Global number field search results

Further refine search

Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying all 8 matches)

Label	Polynomial	Discriminant	Galois group	Class group
21.3.7655337671796811085236857471811.1	x^21 - 6x^20 + 19x^19 - 35x^18 + 34x^17 - 27x^16 + 33x^15 - 73x^14 + 37x^13 + 44x^12 + 137x^11 - 33x^10 + 60x^9 + 177x^8 + 243x^7 - 219x^6 - 876x^5 - 1332x^4 - 1192x^3 - 736x^2 - 288x - 64	\( -\,7^{14}\cdot 29^{3}\cdot 77351^{3} \)	21T45	Trivial (GRH)
21.15.832264666907665525356930624196771.1	x^21 - 21x^19 + 189x^17 - 952x^15 - 2x^14 + 2940x^13 + 28x^12 - 5733x^11 - 154x^10 + 7007x^9 + 420x^8 - 5146x^7 - 588x^6 + 2065x^5 + 392x^4 - 357x^3 - 98x^2 + 7x + 1	\( -\,7^{35}\cdot 13^{3} \)	21T45	Trivial (GRH)
21.15.9239009085667298360459800179123827.1	x^21 - 21x^19 + 189x^17 - 952x^15 - 4x^14 + 2940x^13 + 56x^12 - 5733x^11 - 308x^10 + 7007x^9 + 840x^8 - 5142x^7 - 1176x^6 + 2037x^5 + 784x^4 - 301x^3 - 196x^2 - 21x + 1	\( -\,7^{35}\cdot 29^{3} \)	21T45	Trivial (GRH)
21.9.135583376967496347676843148218885073.1	x^21 - 21x^19 + 189x^17 - 952x^15 - 7x^14 + 2940x^13 + 98x^12 - 5733x^11 - 539x^10 + 7007x^9 + 1470x^8 - 5131x^7 - 2058x^6 + 1960x^5 + 1372x^4 - 147x^3 - 343x^2 - 98x - 7	\( 7^{35}\cdot 71^{3} \)	21T45	Trivial (GRH)
21.9.285466780749329275197427204099492453.1	x^21 - 21x^19 + 189x^17 - 952x^15 - 8x^14 + 2940x^13 + 112x^12 - 5733x^11 - 616x^10 + 7007x^9 + 1680x^8 - 5126x^7 - 2352x^6 + 1925x^5 + 1568x^4 - 77x^3 - 392x^2 - 133x - 13	\( 7^{38}\cdot 13^{3} \)	21T45	Trivial (GRH)
21.3.2246296731094095348200059697976870763.1	x^21 + 21x^19 + 189x^17 + 952x^15 - 16x^14 + 2940x^13 - 224x^12 + 5733x^11 - 1232x^10 + 7007x^9 - 3360x^8 + 5228x^7 - 4704x^6 + 2639x^5 - 3136x^4 + 1505x^3 - 784x^2 + 581x - 139	\( -\,7^{35}\cdot 181^{3} \)	21T45	Trivial (GRH)
21.21.13519355382235439206682551551249436467623411507789824.1	x^21 - 3x^20 - 112x^19 + 534x^18 + 3748x^17 - 27416x^16 - 14628x^15 + 484726x^14 - 943874x^13 - 1915634x^12 + 8184116x^11 - 3181310x^10 - 20222740x^9 + 25975820x^8 + 9469379x^7 - 34903053x^6 + 15488942x^5 + 8410376x^4 - 9898284x^3 + 3544684x^2 - 562728x + 33368	\( 2^{18}\cdot 7^{17}\cdot 43^{3}\cdot 127^{3}\cdot 449^{3}\cdot 24683^{3} \)	21T45	Trivial (GRH)
21.21.3824733046663878899659290908522222609035545322716565602304.1	x^21 - 3x^20 - 154x^19 + 702x^18 + 8067x^17 - 51069x^16 - 141881x^15 + 1481799x^14 - 392050x^13 - 17045238x^12 + 22982466x^11 + 93151164x^10 - 175933680x^9 - 268059978x^8 + 569575429x^7 + 436774783x^6 - 811949642x^5 - 393645138x^4 + 382188985x^3 + 57261767x^2 - 68881097x + 9903431	\( 2^{18}\cdot 7^{17}\cdot 13^{3}\cdot 305624493259^{3} \)	21T45	Trivial (GRH)