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 26 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.8.250188053022644984299584.1	x^18 - 9x^17 + 27x^16 - 11x^15 - 99x^14 + 177x^13 - 38x^12 - 87x^11 + 48x^10 - 201x^9 + 288x^8 + 51x^7 - 186x^6 + 3x^5 + 39x^4 - 8x^3 + 9x^2 - 6x + 1	\( -\,2^{6}\cdot 3^{24}\cdot 7^{12} \)	18T459	Trivial
18.8.277552371321996779457351.1	x^18 - 3x^17 - 9x^16 + 49x^15 - 63x^14 - 27x^13 + 152x^12 - 117x^11 - 99x^10 + 231x^9 - 99x^8 - 117x^7 + 152x^6 - 27x^5 - 63x^4 + 49x^3 - 9x^2 - 3x + 1	\( -\,3^{24}\cdot 7^{12}\cdot 71 \)	18T459	Trivial
18.12.496466917716811140719487.1	x^18 - 9x^17 + 33x^16 - 60x^15 + 27x^14 + 90x^13 - 110x^12 + 3x^11 - 132x^10 + 210x^9 + 198x^8 - 261x^7 - 139x^6 + 111x^5 + 75x^4 - 24x^3 - 18x^2 + 3x + 1	\( -\,3^{24}\cdot 7^{12}\cdot 127 \)	18T459	Trivial (GRH)
18.6.707563087454667846222261.1	x^18 - 6x^17 + 18x^16 - 41x^15 + 60x^14 - 42x^13 + 4x^12 + 51x^11 - 171x^10 + 265x^9 - 141x^8 + 45x^7 - 127x^6 + 24x^5 + 75x^4 - 14x^3 + 6x + 1	\( 3^{24}\cdot 7^{12}\cdot 181 \)	18T459	Trivial
18.10.770110100710329092297157.1	x^18 - 3x^17 - 6x^16 + 29x^15 - 45x^14 + 21x^13 + 110x^12 - 246x^11 + 186x^10 + 44x^9 - 144x^8 + 27x^7 - 62x^6 + 123x^5 - 243x^4 + 214x^3 - 84x^2 + 15x - 1	\( 3^{24}\cdot 7^{12}\cdot 197 \)	18T459	Trivial
18.10.6755077431611414576088768.1	x^18 - 6x^17 + 15x^16 - 35x^15 + 66x^14 - 93x^13 + 189x^12 - 312x^11 + 477x^10 - 696x^9 + 354x^8 + 363x^7 - 1162x^6 + 1686x^5 - 1170x^4 + 329x^3 - 3x^2 - 12x + 1	\( 2^{6}\cdot 3^{27}\cdot 7^{12} \)	18T459	Trivial (GRH)
18.8.16012035393449278995173376.1	x^18 + 6x^16 - 6x^14 - 45x^12 + 21x^10 + 99x^8 - 43x^6 - 60x^4 + 27x^2 + 1	\( -\,2^{12}\cdot 3^{24}\cdot 7^{12} \)	18T459	Trivial
18.10.85814502186767229614757312.1	x^18 - 6x^17 + 9x^16 + 34x^15 - 171x^14 + 177x^13 + 514x^12 - 1461x^11 + 438x^10 + 2633x^9 - 3090x^8 - 963x^7 + 3216x^6 - 801x^5 - 405x^4 + 567x^3 - 351x^2 - 243x - 27	\( 2^{6}\cdot 3^{24}\cdot 7^{15} \)	18T459	Trivial (GRH)
18.12.268299605528119179177846592.1	x^18 - 17x^16 - 19x^15 + 73x^14 + 187x^13 + 146x^12 - 135x^11 - 794x^10 - 1421x^9 - 600x^8 + 1481x^7 + 2066x^6 + 495x^5 - 813x^4 - 707x^3 - 117x^2 + 78x + 13	\( -\,2^{6}\cdot 7^{12}\cdot 13^{13} \)	18T459	Trivial (GRH)
18.16.1024770265180753855691096064.1	x^18 - 12x^16 + 42x^14 - 11x^12 - 243x^10 + 579x^8 - 559x^6 + 234x^4 - 33x^2 + 1	\( -\,2^{18}\cdot 3^{24}\cdot 7^{12} \)	18T459	Trivial (GRH)
18.6.1661674773598166887988122989.1	x^18 - 9x^17 + 45x^16 - 156x^15 + 399x^14 - 777x^13 + 1130x^12 - 1125x^11 + 462x^10 + 781x^9 - 1986x^8 + 2427x^7 - 1853x^6 + 780x^5 + 60x^4 - 329x^3 + 222x^2 - 72x + 8	\( 3^{24}\cdot 7^{12}\cdot 127\cdot 3347 \)	18T459	$[2]$ (GRH)
18.16.17171174753799627467382181888.1	x^18 - 25x^16 + 246x^14 - 1245x^12 + 3470x^10 - 5082x^8 + 2731x^6 + 1768x^4 - 2704x^2 + 832	\( -\,2^{12}\cdot 7^{12}\cdot 13^{13} \)	18T459	Trivial (GRH)
18.4.17171174753799627467382181888.1	x^18 + 10x^16 - 15x^14 - 524x^12 - 2302x^10 - 3592x^8 - 216x^6 + 4017x^4 + 2392x^2 + 13	\( -\,2^{12}\cdot 7^{12}\cdot 13^{13} \)	18T459	$[2]$ (GRH)
18.14.17171174753799627467382181888.1	x^18 - 10x^16 - 15x^14 + 524x^12 - 2302x^10 + 3592x^8 - 216x^6 - 4017x^4 + 2392x^2 - 13	\( 2^{12}\cdot 7^{12}\cdot 13^{13} \)	18T459	Trivial (GRH)
18.2.17171174753799627467382181888.1	x^18 + 25x^16 + 246x^14 + 1245x^12 + 3470x^10 + 5082x^8 + 2731x^6 - 1768x^4 - 2704x^2 - 832	\( 2^{12}\cdot 7^{12}\cdot 13^{13} \)	18T459	$[2]$ (GRH)
18.2.27668797159880354103659593728.1	x^18 + 21x^16 + 162x^14 + 573x^12 + 873x^10 + 81x^8 - 1305x^6 - 1404x^4 - 486x^2 - 27	\( 2^{18}\cdot 3^{27}\cdot 7^{12} \)	18T459	$[2, 4]$ (GRH)
18.14.33843645495460641694050949941.1	x^18 - 9x^17 + 27x^16 - 12x^15 - 105x^14 + 231x^13 - 88x^12 - 369x^11 + 636x^10 - 155x^9 - 636x^8 + 663x^7 + 41x^6 - 492x^5 + 216x^4 + 195x^3 - 84x^2 - 60x - 8	\( 3^{24}\cdot 7^{12}\cdot 8657461 \)	18T459	Trivial (GRH)
18.4.65794168813147199016669383607.1	x^18 - 9x^17 + 54x^16 - 228x^15 + 759x^14 - 2037x^13 + 4511x^12 - 8307x^11 + 12660x^10 - 15824x^9 + 15555x^8 - 11073x^7 + 3686x^6 + 3000x^5 - 6255x^4 + 5568x^3 - 3027x^2 + 966x - 71	\( -\,3^{24}\cdot 7^{12}\cdot 181\cdot 92987 \)	18T459	Trivial (GRH)
18.12.80716670418377815414668988416.1	x^18 - 27x^16 + 228x^14 - 267x^12 - 4743x^10 + 15729x^8 + 12377x^6 - 77400x^4 + 27264x^2 + 5041	\( -\,2^{12}\cdot 3^{24}\cdot 7^{12}\cdot 71^{2} \)	18T459	Trivial (GRH)
18.12.80716670418377815414668988416.2	x^18 - 3x^17 - 18x^16 + 55x^15 - 12x^14 + 36x^13 + 170x^12 - 309x^11 + 786x^10 + 899x^9 - 6411x^8 - 8799x^7 + 7440x^6 + 14742x^5 - 228x^4 - 7179x^3 - 1791x^2 + 558x + 127	\( -\,2^{12}\cdot 3^{24}\cdot 7^{12}\cdot 71^{2} \)	18T459	Trivial (GRH)
18.0.4878304035425204472356922740736.1	x^18 + 30x^16 + 345x^14 + 2066x^12 + 7182x^10 + 15018x^8 + 18624x^6 + 12693x^4 + 3828x^2 + 181	\( -\,2^{12}\cdot 3^{24}\cdot 13^{12}\cdot 181 \)	18T459	$[6, 24]$ (GRH)
18.18.4878304035425204472356922740736.1	x^18 - 30x^16 + 345x^14 - 2066x^12 + 7182x^10 - 15018x^8 + 18624x^6 - 12693x^4 + 3828x^2 - 181	\( 2^{12}\cdot 3^{24}\cdot 13^{12}\cdot 181 \)	18T459	Trivial (GRH)
18.18.4886979270087636565363773739773.1	x^18 - 9x^17 + 9x^16 + 132x^15 - 321x^14 - 777x^13 + 2726x^12 + 2403x^11 - 11790x^10 - 4619x^9 + 29970x^8 + 7587x^7 - 45609x^6 - 13020x^5 + 38220x^4 + 15743x^3 - 12702x^2 - 7944x - 1016	\( 3^{24}\cdot 7^{12}\cdot 251\cdot 4980583 \)	18T459	Trivial (GRH)
18.8.7053072320828130442597556717031.1	x^18 - 6x^17 + 36x^16 - 220x^15 + 960x^14 - 3504x^13 + 8755x^12 - 12102x^11 - 3681x^10 + 66689x^9 - 145626x^8 + 134298x^7 + 77273x^6 - 258648x^5 + 225774x^4 + 293774x^3 + 7236x^2 - 12381x - 881	\( -\,3^{24}\cdot 7^{12}\cdot 71^{5} \)	18T459	Trivial (GRH)
18.10.1159892457286612080082548844598517.1	x^18 - 9x^17 + 24x^16 - 108x^15 + 51x^14 + 1938x^13 + 25x^12 + 20355x^11 - 34395x^10 - 47780x^9 - 380205x^8 - 651636x^7 + 1096380x^6 + 4986567x^5 + 3882756x^4 - 9132658x^3 - 6404370x^2 + 5503983x + 1227113	\( 3^{24}\cdot 7^{12}\cdot 197^{5} \)	18T459	$[2]$ (GRH)
18.0.451985616395723240517472053274603584.1	x^18 + 81x^16 - 221x^15 + 2784x^14 - 10842x^13 + 57423x^12 - 210678x^11 + 718602x^10 - 2094040x^9 + 5830770x^8 - 15415413x^7 + 39375297x^6 - 88940514x^5 + 164458332x^4 - 232245897x^3 + 233241462x^2 - 147873180x + 45232552	\( -\,2^{6}\cdot 3^{24}\cdot 13^{12}\cdot 181^{4} \)	18T459	$[2, 2, 2, 7026]$ (GRH)