Global number field search results

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

Results (displaying all 22 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.6.616211844050013988113.2	x^18 - 6x^17 + 15x^16 - 14x^15 - 21x^14 + 81x^13 - 111x^12 + 81x^11 - 48x^10 + 58x^9 - 36x^8 - 75x^7 + 183x^6 - 171x^5 + 81x^4 - 10x^3 - 9x^2 + 3x - 1	\( 3^{24}\cdot 1297^{3} \)	18T702	Trivial
18.8.2046568007701670002628239.1	x^18 - 9x^17 + 27x^16 - 6x^15 - 146x^14 + 308x^13 - 29x^12 - 711x^11 + 862x^10 + 241x^9 - 1252x^8 + 695x^7 + 505x^6 - 694x^5 + 115x^4 + 171x^3 - 83x^2 + 5x + 1	\( -\,7^{12}\cdot 52879^{3} \)	18T702	Trivial (GRH)
18.8.2051215863777747297612359.1	x^18 - x^17 - 5x^16 - 11x^15 - 7x^14 + 35x^13 + 60x^12 + 108x^11 + 143x^10 + 141x^9 + 183x^8 - 93x^7 - 366x^6 - 179x^5 + 46x^4 + 42x^3 - 6x^2 - 7x - 1	\( -\,7^{12}\cdot 52919^{3} \)	18T702	Trivial (GRH)
18.0.9935038298290147032825856.1	x^18 + 4x^16 + 4x^14 + 75x^12 + 172x^10 + 209x^8 + 1359x^6 + 1749x^4 + 2097x^2 + 1399	\( -\,2^{18}\cdot 7^{12}\cdot 1399^{3} \)	18T702	Trivial (GRH)
18.0.9935038298290147032825856.2	x^18 + 7x^16 - 5x^14 - 104x^12 + 13x^10 + 937x^8 + 942x^6 - 1307x^4 - 776x^2 + 1399	\( -\,2^{18}\cdot 7^{12}\cdot 1399^{3} \)	18T702	Trivial (GRH)
18.10.21106009685505727678262841.1	x^18 - 9x^16 - 15x^15 + 12x^14 + 123x^13 + 23x^12 - 219x^11 - 99x^10 - 124x^9 + 780x^8 - 630x^7 + 3x^6 + 864x^5 - 1728x^4 + 1692x^3 - 891x^2 + 243x - 27	\( 3^{24}\cdot 73^{3}\cdot 577^{3} \)	18T702	Trivial (GRH)
18.6.21106009685505727678262841.1	x^18 - 3x^16 - 22x^15 - 18x^14 - 9x^13 + 134x^12 + 186x^11 + 357x^10 + 116x^9 + 114x^8 - 222x^7 - 80x^6 - 93x^5 + 18x^4 + 50x^3 - 12x^2 - 6x + 1	\( 3^{24}\cdot 73^{3}\cdot 577^{3} \)	18T702	Trivial (GRH)
18.10.21106009685505727678262841.2	x^18 - 9x^16 - 4x^15 + 18x^14 + 27x^13 + 75x^12 + 99x^11 - 240x^10 - 891x^9 - 462x^8 + 1260x^7 + 1525x^6 + 78x^5 - 513x^4 - 144x^3 + 45x^2 + 15x + 1	\( 3^{24}\cdot 73^{3}\cdot 577^{3} \)	18T702	Trivial (GRH)
18.12.100281832377381830128783711.1	x^18 - 4x^17 - 10x^16 + 49x^15 + 6x^14 - 224x^13 + 328x^12 + 577x^11 - 1699x^10 - 997x^9 + 3925x^8 + 1121x^7 - 4983x^6 - 509x^5 + 3336x^4 - 109x^3 - 972x^2 + 92x + 71	\( -\,7^{14}\cdot 52879^{3} \)	18T702	Trivial (GRH)
18.2.161536237646646866899894272.1	x^18 - 6x^16 + 44x^12 - 45x^10 + 1029x^8 + 176x^6 - 8292x^4 - 6621x^2 - 1297	\( 2^{18}\cdot 3^{24}\cdot 1297^{3} \)	18T702	Trivial (GRH)
18.6.161536237646646866899894272.1	x^18 - 48x^14 - 70x^12 + 411x^10 + 1176x^8 + 116x^6 - 3444x^4 - 5034x^2 - 1297	\( 2^{18}\cdot 3^{24}\cdot 1297^{3} \)	18T702	Trivial (GRH)
18.2.161536237646646866899894272.2	x^18 + 3x^14 + 169x^12 + 600x^10 + 492x^8 - 1955x^6 - 5295x^4 - 4599x^2 - 1297	\( 2^{18}\cdot 3^{24}\cdot 1297^{3} \)	18T702	$[2]$ (GRH)
18.14.112473925614060022797462679689.1	x^18 - 9x^17 + 9x^16 + 59x^15 + 138x^14 - 657x^13 - 1784x^12 + 4197x^11 + 4716x^10 - 7341x^9 + 3246x^8 - 9864x^7 - 23374x^6 + 36504x^5 + 11280x^4 - 28213x^3 + 9234x^2 - 30x - 181	\( 3^{24}\cdot 73^{5}\cdot 577^{3} \)	18T702	Trivial (GRH)
18.14.112473925614060022797462679689.2	x^18 - 3x^17 - 36x^16 + 172x^15 + 261x^14 - 2796x^13 + 2491x^12 + 15654x^11 - 33030x^10 - 17779x^9 + 97215x^8 - 53073x^7 - 67416x^6 + 93699x^5 - 39096x^4 - 3132x^3 + 4509x^2 + 243x - 27	\( 3^{24}\cdot 73^{5}\cdot 577^{3} \)	18T702	Trivial (GRH)
18.6.112473925614060022797462679689.3	x^18 - 3x^17 + 9x^16 - 37x^15 + 63x^14 - 111x^13 + 263x^12 - 240x^11 + 345x^10 - 1403x^9 + 123x^8 + 2505x^7 + 4513x^6 + 1953x^5 - 8058x^4 - 11638x^3 - 13008x^2 - 9891x - 2539	\( 3^{24}\cdot 73^{5}\cdot 577^{3} \)	18T702	Trivial (GRH)
18.12.536495523810946581168977084416.1	x^18 - 6x^16 - 46x^14 + 122x^12 + 1596x^10 + 3265x^8 - 77156x^6 + 241955x^4 - 255719x^2 + 52879	\( -\,2^{18}\cdot 7^{12}\cdot 52879^{3} \)	18T702	Trivial (GRH)
18.4.536495523810946581168977084416.1	x^18 + 34x^16 + 407x^14 + 1958x^12 + 641x^10 - 26152x^8 - 68129x^6 + 10243x^4 + 116709x^2 + 52879	\( -\,2^{18}\cdot 7^{12}\cdot 52879^{3} \)	18T702	Trivial (GRH)
18.4.536495523810946581168977084416.2	x^18 - 5x^16 - 148x^14 + 341x^12 + 5349x^10 - 8024x^8 - 56597x^6 + 55609x^4 + 146328x^2 + 52879	\( -\,2^{18}\cdot 7^{12}\cdot 52879^{3} \)	18T702	Trivial (GRH)
18.8.536495523810946581168977084416.3	x^18 - 11x^16 - 68x^14 + 1433x^12 - 6123x^10 - 1484x^8 + 69911x^6 - 150632x^4 + 60735x^2 + 52879	\( -\,2^{18}\cdot 7^{12}\cdot 52879^{3} \)	18T702	Trivial (GRH)
18.8.536495523810946581168977084416.4	x^18 + 27x^16 + 155x^14 - 985x^12 - 9717x^10 + 262x^8 + 133107x^6 + 142494x^4 - 241266x^2 + 52879	\( -\,2^{18}\cdot 7^{12}\cdot 52879^{3} \)	18T702	Trivial (GRH)
18.18.5532813802997213476490534191104.1	x^18 - 48x^16 + 867x^14 - 8006x^12 + 42207x^10 - 132831x^8 + 251956x^6 - 280899x^4 + 168873x^2 - 42121	\( 2^{18}\cdot 3^{24}\cdot 73^{3}\cdot 577^{3} \)	18T702	Trivial (GRH)
18.18.5532813802997213476490534191104.2	x^18 - 54x^16 + 1146x^14 - 12287x^12 + 72249x^10 - 241842x^8 + 461455x^6 - 481872x^4 + 244296x^2 - 42121	\( 2^{18}\cdot 3^{24}\cdot 73^{3}\cdot 577^{3} \)	18T702	Trivial (GRH)