Number field search results

The results below are complete, since the LMFDB contains all number fields with absolute discriminant at most 1656109

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	Narrow class group	Unit group torsion	Unit group rank	Regulator	Unit signature rank
1.1.1.1	$x$	$1$	(1, 0)	$1$	$0$	$1.0$	$1.0$		✓	✓	Trivial (as 1T1)	trivial	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	trivial	$2$	$1$	$0.48121182506$	$2$
2.2.8.1	$x^{2} - 2$	$2$	(2, 0)	$2^{3}$	$1$	$2.82842712475$	$2.8284271247461903$		✓	✓	$C_2$ (as 2T1)	trivial	trivial	$2$	$1$	$0.88137358702$	$2$
2.2.12.1	$x^{2} - 3$	$2$	(2, 0)	$2^{2}\cdot 3$	$2$	$3.46410161514$	$3.4641016151377544$		✓	✓	$C_2$ (as 2T1)	trivial	$[2]$	$2$	$1$	$1.31695789692$	$1$
2.2.13.1	$x^{2} - x - 3$	$2$	(2, 0)	$13$	$1$	$3.60555127546$	$3.605551275463989$		✓	✓	$C_2$ (as 2T1)	trivial	trivial	$2$	$1$	$1.19476321729$	$2$
2.2.17.1	$x^{2} - x - 4$	$2$	(2, 0)	$17$	$1$	$4.12310562562$	$4.123105625617661$		✓	✓	$C_2$ (as 2T1)	trivial	trivial	$2$	$1$	$2.09471254726$	$2$
2.2.21.1	$x^{2} - x - 5$	$2$	(2, 0)	$3\cdot 7$	$2$	$4.58257569496$	$4.58257569495584$		✓	✓	$C_2$ (as 2T1)	trivial	$[2]$	$2$	$1$	$1.56679923697$	$1$
2.2.24.1	$x^{2} - 6$	$2$	(2, 0)	$2^{3}\cdot 3$	$2$	$4.89897948557$	$4.898979485566356$		✓	✓	$C_2$ (as 2T1)	trivial	$[2]$	$2$	$1$	$2.29243166956$	$1$
2.2.28.1	$x^{2} - 7$	$2$	(2, 0)	$2^{2}\cdot 7$	$2$	$5.29150262213$	$5.291502622129181$		✓	✓	$C_2$ (as 2T1)	trivial	$[2]$	$2$	$1$	$2.76865938331$	$1$
2.2.29.1	$x^{2} - x - 7$	$2$	(2, 0)	$29$	$1$	$5.38516480713$	$5.385164807134504$		✓	✓	$C_2$ (as 2T1)	trivial	trivial	$2$	$1$	$1.64723114637$	$2$
2.2.33.1	$x^{2} - x - 8$	$2$	(2, 0)	$3\cdot 11$	$2$	$5.74456264654$	$5.744562646538029$		✓	✓	$C_2$ (as 2T1)	trivial	$[2]$	$2$	$1$	$3.82816847133$	$1$
2.2.37.1	$x^{2} - x - 9$	$2$	(2, 0)	$37$	$1$	$6.0827625303$	$6.082762530298219$		✓	✓	$C_2$ (as 2T1)	trivial	trivial	$2$	$1$	$2.49177985264$	$2$
2.2.40.1	$x^{2} - 10$	$2$	(2, 0)	$2^{3}\cdot 5$	$2$	$6.32455532034$	$6.324555320336759$		✓	✓	$C_2$ (as 2T1)	$[2]$	$[2]$	$2$	$1$	$1.81844645923$	$2$
2.2.41.1	$x^{2} - x - 10$	$2$	(2, 0)	$41$	$1$	$6.40312423743$	$6.4031242374328485$		✓	✓	$C_2$ (as 2T1)	trivial	trivial	$2$	$1$	$4.15912713463$	$2$
2.2.44.1	$x^{2} - 11$	$2$	(2, 0)	$2^{2}\cdot 11$	$2$	$6.63324958071$	$6.6332495807108$		✓	✓	$C_2$ (as 2T1)	trivial	$[2]$	$2$	$1$	$2.99322284613$	$1$
2.2.53.1	$x^{2} - x - 13$	$2$	(2, 0)	$53$	$1$	$7.28010988928$	$7.280109889280518$		✓	✓	$C_2$ (as 2T1)	trivial	trivial	$2$	$1$	$1.96572047165$	$2$
2.2.56.1	$x^{2} - 14$	$2$	(2, 0)	$2^{3}\cdot 7$	$2$	$7.48331477355$	$7.483314773547883$		✓	✓	$C_2$ (as 2T1)	trivial	$[2]$	$2$	$1$	$3.40008441411$	$1$
2.2.57.1	$x^{2} - x - 14$	$2$	(2, 0)	$3\cdot 19$	$2$	$7.54983443527$	$7.54983443527075$		✓	✓	$C_2$ (as 2T1)	trivial	$[2]$	$2$	$1$	$5.71041605276$	$1$
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)	$[2]$	$[2, 2]$	$2$	$1$	$2.0634370689$	$1$
2.2.61.1	$x^{2} - x - 15$	$2$	(2, 0)	$61$	$1$	$7.81024967591$	$7.810249675906654$		✓	✓	$C_2$ (as 2T1)	trivial	trivial	$2$	$1$	$3.66421846089$	$2$
2.2.65.1	$x^{2} - x - 16$	$2$	(2, 0)	$5\cdot 13$	$2$	$8.0622577483$	$8.06225774829855$		✓	✓	$C_2$ (as 2T1)	$[2]$	$[2]$	$2$	$1$	$2.77647228072$	$2$
2.2.69.1	$x^{2} - x - 17$	$2$	(2, 0)	$3\cdot 23$	$2$	$8.30662386292$	$8.306623862918075$		✓	✓	$C_2$ (as 2T1)	trivial	$[2]$	$2$	$1$	$3.21727197116$	$1$
2.2.73.1	$x^{2} - x - 18$	$2$	(2, 0)	$73$	$1$	$8.54400374532$	$8.54400374531753$		✓	✓	$C_2$ (as 2T1)	trivial	trivial	$2$	$1$	$7.66669041926$	$2$
2.2.76.1	$x^{2} - 19$	$2$	(2, 0)	$2^{2}\cdot 19$	$2$	$8.71779788708$	$8.717797887081348$		✓	✓	$C_2$ (as 2T1)	trivial	$[2]$	$2$	$1$	$5.82893696698$	$1$
2.2.77.1	$x^{2} - x - 19$	$2$	(2, 0)	$7\cdot 11$	$2$	$8.77496438739$	$8.774964387392123$		✓	✓	$C_2$ (as 2T1)	trivial	$[2]$	$2$	$1$	$2.18464379161$	$1$
2.2.85.1	$x^{2} - x - 21$	$2$	(2, 0)	$5\cdot 17$	$2$	$9.21954445729$	$9.219544457292887$		✓	✓	$C_2$ (as 2T1)	$[2]$	$[2]$	$2$	$1$	$2.20934770862$	$2$
2.2.88.1	$x^{2} - 22$	$2$	(2, 0)	$2^{3}\cdot 11$	$2$	$9.38083151965$	$9.38083151964686$		✓	✓	$C_2$ (as 2T1)	trivial	$[2]$	$2$	$1$	$5.97634446743$	$1$
2.2.89.1	$x^{2} - x - 22$	$2$	(2, 0)	$89$	$1$	$9.43398113206$	$9.433981132056603$		✓	✓	$C_2$ (as 2T1)	trivial	trivial	$2$	$1$	$6.90775627898$	$2$
2.2.92.1	$x^{2} - 23$	$2$	(2, 0)	$2^{2}\cdot 23$	$2$	$9.59166304663$	$9.591663046625438$		✓	✓	$C_2$ (as 2T1)	trivial	$[2]$	$2$	$1$	$3.87076670029$	$1$
2.2.93.1	$x^{2} - x - 23$	$2$	(2, 0)	$3\cdot 31$	$2$	$9.64365076099$	$9.643650760992955$		✓	✓	$C_2$ (as 2T1)	trivial	$[2]$	$2$	$1$	$3.36610464293$	$1$
2.2.97.1	$x^{2} - x - 24$	$2$	(2, 0)	$97$	$1$	$9.8488578018$	$9.848857801796104$		✓	✓	$C_2$ (as 2T1)	trivial	trivial	$2$	$1$	$9.32438309598$	$2$
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	trivial	$2$	$2$	$0.525454682123$	$3$
3.3.81.1	$x^{3} - 3 x - 1$	$3$	(3, 0)	$3^{4}$	$1$	$4.32674871092$	$4.326748710922225$		✓	✓	$C_3$ (as 3T1)	trivial	trivial	$2$	$2$	$0.849287450646$	$3$

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