Number field search results

Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)

Results (1-50 of 10217788 matches)

 

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	$1$
2.0.3.1	$x^{2} - x + 1$	$2$	[0,1]	$-\,3$	$1$	$1.73205080757$	$1.7320508075688772$	✓	✓	✓	$C_2$ (as 2T1)	trivial	$6$	0	$1$
2.0.4.1	$x^{2} + 1$	$2$	[0,1]	$-\,2^{2}$	$1$	$2.0$	$2.0$	✓	✓	✓	$C_2$ (as 2T1)	trivial	$4$	0	$1$
2.2.5.1	$x^{2} - x - 1$	$2$	[2,0]	$5$	$1$	$2.2360679775$	$2.23606797749979$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$0.48121182506$
2.0.7.1	$x^{2} - x + 2$	$2$	[0,1]	$-\,7$	$1$	$2.64575131106$	$2.6457513110645907$	✓	✓	✓	$C_2$ (as 2T1)	trivial	$2$	0	$1$
2.0.8.1	$x^{2} + 2$	$2$	[0,1]	$-\,2^{3}$	$1$	$2.82842712475$	$2.8284271247461903$	✓	✓	✓	$C_2$ (as 2T1)	trivial	$2$	0	$1$
2.2.8.1	$x^{2} - 2$	$2$	[2,0]	$2^{3}$	$1$	$2.82842712475$	$2.8284271247461903$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$0.88137358702$
2.0.11.1	$x^{2} - x + 3$	$2$	[0,1]	$-\,11$	$1$	$3.31662479036$	$3.3166247903554$	✓	✓	✓	$C_2$ (as 2T1)	trivial	$2$	0	$1$
2.2.12.1	$x^{2} - 3$	$2$	[2,0]	$2^{2}\cdot 3$	$2$	$3.46410161514$	$3.4641016151377544$		✓	✓	$C_2$ (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	$2$	$1$	$2.09471254726$
2.0.19.1	$x^{2} - x + 5$	$2$	[0,1]	$-\,19$	$1$	$4.35889894354$	$4.358898943540674$	✓	✓	✓	$C_2$ (as 2T1)	trivial	$2$	0	$1$
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	$2$	$1$	$2.49177985264$
2.2.41.1	$x^{2} - x - 10$	$2$	[2,0]	$41$	$1$	$6.40312423743$	$6.4031242374328485$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$4.15912713463$
2.0.43.1	$x^{2} - x + 11$	$2$	[0,1]	$-\,43$	$1$	$6.5574385243$	$6.557438524302$	✓	✓	✓	$C_2$ (as 2T1)	trivial	$2$	0	$1$
2.2.44.1	$x^{2} - 11$	$2$	[2,0]	$2^{2}\cdot 11$	$2$	$6.63324958071$	$6.6332495807108$		✓	✓	$C_2$ (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	$2$	$1$	$5.71041605276$
2.2.61.1	$x^{2} - x - 15$	$2$	[2,0]	$61$	$1$	$7.81024967591$	$7.810249675906654$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$3.66421846089$
2.0.67.1	$x^{2} - x + 17$	$2$	[0,1]	$-\,67$	$1$	$8.18535277187$	$8.18535277187245$	✓	✓	✓	$C_2$ (as 2T1)	trivial	$2$	0	$1$
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	$2$	$1$	$2.18464379161$
2.2.88.1	$x^{2} - 22$	$2$	[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	$2$	$1$	$9.32438309598$
2.2.101.1	$x^{2} - x - 25$	$2$	[2,0]	$101$	$1$	$10.0498756211$	$10.04987562112089$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$2.9982229503$
2.2.109.1	$x^{2} - x - 27$	$2$	[2,0]	$109$	$1$	$10.4403065089$	$10.44030650891055$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$5.56453508676$
2.2.113.1	$x^{2} - x - 28$	$2$	[2,0]	$113$	$1$	$10.6301458127$	$10.63014581273465$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$7.3473001159$
2.2.124.1	$x^{2} - 31$	$2$	[2,0]	$2^{2}\cdot 31$	$2$	$11.1355287257$	$11.135528725660043$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$8.01961268619$
2.2.129.1	$x^{2} - x - 32$	$2$	[2,0]	$3\cdot 43$	$2$	$11.3578166916$	$11.357816691600547$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$10.4255498073$
2.2.133.1	$x^{2} - x - 33$	$2$	[2,0]	$7\cdot 19$	$2$	$11.5325625947$	$11.532562594670797$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$5.15325818041$
2.2.137.1	$x^{2} - x - 34$	$2$	[2,0]	$137$	$1$	$11.7046999107$	$11.704699910719626$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$8.15708386722$
2.2.141.1	$x^{2} - x - 35$	$2$	[2,0]	$3\cdot 47$	$2$	$11.874342087$	$11.874342087037917$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$5.24699637018$
2.2.149.1	$x^{2} - x - 37$	$2$	[2,0]	$149$	$1$	$12.2065556157$	$12.206555615733702$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$4.11114250086$
2.2.152.1	$x^{2} - 38$	$2$	[2,0]	$2^{3}\cdot 19$	$2$	$12.3288280059$	$12.328828005937952$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$4.30388242811$
2.2.157.1	$x^{2} - x - 39$	$2$	[2,0]	$157$	$1$	$12.5299640861$	$12.529964086141668$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$5.36131420646$
2.2.161.1	$x^{2} - x - 40$	$2$	[2,0]	$7\cdot 23$	$2$	$12.6885775404$	$12.68857754044952$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$10.0668810976$
2.0.163.1	$x^{2} - x + 41$	$2$	[0,1]	$-\,163$	$1$	$12.7671453348$	$12.767145334803704$	✓	✓	✓	$C_2$ (as 2T1)	trivial	$2$	0	$1$
2.2.172.1	$x^{2} - 43$	$2$	[2,0]	$2^{2}\cdot 43$	$2$	$13.1148770486$	$13.114877048604$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$8.84850928027$
2.2.173.1	$x^{2} - x - 43$	$2$	[2,0]	$173$	$1$	$13.152946438$	$13.152946437965905$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$2.5708146781$