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 20 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.10.1463561466371433349940873.1	x^18 - 2x^17 - 20x^16 + 43x^15 + 145x^14 - 357x^13 - 407x^12 + 1369x^11 + 61x^10 - 2231x^9 + 1333x^8 + 932x^7 - 1192x^6 + 161x^5 + 363x^4 - 253x^3 + 46x^2 + 8x - 1	\( 7^{12}\cdot 41^{5}\cdot 97^{3} \)	18T401	Trivial (GRH)
18.2.1463561466371433349940873.1	x^18 - x^17 + 3x^16 + 5x^14 + 2x^13 - 31x^12 + 136x^11 - 197x^10 - 18x^9 + 488x^8 - 745x^7 + 300x^6 - 404x^5 + 1476x^4 - 2983x^3 + 2108x^2 - 544x - 659	\( 7^{12}\cdot 41^{5}\cdot 97^{3} \)	18T401	Trivial
18.10.8191939224918986549431097.1	x^18 - 4x^17 - 5x^16 + 33x^15 + 12x^14 - 67x^13 - 187x^12 + 132x^11 + 542x^10 - 389x^9 + 405x^8 - 10x^7 - 2713x^6 + 1458x^5 + 2527x^4 - 1700x^3 - 535x^2 + 680x + 127	\( 7^{12}\cdot 41^{3}\cdot 97^{5} \)	18T401	Trivial (GRH)
18.2.8191939224918986549431097.1	x^18 - x^17 + 6x^16 - 16x^15 + 72x^14 - 131x^13 + 328x^12 - 614x^11 + 1163x^10 - 1744x^9 + 2842x^8 - 2725x^7 + 2153x^6 - 1349x^5 - 930x^4 + 1765x^3 - 1601x^2 + 713x - 113	\( 7^{12}\cdot 41^{3}\cdot 97^{5} \)	18T401	Trivial (GRH)
18.4.9935038298290147032825856.1	x^18 + 2x^16 - 3x^14 - 46x^12 - 140x^10 - 249x^8 - 36x^6 - 209x^4 - 522x^2 + 1399	\( -\,2^{18}\cdot 7^{12}\cdot 1399^{3} \)	18T401	Trivial (GRH)
18.4.9935038298290147032825856.2	x^18 + 4x^16 + 2x^14 - 46x^12 - 133x^10 - 261x^8 + 104x^6 + 170x^4 - 317x^2 + 1399	\( -\,2^{18}\cdot 7^{12}\cdot 1399^{3} \)	18T401	Trivial (GRH)
18.6.13770649837088816389593674057.1	x^18 - x^17 - 19x^16 - 12x^15 + 57x^14 + 333x^13 + 547x^12 - 2168x^11 - 6494x^10 + 4271x^9 + 32550x^8 + 8652x^7 - 81088x^6 - 63504x^5 + 42336x^4 + 159936x^3 + 175616x^2 - 175616x - 175616	\( 7^{12}\cdot 41^{5}\cdot 97^{5} \)	18T401	Trivial (GRH)
18.6.112473925614060022797462679689.1	x^18 - 3x^17 + 9x^16 - 10x^15 - 99x^14 + 834x^13 - 3554x^12 + 9033x^11 - 13365x^10 + 6973x^9 + 10632x^8 - 14829x^7 - 18363x^6 + 40296x^5 + 684x^4 - 68277x^3 + 15651x^2 + 46071x + 10259	\( 3^{24}\cdot 73^{5}\cdot 577^{3} \)	18T401	Trivial (GRH)
18.6.112473925614060022797462679689.2	x^18 - 9x^17 + 33x^16 - 34x^15 - 258x^14 + 1455x^13 - 3982x^12 + 5931x^11 - 1518x^10 - 18927x^9 + 60993x^8 - 119193x^7 + 161951x^6 - 148209x^5 + 84738x^4 - 24970x^3 + 2862x^2 + 3366x + 289	\( 3^{24}\cdot 73^{5}\cdot 577^{3} \)	18T401	$[3]$ (GRH)
18.6.301336141724322998158191792033.1	x^18 - 3x^16 - 69x^14 - 180x^13 - 202x^12 + 36x^11 + 669x^10 - 755x^9 - 2808x^8 + 14616x^7 + 20736x^6 - 58320x^5 - 106272x^4 - 20736x^3 + 373248x^2 + 186624x - 373248	\( 3^{24}\cdot 37^{5}\cdot 109^{5} \)	18T401	Trivial (GRH)
18.0.536495523810946581168977084416.1	x^18 + 12x^16 - 38x^14 - 642x^12 + 1195x^10 + 28537x^8 + 111638x^6 + 195808x^4 + 163791x^2 + 52879	\( -\,2^{18}\cdot 7^{12}\cdot 52879^{3} \)	18T401	$[100]$ (GRH)
18.8.536495523810946581168977084416.1	x^18 - 16x^16 + 18x^14 + 579x^12 - 1987x^10 + 6412x^8 - 5234x^6 - 155305x^4 - 8856x^2 + 52879	\( -\,2^{18}\cdot 7^{12}\cdot 52879^{3} \)	18T401	Trivial (GRH)
18.8.536495523810946581168977084416.2	x^18 + 2x^16 - 129x^14 - 554x^12 + 2083x^10 + 13606x^8 - 2176x^6 - 81732x^4 + 40631x^2 + 52879	\( -\,2^{18}\cdot 7^{12}\cdot 52879^{3} \)	18T401	Trivial (GRH)
18.0.537713931394153787585294237696.1	x^18 + 26x^16 + 277x^14 + 1739x^12 + 8504x^10 + 34994x^8 + 100505x^6 + 170701x^4 + 150743x^2 + 52919	\( -\,2^{18}\cdot 7^{12}\cdot 52919^{3} \)	18T401	$[128]$ (GRH)
18.12.8639459804616015706536001649246208.1	x^18 - 42x^16 - 65x^15 + 540x^14 + 1110x^13 - 4261x^12 - 10992x^11 + 21036x^10 + 88668x^9 + 53907x^8 - 122169x^7 - 200931x^6 - 74706x^5 + 56496x^4 + 78674x^3 + 48510x^2 + 17160x + 2416	\( -\,2^{20}\cdot 3^{21}\cdot 31^{12} \)	18T401	Trivial (GRH)
18.12.17278919609232031413072003298492416.1	x^18 - 3x^17 - 63x^16 + 272x^15 + 912x^14 - 5694x^13 - 1831x^12 + 45597x^11 - 34410x^10 - 161553x^9 + 223701x^8 + 237594x^7 - 506346x^6 - 70506x^5 + 460821x^4 - 106067x^3 - 141117x^2 + 56400x + 1084	\( -\,2^{21}\cdot 3^{21}\cdot 31^{12} \)	18T401	$[2]$ (GRH)
18.18.29484364756172150616218056704393216.1	x^18 - 102x^16 + 4320x^14 - 99279x^12 + 1361019x^10 - 11538072x^8 + 60505829x^6 - 189311046x^4 + 320795142x^2 - 224462809	\( 2^{18}\cdot 3^{24}\cdot 73^{5}\cdot 577^{3} \)	18T401	Trivial (GRH)
18.18.29484364756172150616218056704393216.2	x^18 - 108x^16 + 4917x^14 - 122654x^12 + 1824759x^10 - 16535280x^8 + 89604126x^6 - 274075653x^4 + 416717142x^2 - 224462809	\( 2^{18}\cdot 3^{24}\cdot 73^{5}\cdot 577^{3} \)	18T401	Trivial (GRH)
18.0.8275608770373144126499153648830644224.1	x^18 + 44x^16 - 486x^14 + 560850x^12 - 132405x^10 - 443361489x^8 + 89577029604x^6 - 2977593837154x^4 + 40489309311755x^2 + 1165327834895671	\( -\,2^{18}\cdot 7^{12}\cdot 97^{6}\cdot 1399^{3} \)	18T401	$[2, 4, 276]$ (GRH)
18.0.8275608770373144126499153648830644224.2	x^18 - 6x^16 - 1931x^14 + 612762x^12 - 20867028x^10 - 38209949x^8 + 69465367376x^6 - 56039034873x^4 + 27840157113194x^2 + 1165327834895671	\( -\,2^{18}\cdot 7^{12}\cdot 97^{6}\cdot 1399^{3} \)	18T401	$[2, 2, 2, 468]$ (GRH)