Number field search results

Results (33 matches)

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Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois 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]	$1$	$0$	$1.0$	$1.0$		✓	✓	Trivial (as 1T1)	trivial	$2$	0	$1$
2.2.5.1	$x^{2} - x - 1$	$2$	[2,0]	$5$	$1$	$2.2360679775$	$2.23606797749979$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$0.48121182506$
2.2.8.1	$x^{2} - 2$	$2$	[2,0]	$2^{3}$	$1$	$2.82842712475$	$2.8284271247461903$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$0.88137358702$
2.2.12.1	$x^{2} - 3$	$2$	[2,0]	$2^{2}\cdot 3$	$2$	$3.46410161514$	$3.4641016151377544$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$1.31695789692$
2.2.13.1	$x^{2} - x - 3$	$2$	[2,0]	$13$	$1$	$3.60555127546$	$3.605551275463989$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$1.19476321729$
2.2.17.1	$x^{2} - x - 4$	$2$	[2,0]	$17$	$1$	$4.12310562562$	$4.123105625617661$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$2.09471254726$
2.2.21.1	$x^{2} - x - 5$	$2$	[2,0]	$3\cdot 7$	$2$	$4.58257569496$	$4.58257569495584$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$1.56679923697$
2.2.24.1	$x^{2} - 6$	$2$	[2,0]	$2^{3}\cdot 3$	$2$	$4.89897948557$	$4.898979485566356$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$2.29243166956$
2.2.28.1	$x^{2} - 7$	$2$	[2,0]	$2^{2}\cdot 7$	$2$	$5.29150262213$	$5.291502622129181$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$2.76865938331$
2.2.29.1	$x^{2} - x - 7$	$2$	[2,0]	$29$	$1$	$5.38516480713$	$5.385164807134504$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$1.64723114637$
2.2.33.1	$x^{2} - x - 8$	$2$	[2,0]	$3\cdot 11$	$2$	$5.74456264654$	$5.744562646538029$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$3.82816847133$
2.2.37.1	$x^{2} - x - 9$	$2$	[2,0]	$37$	$1$	$6.0827625303$	$6.082762530298219$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$2.49177985264$
2.2.40.1	$x^{2} - 10$	$2$	[2,0]	$2^{3}\cdot 5$	$2$	$6.32455532034$	$6.324555320336759$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$1.81844645923$
2.2.41.1	$x^{2} - x - 10$	$2$	[2,0]	$41$	$1$	$6.40312423743$	$6.4031242374328485$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$4.15912713463$
2.2.44.1	$x^{2} - 11$	$2$	[2,0]	$2^{2}\cdot 11$	$2$	$6.63324958071$	$6.6332495807108$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$2.99322284613$
2.2.53.1	$x^{2} - x - 13$	$2$	[2,0]	$53$	$1$	$7.28010988928$	$7.280109889280518$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$1.96572047165$
2.2.56.1	$x^{2} - 14$	$2$	[2,0]	$2^{3}\cdot 7$	$2$	$7.48331477355$	$7.483314773547883$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$3.40008441411$
2.2.57.1	$x^{2} - x - 14$	$2$	[2,0]	$3\cdot 19$	$2$	$7.54983443527$	$7.54983443527075$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$5.71041605276$
2.2.60.1	$x^{2} - 15$	$2$	[2,0]	$2^{2}\cdot 3\cdot 5$	$3$	$7.74596669241$	$7.745966692414834$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$2.0634370689$
2.2.61.1	$x^{2} - x - 15$	$2$	[2,0]	$61$	$1$	$7.81024967591$	$7.810249675906654$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$3.66421846089$
2.2.65.1	$x^{2} - x - 16$	$2$	[2,0]	$5\cdot 13$	$2$	$8.0622577483$	$8.06225774829855$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$2.77647228072$
2.2.69.1	$x^{2} - x - 17$	$2$	[2,0]	$3\cdot 23$	$2$	$8.30662386292$	$8.306623862918075$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$3.21727197116$
2.2.73.1	$x^{2} - x - 18$	$2$	[2,0]	$73$	$1$	$8.54400374532$	$8.54400374531753$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$7.66669041926$
2.2.76.1	$x^{2} - 19$	$2$	[2,0]	$2^{2}\cdot 19$	$2$	$8.71779788708$	$8.717797887081348$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$5.82893696698$
2.2.77.1	$x^{2} - x - 19$	$2$	[2,0]	$7\cdot 11$	$2$	$8.77496438739$	$8.774964387392123$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$2.18464379161$
2.2.85.1	$x^{2} - x - 21$	$2$	[2,0]	$5\cdot 17$	$2$	$9.21954445729$	$9.219544457292887$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$2.20934770862$
2.2.88.1	$x^{2} - 22$	$2$	[2,0]	$2^{3}\cdot 11$	$2$	$9.38083151965$	$9.38083151964686$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$5.97634446743$
2.2.89.1	$x^{2} - x - 22$	$2$	[2,0]	$89$	$1$	$9.43398113206$	$9.433981132056603$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$6.90775627898$
2.2.92.1	$x^{2} - 23$	$2$	[2,0]	$2^{2}\cdot 23$	$2$	$9.59166304663$	$9.591663046625438$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$3.87076670029$
2.2.93.1	$x^{2} - x - 23$	$2$	[2,0]	$3\cdot 31$	$2$	$9.64365076099$	$9.643650760992955$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$3.36610464293$
2.2.97.1	$x^{2} - x - 24$	$2$	[2,0]	$97$	$1$	$9.8488578018$	$9.848857801796104$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$9.32438309598$
3.3.49.1	$x^{3} - x^{2} - 2 x + 1$	$3$	[3,0]	$7^{2}$	$1$	$3.65930571002$	$3.6593057100229713$		✓	✓	$C_3$ (as 3T1)	trivial	$2$	$2$	$0.525454682123$
3.3.81.1	$x^{3} - 3 x - 1$	$3$	[3,0]	$3^{4}$	$1$	$4.32674871092$	$4.326748710922225$		✓	✓	$C_3$ (as 3T1)	trivial	$2$	$2$	$0.849287450646$

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