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 16 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.6.1989648926436453792453.1	x^18 - 6x^17 + 15x^16 - 21x^15 + 12x^14 + 15x^13 - 42x^12 + 39x^11 - 21x^10 + 91x^9 - 327x^8 + 615x^7 - 708x^6 + 528x^5 - 240x^4 + 51x^3 + 6x^2 - 6x + 1	\( 3^{33}\cdot 71^{3} \)	18T285	Trivial
18.2.11781188967994492251933.3	x^18 - 2x^15 + 2x^12 - 3x^9 + 2x^6 - 2x^3 + 1	\( 3^{18}\cdot 7^{12}\cdot 13^{3} \)	18T285	Trivial
18.6.12999413056615907410657.1	x^18 - 6x^17 + 15x^16 - 24x^15 + 35x^14 - 46x^13 + x^12 + 140x^11 - 236x^10 + 138x^9 + 26x^8 - 66x^7 + 89x^6 - 134x^5 + 67x^4 - 16x^3 + 16x^2 + 1	\( 7^{15}\cdot 1399^{3} \)	18T285	Trivial
18.4.16637719789350377679051.1	x^18 - 6x^17 + 18x^16 - 33x^15 + 42x^14 - 51x^13 + 49x^12 + 12x^11 - 90x^10 + 89x^9 - 39x^8 - 3x^7 + 64x^6 - 108x^5 + 30x^4 + 28x^3 - 21x^2 + 1	\( -\,3^{27}\cdot 1297^{3} \)	18T285	Trivial
18.4.298632708486259154687519.1	x^18 - 6x^17 + 17x^16 - 34x^15 + 52x^14 - 49x^13 - 33x^12 + 234x^11 - 574x^10 + 1083x^9 - 1498x^8 + 1858x^7 - 2117x^6 + 1998x^5 - 1543x^4 + 1177x^3 - 633x^2 + 207x - 27	\( -\,7^{15}\cdot 41^{3}\cdot 97^{3} \)	18T285	Trivial (GRH)
18.2.369581850188051160899169.1	x^18 - 5x^15 + 9x^12 - 11x^9 + 9x^6 - 5x^3 + 1	\( 3^{18}\cdot 7^{12}\cdot 41^{3} \)	18T285	Trivial
18.0.564231929965125534314496.1	x^18 - 3x^17 + 7x^16 - 20x^15 + 51x^14 - 92x^13 + 159x^12 - 272x^11 + 423x^10 - 560x^9 + 699x^8 - 790x^7 + 975x^6 - 1160x^5 + 1078x^4 - 659x^3 + 254x^2 - 56x + 8	\( -\,2^{12}\cdot 3^{6}\cdot 7^{12}\cdot 239^{3} \)	18T285	Trivial
18.6.48255750012905440263917568.1	x^18 - 6x^16 - 4x^15 - 27x^14 + 48x^13 + 162x^12 - 54x^11 - 90x^10 - 630x^9 + 36x^8 + 1416x^7 - 251x^6 - 1278x^5 + 336x^4 + 624x^3 - 192x - 64	\( 2^{12}\cdot 3^{18}\cdot 7^{12}\cdot 13^{3} \)	18T285	Trivial (GRH)
18.12.89966113815594302831591424.1	x^18 - 18x^16 - 2x^15 + 135x^14 + 30x^13 - 544x^12 - 180x^11 + 1263x^10 + 552x^9 - 1674x^8 - 918x^7 + 1165x^6 + 810x^5 - 348x^4 - 340x^3 + 36x^2 + 48x - 8	\( -\,2^{24}\cdot 3^{18}\cdot 7^{12} \)	18T285	Trivial (GRH)
18.6.482162141230450716738060288.1	x^18 - 18x^16 - 10x^15 + 135x^14 + 150x^13 - 503x^12 - 900x^11 + 771x^10 + 2652x^9 + 540x^8 - 3618x^7 - 3305x^6 + 1134x^5 + 3225x^4 + 1466x^3 - 342x^2 - 510x - 139	\( 2^{18}\cdot 3^{18}\cdot 7^{15} \)	18T285	Trivial (GRH)
18.0.569862261508654647313096707.1	x^18 + 6x^16 - 18x^15 + 60x^14 - 75x^13 + 256x^12 - 459x^11 + 966x^10 - 871x^9 + 1740x^8 - 1116x^7 + 2869x^6 - 2424x^5 + 6450x^4 - 2606x^3 + 3006x^2 - 513x + 361	\( -\,3^{27}\cdot 73^{3}\cdot 577^{3} \)	18T285	$[2, 12]$
18.0.861408683019814427292598272.1	x^18 - 7x^16 + x^14 + 111x^12 - 387x^10 + 879x^8 - 1984x^6 + 2054x^4 + 977x^2 + 43	\( -\,2^{30}\cdot 3^{6}\cdot 7^{12}\cdot 43^{3} \)	18T285	$[2]$
18.0.12488057521927227046014543503.1	x^18 - 8x^17 + 44x^16 - 148x^15 + 337x^14 - 355x^13 - 409x^12 + 2535x^11 - 3290x^10 - 6263x^9 + 43736x^8 - 119075x^7 + 221321x^6 - 296751x^5 + 303777x^4 - 226521x^3 + 141287x^2 - 71712x + 44507	\( -\,7^{15}\cdot 138041^{3} \)	18T285	$[2, 56]$ (GRH)
18.12.46062650273584283049774809088.1	x^18 - 18x^16 + 135x^14 - 542x^12 + 1239x^10 - 1566x^8 + 937x^6 - 114x^4 - 72x^2 + 8	\( -\,2^{33}\cdot 3^{18}\cdot 7^{12} \)	18T285	Trivial (GRH)
18.18.149385972680924763865244423159808.1	x^18 - 66x^16 + 1773x^14 - 25341x^12 + 210438x^10 - 1039797x^8 + 3014559x^6 - 4873932x^4 + 3914973x^2 - 1137267	\( 2^{18}\cdot 3^{27}\cdot 73^{3}\cdot 577^{3} \)	18T285	$[2]$ (GRH)
18.18.4886643462759132931359252139737088.1	x^18 - 104x^16 + 4488x^14 - 104360x^12 + 1421392x^10 - 11556672x^8 + 54900096x^6 - 143185024x^4 + 178038272x^2 - 70676992	\( 2^{27}\cdot 7^{12}\cdot 138041^{3} \)	18T285	$[4]$ (GRH)