	x^2 - 2	$2$	[2,0]	$2^{3}$	$1$	$2.82842712475$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$0.88137358702$
2.0.11.1	x^2 - x + 3	$2$	[0,1]	$-\,11$	$1$	$3.31662479036$	✓	✓	✓	$C_2$ (as 2T1)	trivial	$2$	$0$	$1$
2.2.12.1	x^2 - 3	$2$	[2,0]	$2^{2}\cdot 3$	$2$	$3.46410161514$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$1.31695789692$
2.2.13.1	x^2 - x - 3	$2$	[2,0]	$13$	$1$	$3.60555127546$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$1.19476321729$
2.0.15.1	x^2 - x + 4	$2$	[0,1]	$-\,3\cdot 5$	$2$	$3.87298334621$	✓	✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$0$	$1$
2.2.17.1	x^2 - x - 4	$2$	[2,0]	$17$	$1$	$4.12310562562$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$2.09471254726$
2.0.19.1	x^2 - x + 5	$2$	[0,1]	$-\,19$	$1$	$4.35889894354$	✓	✓	✓	$C_2$ (as 2T1)	trivial	$2$	$0$	$1$
2.0.20.1	x^2 + 5	$2$	[0,1]	$-\,2^{2}\cdot 5$	$2$	$4.472135955$	✓	✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$0$	$1$
2.2.21.1	x^2 - x - 5	$2$	[2,0]	$3\cdot 7$	$2$	$4.58257569496$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$1.56679923697$
2.0.23.1	x^2 - x + 6	$2$	[0,1]	$-\,23$	$1$	$4.79583152331$	✓	✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	$0$	$1$
2.0.24.1	x^2 + 6	$2$	[0,1]	$-\,2^{3}\cdot 3$	$2$	$4.89897948557$	✓	✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$0$	$1$
2.2.24.1	x^2 - 6	$2$	[2,0]	$2^{3}\cdot 3$	$2$	$4.89897948557$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$2.29243166956$
2.2.28.1	x^2 - 7	$2$	[2,0]	$2^{2}\cdot 7$	$2$	$5.29150262213$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$2.76865938331$
2.2.29.1	x^2 - x - 7	$2$	[2,0]	$29$	$1$	$5.38516480713$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$1.64723114637$
2.0.31.1	x^2 - x + 8	$2$	[0,1]	$-\,31$	$1$	$5.56776436283$	✓	✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	$0$	$1$
2.2.33.1	x^2 - x - 8	$2$	[2,0]	$3\cdot 11$	$2$	$5.74456264654$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$3.82816847133$
2.0.35.1	x^2 - x + 9	$2$	[0,1]	$-\,5\cdot 7$	$2$	$5.9160797831$	✓	✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$0$	$1$
2.2.37.1	x^2 - x - 9	$2$	[2,0]	$37$	$1$	$6.0827625303$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$2.49177985264$
2.0.39.1	x^2 - x + 10	$2$	[0,1]	$-\,3\cdot 13$	$2$	$6.2449979984$	✓	✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$0$	$1$
2.0.40.1	x^2 + 10	$2$	[0,1]	$-\,2^{3}\cdot 5$	$2$	$6.32455532034$	✓	✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$0$	$1$
2.2.40.1	x^2 - 10	$2$	[2,0]	$2^{3}\cdot 5$	$2$	$6.32455532034$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$1.81844645923$
2.2.41.1	x^2 - x - 10	$2$	[2,0]	$41$	$1$	$6.40312423743$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$4.15912713463$
2.0.43.1	x^2 - x + 11	$2$	[0,1]	$-\,43$	$1$	$6.5574385243$	✓	✓	✓	$C_2$ (as 2T1)	trivial	$2$	$0$	$1$
2.2.44.1	x^2 - 11	$2$	[2,0]	$2^{2}\cdot 11$	$2$	$6.63324958071$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$2.99322284613$
2.0.47.1	x^2 - x + 12	$2$	[0,1]	$-\,47$	$1$	$6.8556546004$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$0$	$1$
2.0.51.1	x^2 - x + 13	$2$	[0,1]	$-\,3\cdot 17$	$2$	$7.14142842854$	✓	✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$0$	$1$
2.0.52.1	x^2 + 13	$2$	[0,1]	$-\,2^{2}\cdot 13$	$2$	$7.21110255093$	✓	✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$0$	$1$
2.2.53.1	x^2 - x - 13	$2$	[2,0]	$53$	$1$	$7.28010988928$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$1.96572047165$
2.0.55.1	x^2 - x + 14	$2$	[0,1]	$-\,5\cdot 11$	$2$	$7.4161984871$	✓	✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$0$	$1$
2.0.56.1	x^2 + 14	$2$	[0,1]	$-\,2^{3}\cdot 7$	$2$	$7.48331477355$	✓	✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$0$	$1$
2.2.56.1	x^2 - 14	$2$	[2,0]	$2^{3}\cdot 7$	$2$	$7.48331477355$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$3.40008441411$
2.2.57.1	x^2 - x - 14	$2$	[2,0]	$3\cdot 19$	$2$	$7.54983443527$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$5.71041605276$
2.0.59.1	x^2 - x + 15	$2$	[0,1]	$-\,59$	$1$	$7.68114574787$	✓	✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	$0$	$1$
2.2.60.1	x^2 - 15	$2$	[2,0]	$2^{2}\cdot 3\cdot 5$	$3$	$7.74596669241$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$2.0634370689$
2.2.61.1	x^2 - x - 15	$2$	[2,0]	$61$	$1$	$7.81024967591$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$3.66421846089$
2.2.65.1	x^2 - x - 16	$2$	[2,0]	$5\cdot 13$	$2$	$8.0622577483$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$2.77647228072$
2.0.67.1	x^2 - x + 17	$2$	[0,1]	$-\,67$	$1$	$8.18535277187$	✓	✓	✓	$C_2$ (as 2T1)	trivial	$2$	$0$	$1$
2.0.68.1	x^2 + 17	$2$	[0,1]	$-\,2^{2}\cdot 17$	$2$	$8.24621125124$	✓	✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$0$	$1$
2.2.69.1	x^2 - x - 17	$2$	[2,0]	$3\cdot 23$	$2$	$8.30662386292$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$3.21727197116$
2.0.71.1	x^2 - x + 18	$2$	[0,1]	$-\,71$	$1$	$8.42614977318$	✓	✓	✓	$C_2$ (as 2T1)	$[7]$	$2$	$0$	$1$
2.2.73.1	x^2 - x - 18	$2$	[2,0]	$73$	$1$	$8.54400374532$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$7.66669041926$
2.2.76.1	x^2 - 19	$2$	[2,0]	$2^{2}\cdot 19$	$2$	$8.71779788708$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$5.82893696698$
2.2.77.1	x^2 - x - 19	$2$	[2,0]	$7\cdot 11$	$2$	$8.77496438739$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$2.18464379161$
2.0.79.1	x^2 - x + 20	$2$	[0,1]	$-\,79$	$1$	$8.88819441732$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$0$	$1$
2.0.83.1	x^2 - x + 21	$2$	[0,1]	$-\,83$	$1$	$9.11043357914$	✓	✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	$0$	$1$

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