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
18.0.9291932134821949543.1	x^18 - 4x^17 + 10x^16 - 21x^15 + 37x^14 - 58x^13 + 80x^12 - 97x^11 + 107x^10 - 106x^9 + 92x^8 - 71x^7 + 52x^6 - 39x^5 + 30x^4 - 20x^3 + 11x^2 - 4x + 1	\( -\,7^{15}\cdot 1399^{2} \)	18T286	Trivial
18.0.10839257382142572103.1	x^18 - 3x^17 + 6x^16 - 6x^15 - 2x^14 + 21x^13 - 47x^12 + 61x^11 - 35x^10 - 37x^9 + 119x^8 - 155x^7 + 130x^6 - 79x^5 + 43x^4 - 27x^3 + 16x^2 - 6x + 1	\( -\,7^{15}\cdot 1511^{2} \)	18T286	Trivial
18.0.12827848719622496283.1	x^18 - 3x^17 + 6x^16 - 9x^15 + 3x^14 + 18x^13 - 47x^12 + 90x^11 - 87x^10 + 43x^9 + 63x^8 - 186x^7 + 274x^6 - 270x^5 + 198x^4 - 106x^3 + 39x^2 - 9x + 1	\( -\,3^{27}\cdot 1297^{2} \)	18T286	Trivial
18.0.75089944301297247847.1	x^18 - 3x^17 + 6x^16 - 7x^15 + 4x^14 + 7x^13 - 19x^12 + 33x^11 - 28x^10 + 17x^9 + 15x^8 - 33x^7 + 53x^6 - 44x^5 + 36x^4 - 17x^3 + 9x^2 - 2x + 1	\( -\,7^{15}\cdot 41^{2}\cdot 97^{2} \)	18T286	Trivial
18.0.2441846738989574698663.1	x^18 + 7x^16 - 4x^15 + 21x^14 - 14x^13 + 44x^12 - 42x^11 + 63x^10 - 29x^9 - 7x^8 - 14x^7 + 67x^6 - 112x^5 + 105x^4 - 65x^3 + 28x^2 - 7x + 1	\( -\,7^{15}\cdot 22679^{2} \)	18T286	Trivial
18.0.13275077566551425157463.1	x^18 - 3x^17 + 8x^16 - 9x^15 + 11x^14 - 12x^13 + 36x^12 - 59x^11 + 25x^10 - 11x^9 + 77x^8 - 221x^7 + 279x^6 - 210x^5 + 129x^4 - 49x^3 + 18x^2 - 4x + 1	\( -\,7^{15}\cdot 52879^{2} \)	18T286	Trivial
18.0.13529172182727253562667.1	x^18 + 9x^16 - 2x^15 + 57x^14 - 12x^13 + 173x^12 - 30x^11 + 375x^10 - 30x^9 + 429x^8 + 63x^7 + 342x^6 + 60x^5 + 135x^4 + 44x^3 + 36x^2 + 6x + 1	\( -\,3^{27}\cdot 73^{2}\cdot 577^{2} \)	18T286	Trivial
18.0.90466292782051905202183.1	x^18 - 2x^17 + 4x^16 + 5x^15 + 13x^14 - 16x^13 + 41x^12 - 37x^11 + 69x^10 - 186x^9 + 472x^8 - 593x^7 + 672x^6 - 521x^5 + 389x^4 - 176x^3 + 75x^2 - 14x + 1	\( -\,7^{15}\cdot 138041^{2} \)	18T286	$[2]$
18.10.427580313304580720703125.1	x^18 - 2x^17 - x^16 + 10x^15 - 22x^14 - 16x^13 + 27x^12 - 47x^11 - 41x^10 + 83x^9 + 135x^8 + 65x^7 - 52x^6 - 66x^5 - 20x^4 + 7x^3 + 10x^2 + x - 1	\( 5^{9}\cdot 7^{12}\cdot 41^{2}\cdot 97^{2} \)	18T286	Trivial (GRH)
18.6.2435824257550765141000192.1	x^18 + 14x^14 - 35x^12 + 49x^10 - 49x^8 - 294x^6 + 343x^4 + 343x^2 - 343	\( 2^{18}\cdot 7^{15}\cdot 1399^{2} \)	18T286	Trivial (GRH)
18.6.2841446287184382421368832.1	x^18 - 98x^10 - 147x^8 + 98x^6 + 343x^4 + 343x^2 - 343	\( 2^{18}\cdot 7^{15}\cdot 1511^{2} \)	18T286	Trivial (GRH)
18.10.3362743574756719665610752.1	x^18 - 36x^12 + 126x^10 - 351x^8 + 666x^6 - 621x^4 + 243x^2 - 27	\( 2^{18}\cdot 3^{27}\cdot 1297^{2} \)	18T286	Trivial (GRH)
18.14.75591504000497820001953125.1	x^18 - 2x^17 - 19x^16 + 38x^15 + 118x^14 - 245x^13 - 329x^12 + 701x^11 + 606x^10 - 970x^9 - 800x^8 + 626x^7 + 622x^6 - 136x^5 - 224x^4 - 14x^3 + 25x^2 + 2x - 1	\( 5^{9}\cdot 7^{12}\cdot 52879^{2} \)	18T286	Trivial (GRH)
18.14.2429085073021046176452968448.1	x^18 - 15x^16 - 8x^15 + 15x^14 - 60x^13 + 225x^12 + 624x^11 - 540x^10 - 1296x^9 + 42x^8 + 612x^7 + 1016x^6 + 408x^5 - 1152x^4 - 232x^3 + 360x^2 - 8	\( 2^{24}\cdot 3^{21}\cdot 7^{12} \)	18T286	Trivial (GRH)
18.18.3546591312668853157931778048.1	x^18 - 24x^16 + 234x^14 - 1209x^12 + 3627x^10 - 6480x^8 + 6741x^6 - 3753x^4 + 891x^2 - 27	\( 2^{18}\cdot 3^{27}\cdot 73^{2}\cdot 577^{2} \)	18T286	Trivial (GRH)
18.18.35399942500844915143756218368.1	x^18 - 2x^17 - 35x^16 + 58x^15 + 469x^14 - 652x^13 - 3016x^12 + 3628x^11 + 9642x^10 - 10322x^9 - 14412x^8 + 13846x^7 + 8833x^6 - 6794x^5 - 2455x^4 + 1120x^3 + 231x^2 - 42x - 1	\( 2^{27}\cdot 7^{12}\cdot 138041^{2} \)	18T286	Trivial (GRH)