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. \(p\)

Sort order

Select

Results (1-50 of 352943 matches)

  There are too many results (352943) to download.

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
9.1.29510281.1	x^9 - 2x^8 + 2x^7 - 3x^5 + 7x^4 - 8x^3 + 6x^2 - 3x + 1	$9$	[1,4]	$101\cdot 292181$	$$	$6.76078364853$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.680531134278$
9.1.30073129.1	x^9 - 2x^8 + 2x^7 - x^5 + x^3 + x^2 - 2x + 1	$9$	[1,4]	$353\cdot 85193$	$$	$6.77499119692$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.688991454074$
9.1.30626693.1	x^9 - x^6 - 2x^5 - x^4 + 2x^2 + x + 1	$9$	[1,4]	$30626693$	$$	$6.78873569358$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.697791262451$
9.1.32029433.1	x^9 - 2x^8 + 3x^6 - x^5 - 3x^4 + 3x^3 + x^2 - 2x + 1	$9$	[1,4]	$32029433$	$$	$6.82260010718$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7178935503824918$
9.1.32206049.1	x^9 - 2x^8 + 4x^7 - 5x^6 + 6x^5 - 6x^4 + 5x^3 - 4x^2 + 3x - 1	$9$	[1,4]	$23^{3}\cdot 2647$	$$	$6.82677001293$			✓	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$4$	$0.720252095298$
9.1.32344469.1	x^9 - x^7 - x^6 + 2x^5 + 2x^4 - x^3 - 2x^2 + 1	$9$	[1,4]	$53\cdot 89\cdot 6857$	$$	$6.83002392654$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.722703704685$
9.1.33860761.1	x^9 - 2x^8 + 2x^7 - 2x^5 + 2x^4 - x + 1	$9$	[1,4]	$11^{2}\cdot 23^{4}$	$$	$6.8648802879$			✓	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T30)	trivial	$2$	$4$	$0.744153660637$
9.1.35028793.1	x^9 - 2x^8 + 4x^7 - 7x^6 + 10x^5 - 11x^4 + 11x^3 - 8x^2 + 4x - 1	$9$	[1,4]	$23^{3}\cdot 2879$	$$	$6.89079712201$			✓	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$4$	$0.760652964324$
9.1.35050633.1	x^9 - x^8 + x^7 - 3x^6 + 3x^5 - 2x^4 + 4x^3 - 2x^2 + x - 1	$9$	[1,4]	$43\cdot 311\cdot 2621$	$$	$6.891274359$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7613732494747866$
9.1.38817673.1	x^9 - x^7 - 2x^4 - 2x^3 + x^2 + 3x + 1	$9$	[1,4]	$31^{3}\cdot 1303$	$$	$6.96988318969$			✓	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$4$	$0.822727339615$
9.1.43302353.1	x^9 - 2x^7 + 2x^5 - x^4 + 2x^3 - 2x + 1	$9$	[1,4]	$23^{3}\cdot 3559$	$$	$7.05506919073$			not computed	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$4$	$0.876375147614$
9.1.44555813.1	x^9 - x^8 + 2x^7 - 2x^5 + 2x^4 - 2x^3 - x^2 + x - 1	$9$	[1,4]	$44555813$	$$	$7.07747369057$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.8927353251611637$
9.1.44656709.1	x^9 - 3x^8 + 6x^7 - 10x^6 + 13x^5 - 13x^4 + 10x^3 - 7x^2 + 3x - 1	$9$	[1,4]	$31^{3}\cdot 1499$	$$	$7.07925266065$			✓	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$4$	$0.904627574852$
9.1.44908397.1	x^9 + x^7 - x^6 + 3x^5 + 2x^3 + x + 1	$9$	[1,4]	$23^{3}\cdot 3691$	$$	$7.08367482946$			not computed	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$4$	$0.909270314$
9.1.47159153.1	x^9 - x^8 - 2x^7 + x^6 + 2x^5 + x^3 - 2x - 1	$9$	[1,4]	$31^{3}\cdot 1583$	$$	$7.12227017395$			✓	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$4$	$0.927340454576$
9.1.49483189.1	x^9 - 2x^8 + 2x^7 - 2x^6 + 3x^5 - 4x^4 + 2x^3 - x^2 + x - 1	$9$	[1,4]	$7^{2}\cdot 23^{3}\cdot 83$	$$	$7.16044053251$			✓	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$4$	$0.967836435735$
9.1.50797225.1	x^9 - 2x^8 + x^7 + 2x^6 - 4x^5 + x^4 + 3x^3 - 2x^2 + 1	$9$	[1,4]	$5^{2}\cdot 23^{3}\cdot 167$	$$	$7.18132270776$			✓	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$4$	$0.99135399817$
9.1.51478577.1	x^9 - x^8 + 3x^7 - 5x^6 + 6x^5 - 7x^4 + 6x^3 - 5x^2 + 2x - 1	$9$	[1,4]	$23^{3}\cdot 4231$	$$	$7.1919621414$			✓	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$4$	$1.00101578952$
9.1.53628353.1	x^9 - 3x^8 + 4x^7 - 3x^6 + 3x^5 - 2x^4 - x^3 + 4x^2 - 3x + 1	$9$	[1,4]	$17\cdot 43\cdot 73363$	$$	$7.22472975319$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$1.0267525800082251$
9.1.53814641.1	x^9 - 3x^8 + 5x^7 - 6x^6 + 4x^5 - 2x^4 + x^2 + 1	$9$	[1,4]	$23^{3}\cdot 4423$	$$	$7.22751395028$			✓	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$4$	$1.00414538811$
9.1.54982673.1	x^9 - 2x^8 + 3x^7 - 4x^6 + 4x^5 - 3x^4 + 3x^3 - 2x^2 - 1	$9$	[1,4]	$23^{3}\cdot 4519$	$$	$7.24477820597$			✓	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$4$	$1.04181323068$
9.1.56491381.1	x^9 - 4x^8 + 9x^7 - 15x^6 + 20x^5 - 20x^4 + 16x^3 - 10x^2 + 5x - 1	$9$	[1,4]	$23^{3}\cdot 4643$	$$	$7.26660167523$			✓	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$4$	$1.05040427633$
9.1.58778777.1	x^9 - 2x^8 + 3x^7 - 3x^6 + x^5 + x^4 - 2x^3 + x^2 - 1	$9$	[1,4]	$23^{3}\cdot 4831$	$$	$7.29872040509$			✓	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$4$	$1.09704059882$
9.1.58956389.1	x^9 - 2x^8 + 2x^7 - 2x^5 + 4x^4 - 5x^3 + 4x^2 - 2x + 1	$9$	[1,4]	$31^{3}\cdot 1979$	$$	$7.30116762752$			✓	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$4$	$1.08378947669$
9.1.59552209.1	x^9 - 2x^8 + 4x^7 - 6x^6 + 8x^5 - 9x^4 + 8x^3 - 5x^2 + 3x - 1	$9$	[1,4]	$31^{3}\cdot 1999$	$$	$7.30932952839$			✓	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$4$	$1.08316800712$
9.1.59849473.1	x^9 - 3x^8 + 5x^7 - 6x^6 + 8x^5 - 10x^4 + 11x^3 - 9x^2 + 5x - 1	$9$	[1,4]	$23^{3}\cdot 4919$	$$	$7.31337452293$			✓	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$4$	$1.14447533875$
9.1.66078977.1	x^9 - x^8 - x^7 + x^6 + 2x^4 - x^3 - 2x^2 + x + 1	$9$	[1,4]	$23^{3}\cdot 5431$	$$	$7.39428053466$			✓	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$4$	$1.21658528983$
9.1.66711661.1	x^9 - 3x^8 + 5x^7 - 8x^6 + 11x^5 - 11x^4 + 10x^3 - 6x^2 + 3x - 1	$9$	[1,4]	$23^{3}\cdot 5483$	$$	$7.4021136771$			✓	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$4$	$1.17347955045$
9.1.67149673.1	x^9 - 3x^8 + 4x^7 - 5x^5 + 5x^4 + x^3 - 4x^2 + 3x - 1	$9$	[1,4]	$23^{3}\cdot 5519$	$$	$7.40749803046$			✓	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$4$	$1.1924024692$
9.1.68755717.1	x^9 - x^8 + 3x^7 - 2x^6 + 3x^5 + x^4 + x^2 + x + 1	$9$	[1,4]	$23^{3}\cdot 5651$	$$	$7.42697719851$			not computed	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$4$	$1.19722306716$
9.1.72503153.1	x^9 - 3x^8 + 7x^7 - 12x^6 + 17x^5 - 19x^4 + 17x^3 - 12x^2 + 6x - 1	$9$	[1,4]	$23^{3}\cdot 59\cdot 101$	$$	$7.47090111582$			✓	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$4$	$1.28904079212$
9.1.73513792.1	x^9 - 3x^8 + 3x^7 - 4x^5 + 7x^4 - 7x^3 + 5x^2 - 2x + 1	$9$	[1,4]	$2^{6}\cdot 11^{3}\cdot 863$	$$	$7.48240102059$			✓	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$4$	$1.2490309659$
9.1.74566873.1	x^9 - x^8 - x^7 + 2x^6 - 2x^5 + x^3 - x^2 + x - 1	$9$	[1,4]	$31^{3}\cdot 2503$	$$	$7.49423531658$			✓	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$4$	$1.24751877939$
9.1.74839217.1	x^9 - 3x^8 + 2x^7 + 2x^4 - 2x^2 - 1	$9$	[1,4]	$23^{3}\cdot 6151$	$$	$7.49727167313$			✓	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$4$	$1.26299231697$
9.1.75401021.1	x^9 - x^8 + 3x^7 - 3x^6 + 4x^5 - 5x^4 + 5x^3 - 5x^2 + 3x - 1	$9$	[1,4]	$31^{3}\cdot 2531$	$$	$7.50350430936$			✓	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$4$	$1.27276589382$
9.1.75909913.1	x^9 - 2x^8 + 2x^7 - x^6 + x^5 - 3x^4 + 6x^3 - 3x^2 - x + 1	$9$	[1,4]	$17\cdot 23^{3}\cdot 367$	$$	$7.50911441287$			not computed	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$4$	$1.27659179008$
9.1.76639933.1	x^9 - x^8 + 4x^7 - 2x^6 + 4x^5 + 2x^4 - x^3 + 5x^2 - 2x + 1	$9$	[1,4]	$23^{3}\cdot 6299$	$$	$7.51710416768$			✓	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$4$	$1.27907520419$
9.1.76931941.1	x^9 - 2x^8 + x^7 - x^6 + 3x^5 - 4x^4 + x^3 + 3x^2 - 2x + 1	$9$	[1,4]	$23^{3}\cdot 6323$	$$	$7.52028113978$			not computed	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$4$	$1.31828660102$
9.1.78284096.1	x^9 - x^8 - x^7 + 2x^6 - 3x^4 + x^3 + 3x^2 - 1	$9$	[1,4]	$2^{6}\cdot 11^{3}\cdot 919$	$$	$7.53485393578$			✓	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$4$	$1.30168122946$
9.1.79073333.1	x^9 - x^8 - 2x^7 + x^6 + x^4 + 4x^3 - x^2 - 3x - 1	$9$	[1,4]	$23^{3}\cdot 67\cdot 97$	$$	$7.54325681657$			✓	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$4$	$1.30723193327$
9.1.80387369.1	x^9 - x^8 + 4x^7 - 5x^6 + 6x^5 - 6x^4 + 3x^3 - x^2 - x + 1	$9$	[1,4]	$23^{3}\cdot 6607$	$$	$7.55708316564$			✓	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$4$	$1.38872615482$
9.1.81117389.1	x^9 - x^8 + x^7 + x^6 - x^5 + 2x^4 + x^3 + x^2 + x + 1	$9$	[1,4]	$23^{3}\cdot 59\cdot 113$	$$	$7.56467789356$			✓	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$4$	$1.36429268784$
9.1.82042081.1	x^9 - 3x^8 + 7x^7 - 12x^6 + 15x^5 - 16x^4 + 12x^3 - 8x^2 + 4x - 1	$9$	[1,4]	$11\cdot 23^{3}\cdot 613$	$$	$7.57421114183$			✓	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$4$	$1.31089303171$
9.1.82334089.1	x^9 - 2x^8 + x^7 - x^6 + 3x^5 - x^4 - x^3 + 1	$9$	[1,4]	$23^{3}\cdot 67\cdot 101$	$$	$7.57720180133$			✓	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$4$	$1.35402539747$
9.1.82431425.1	x^9 - 2x^8 + 2x^7 + x^6 - 2x^5 + 3x^3 - 2x^2 - x + 1	$9$	[1,4]	$5^{2}\cdot 23^{3}\cdot 271$	$$	$7.57819659285$			✓	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$4$	$1.40959411571$
9.1.83319616.1	x^9 - 4x^8 + 9x^7 - 15x^6 + 17x^5 - 14x^4 + 8x^3 - x^2 - x + 1	$9$	[1,4]	$2^{6}\cdot 23^{3}\cdot 107$	$$	$7.58722614521$			✓	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$4$	$1.34933902572$
9.1.89611328.1	x^9 - 2x^8 + 2x^7 + x^6 - x^5 - x^4 + x^3 + 2x^2 - 3x + 1	$9$	[1,4]	$2^{6}\cdot 31^{3}\cdot 47$	$$	$7.64884533493$			✓	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$4$	$1.43102382388$
9.1.90161381.1	x^9 - 3x^8 + 5x^7 - 8x^6 + 10x^5 - 11x^4 + 10x^3 - 8x^2 + 4x - 1	$9$	[1,4]	$59^{3}\cdot 439$	$$	$7.65404784765$			✓	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$4$	$1.42329967324$
9.1.92371321.1	x^9 - 2x^8 + 5x^7 - 7x^6 + 8x^5 - 9x^4 + 7x^3 - 4x^2 + 3x - 1	$9$	[1,4]	$7^{2}\cdot 1373^{2}$	$$	$7.67466952877$			✓	$A_9$ (as 9T33)	trivial	$2$	$4$	$1.49260534207$
9.1.92943713.1	x^9 - 3x^8 + 6x^7 - 7x^6 + 5x^5 - 4x^3 + 6x^2 - 4x + 1	$9$	[1,4]	$23^{3}\cdot 7639$	$$	$7.67993916346$			✓	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$4$	$1.45753700948$

  There are too many results (352943) to download.