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Degree	Signature	Ramified prime count	Ramified	Unramified primes

Galois group	Field is	Intermediate field	Class group structure	Class number

Discriminant	Root discriminant	Galois root discriminant	CM field	Relative class number

Regulator	$p$ -adic completions	Monogenic	Index	Ines. $p$

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Results (38 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
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	$1$
2.0.7.1	$x^{2} - x + 2$	$2$	[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	$1$
2.0.11.1	$x^{2} - x + 3$	$2$	[0,1]	$-\,11$	$1$	$3.31662479036$	$3.3166247903554$	✓	✓	✓	$C_2$ (as 2T1)	trivial	$2$	0	$1$
2.0.15.1	$x^{2} - x + 4$	$2$	[0,1]	$-\,3\cdot 5$	$2$	$3.87298334621$	$3.872983346207417$	✓	✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	0	$1$
2.0.19.1	$x^{2} - x + 5$	$2$	[0,1]	$-\,19$	$1$	$4.35889894354$	$4.358898943540674$	✓	✓	✓	$C_2$ (as 2T1)	trivial	$2$	0	$1$
2.0.20.1	$x^{2} + 5$	$2$	[0,1]	$-\,2^{2}\cdot 5$	$2$	$4.472135955$	$4.47213595499958$	✓	✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	0	$1$
2.0.23.1	$x^{2} - x + 6$	$2$	[0,1]	$-\,23$	$1$	$4.79583152331$	$4.795831523312719$	✓	✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	0	$1$
2.0.24.1	$x^{2} + 6$	$2$	[0,1]	$-\,2^{3}\cdot 3$	$2$	$4.89897948557$	$4.898979485566356$	✓	✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	0	$1$
2.0.31.1	$x^{2} - x + 8$	$2$	[0,1]	$-\,31$	$1$	$5.56776436283$	$5.5677643628300215$	✓	✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	0	$1$
2.0.35.1	$x^{2} - x + 9$	$2$	[0,1]	$-\,5\cdot 7$	$2$	$5.9160797831$	$5.916079783099616$	✓	✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	0	$1$
2.0.39.1	$x^{2} - x + 10$	$2$	[0,1]	$-\,3\cdot 13$	$2$	$6.2449979984$	$6.244997998398398$	✓	✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	0	$1$
2.0.40.1	$x^{2} + 10$	$2$	[0,1]	$-\,2^{3}\cdot 5$	$2$	$6.32455532034$	$6.324555320336759$	✓	✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	0	$1$
2.0.43.1	$x^{2} - x + 11$	$2$	[0,1]	$-\,43$	$1$	$6.5574385243$	$6.557438524302$	✓	✓	✓	$C_2$ (as 2T1)	trivial	$2$	0	$1$
2.0.47.1	$x^{2} - x + 12$	$2$	[0,1]	$-\,47$	$1$	$6.8556546004$	$6.855654600401044$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	0	$1$
2.0.51.1	$x^{2} - x + 13$	$2$	[0,1]	$-\,3\cdot 17$	$2$	$7.14142842854$	$7.14142842854285$	✓	✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	0	$1$
2.0.52.1	$x^{2} + 13$	$2$	[0,1]	$-\,2^{2}\cdot 13$	$2$	$7.21110255093$	$7.211102550927978$	✓	✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	0	$1$
2.0.55.1	$x^{2} - x + 14$	$2$	[0,1]	$-\,5\cdot 11$	$2$	$7.4161984871$	$7.416198487095663$	✓	✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	0	$1$
2.0.56.1	$x^{2} + 14$	$2$	[0,1]	$-\,2^{3}\cdot 7$	$2$	$7.48331477355$	$7.483314773547883$	✓	✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	0	$1$
2.0.59.1	$x^{2} - x + 15$	$2$	[0,1]	$-\,59$	$1$	$7.68114574787$	$7.681145747868608$	✓	✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	0	$1$
2.0.67.1	$x^{2} - x + 17$	$2$	[0,1]	$-\,67$	$1$	$8.18535277187$	$8.18535277187245$	✓	✓	✓	$C_2$ (as 2T1)	trivial	$2$	0	$1$
2.0.68.1	$x^{2} + 17$	$2$	[0,1]	$-\,2^{2}\cdot 17$	$2$	$8.24621125124$	$8.246211251235321$	✓	✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	0	$1$
2.0.71.1	$x^{2} - x + 18$	$2$	[0,1]	$-\,71$	$1$	$8.42614977318$	$8.426149773176359$	✓	✓	✓	$C_2$ (as 2T1)	$[7]$	$2$	0	$1$
2.0.79.1	$x^{2} - x + 20$	$2$	[0,1]	$-\,79$	$1$	$8.88819441732$	$8.888194417315589$	✓	✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	0	$1$
2.0.83.1	$x^{2} - x + 21$	$2$	[0,1]	$-\,83$	$1$	$9.11043357914$	$9.1104335791443$	✓	✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	0	$1$
2.0.84.1	$x^{2} + 21$	$2$	[0,1]	$-\,2^{2}\cdot 3\cdot 7$	$3$	$9.16515138991$	$9.16515138991168$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 2]$	$2$	0	$1$
2.0.87.1	$x^{2} - x + 22$	$2$	[0,1]	$-\,3\cdot 29$	$2$	$9.32737905309$	$9.327379053088816$	✓	✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	0	$1$
2.0.88.1	$x^{2} + 22$	$2$	[0,1]	$-\,2^{3}\cdot 11$	$2$	$9.38083151965$	$9.38083151964686$	✓	✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	0	$1$
2.0.91.1	$x^{2} - x + 23$	$2$	[0,1]	$-\,7\cdot 13$	$2$	$9.53939201417$	$9.539392014169456$	✓	✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	0	$1$
2.0.95.1	$x^{2} - x + 24$	$2$	[0,1]	$-\,5\cdot 19$	$2$	$9.74679434481$	$9.746794344808963$	✓	✓	✓	$C_2$ (as 2T1)	$[8]$	$2$	0	$1$
3.1.23.1	$x^{3} - x^{2} + 1$	$3$	[1,1]	$-\,23$	$1$	$2.84386697985$	$4.795831523312719$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$0.281199574323$
3.1.31.1	$x^{3} + x - 1$	$3$	[1,1]	$-\,31$	$1$	$3.14138065239$	$5.5677643628300215$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$0.38224508584$
3.1.44.1	$x^{3} - x^{2} + x + 1$	$3$	[1,1]	$-\,2^{2}\cdot 11$	$2$	$3.53034833533$	$5.264813681193971$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$0.609377863436$
3.1.59.1	$x^{3} + 2 x - 1$	$3$	[1,1]	$-\,59$	$1$	$3.89299641587$	$7.681145747868608$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$0.790985720639$
3.1.76.1	$x^{3} - 2 x - 2$	$3$	[1,1]	$-\,2^{2}\cdot 19$	$2$	$4.23582358425$	$6.919320768399539$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$1.01859181978$
3.1.83.1	$x^{3} - x^{2} + x - 2$	$3$	[1,1]	$-\,83$	$1$	$4.36207067145$	$9.1104335791443$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$1.04069259944$
3.1.87.1	$x^{3} - x^{2} + 2 x + 1$	$3$	[1,1]	$-\,3\cdot 29$	$2$	$4.43104762169$	$9.327379053088816$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$0.934844845546$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.