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 matches 1-50 of 431)

Label	Polynomial	Discriminant	Galois group	Class group
18.8.1077219661051651207168.1	x^18 - 10x^16 + 38x^14 - 5x^13 - 69x^12 + 36x^11 + 60x^10 - 90x^9 - 21x^8 + 106x^7 - 9x^6 - 64x^5 + 16x^4 + 21x^3 - 7x^2 - 3x + 1	\( -\,2^{12}\cdot 13^{2}\cdot 37^{6}\cdot 61^{2}\cdot 163 \)	18T912	Trivial
18.8.2533098531640743051723.1	x^18 - 9x^16 - 4x^15 + 24x^14 + 21x^13 - 18x^12 - 27x^11 + 9x^10 + 33x^9 + 9x^8 - 27x^7 - 18x^6 + 21x^5 + 24x^4 - 4x^3 - 9x^2 + 1	\( -\,3^{3}\cdot 9685993193^{2} \)	18T968	Trivial
18.8.2908372388180112392719.1	x^18 - 9x^17 + 31x^16 - 41x^15 - 36x^14 + 217x^13 - 323x^12 + 108x^11 + 361x^10 - 641x^9 + 423x^8 + 68x^7 - 358x^6 + 294x^5 - 94x^4 - 20x^3 + 28x^2 - 9x + 1	\( -\,31\cdot 9685993193^{2} \)	18T968	Trivial
18.8.3078687716353187161727.1	x^18 - 5x^17 + 4x^16 + 18x^15 - 42x^14 + 40x^13 - 48x^12 + 70x^11 - 69x^10 + 89x^9 - 67x^8 - 96x^7 + 187x^6 - 65x^5 - 54x^4 + 47x^3 - 3x^2 - 7x + 1	\( -\,7^{15}\cdot 41^{3}\cdot 97^{2} \)	18T472	Trivial
18.8.4714971270006434875019.1	x^18 - x^17 - 8x^16 + 5x^15 + 28x^14 - 18x^13 - 64x^12 + 44x^11 + 86x^10 - 56x^9 - 56x^8 + 38x^7 + 23x^6 - 16x^5 - 17x^4 + 6x^3 + 8x^2 - x - 1	\( -\,19\cdot 37^{2}\cdot 89\cdot 757^{2}\cdot 59617^{2} \)	18T968	Trivial
18.8.6921799028386293612544.1	x^18 - 5x^16 + x^14 + 36x^12 - 88x^10 + 99x^8 - 69x^6 + 35x^4 - 10x^2 + 1	\( -\,2^{24}\cdot 37^{6}\cdot 401^{2} \)	18T556	Trivial
18.8.7283724597225833041159.1	x^18 + x^16 - 5x^15 - 13x^14 + 11x^13 - 2x^12 + 41x^11 + 6x^10 - 68x^9 + 53x^8 - 63x^7 + x^6 + 50x^5 - 28x^4 + 24x^3 - 5x^2 - 4x + 1	\( -\,7^{15}\cdot 41^{2}\cdot 97^{3} \)	18T472	Trivial
18.8.18109005182056552997227.1	x^18 - 4x^17 - x^16 + 20x^15 - 21x^14 - 22x^13 + 73x^12 - 38x^11 - 94x^10 + 88x^9 + 26x^8 - 48x^7 + 42x^6 - 7x^5 - 33x^4 + 13x^3 + 8x^2 - 3x - 1	\( -\,37^{4}\cdot 67\cdot 229^{6} \)	18T764	Trivial (GRH)
18.8.18109005182056552997227.2	x^18 - 5x^17 + 4x^16 + 23x^15 - 74x^14 + 100x^13 - 53x^12 - 48x^11 + 139x^10 - 173x^9 + 139x^8 - 48x^7 - 53x^6 + 100x^5 - 74x^4 + 23x^3 + 4x^2 - 5x + 1	\( -\,37^{4}\cdot 67\cdot 229^{6} \)	18T764	Trivial (GRH)
18.8.19394593215706131190039.1	x^18 - 5x^17 - x^16 + 38x^15 - 29x^14 - 110x^13 + 108x^12 + 172x^11 - 126x^10 - 215x^9 + 30x^8 + 215x^7 + 49x^6 - 105x^5 - 81x^4 + 44x^3 + 23x^2 - 8x - 1	\( -\,2791^{3}\cdot 944497^{2} \)	18T968	Trivial
18.8.21781613448935042304959.1	x^18 - x^17 - 7x^16 - 4x^15 + 13x^14 + 36x^13 + 35x^12 - 5x^11 - 60x^10 - 87x^9 - 60x^8 - 5x^7 + 35x^6 + 36x^5 + 13x^4 - 4x^3 - 7x^2 - x + 1	\( -\,7^{12}\cdot 53^{6}\cdot 71 \)	18T544	Trivial
18.8.21781613448935042304959.2	x^18 - 3x^17 - 3x^16 + 15x^15 - 8x^14 - 15x^13 + 17x^12 - 3x^11 + 11x^10 - 23x^9 + 11x^8 - 3x^7 + 17x^6 - 15x^5 - 8x^4 + 15x^3 - 3x^2 - 3x + 1	\( -\,7^{12}\cdot 53^{6}\cdot 71 \)	18T544	Trivial
18.8.26935372233110278582272.1	x^18 - x^17 - 5x^16 - 7x^15 + 22x^14 + 38x^13 - 23x^12 - 74x^11 - 83x^10 + 128x^9 + 108x^8 + 8x^7 - 143x^6 - 83x^5 + 114x^4 + 24x^3 - 16x^2 - 6x - 1	\( -\,2^{12}\cdot 3^{3}\cdot 101^{6}\cdot 479^{2} \)	18T556	Trivial
18.8.27069274427408364077056.1	x^18 - x^16 + x^14 - 8x^12 + 4x^10 + 3x^8 + 11x^6 - 9x^4 - 2x^2 + 1	\( -\,2^{24}\cdot 13^{2}\cdot 37^{6}\cdot 61^{2} \)	18T556	Trivial
18.8.28598532373693453982147.1	x^18 - 12x^16 - 6x^15 + 58x^14 + 60x^13 - 127x^12 - 232x^11 + 60x^10 + 406x^9 + 241x^8 - 240x^7 - 388x^6 - 125x^5 + 120x^4 + 136x^3 + 58x^2 + 12x + 1	\( -\,197^{3}\cdot 397\cdot 479^{3}\cdot 85733 \)	18T962	Trivial
18.8.33882845805158779964647.1	x^18 - 2x^17 - 10x^16 + 26x^15 - 8x^14 - 53x^13 + 95x^12 - 43x^11 - 80x^10 + 147x^9 - 80x^8 - 43x^7 + 95x^6 - 53x^5 - 8x^4 + 26x^3 - 10x^2 - 2x + 1	\( -\,7^{13}\cdot 769^{4} \)	18T552	Trivial
18.8.36491143759213924473147.1	x^18 - 3x^17 - 8x^16 + 26x^15 + 13x^14 - 60x^13 - 20x^12 + 93x^11 + 7x^10 - 99x^9 + 7x^8 + 93x^7 - 20x^6 - 60x^5 + 13x^4 + 26x^3 - 8x^2 - 3x + 1	\( -\,3^{3}\cdot 7^{12}\cdot 13^{4}\cdot 43^{4} \)	18T552	Trivial
18.8.42642877033830575780131.1	x^18 - 4x^17 + 3x^16 + x^15 + 7x^14 - 23x^13 + 39x^12 - 7x^11 - 20x^10 - 42x^9 - 50x^8 + 196x^7 - 176x^6 + 257x^5 - 294x^4 + 78x^3 + 128x^2 - 134x + 41	\( -\,7^{12}\cdot 53^{6}\cdot 139 \)	18T544	Trivial
18.8.43554653448710796319831.1	x^18 - 2x^17 - 5x^16 + 8x^15 + 7x^14 - 14x^13 - x^12 - x^11 + 23x^10 + 34x^9 - 64x^8 - 9x^7 + 11x^6 - 13x^5 + 48x^4 - 20x^3 - 10x^2 + 7x - 1	\( -\,19^{16}\cdot 151 \)	18T460	Trivial
18.8.44348448637915901374464.1	x^18 - 3x^17 + 3x^16 - 12x^15 + 15x^14 - 6x^13 + 39x^12 + 42x^11 - 60x^10 - 2x^9 - 213x^8 - 3x^7 + 282x^6 - 15x^5 - 102x^4 - 12x^3 + 12x^2 + 6x + 1	\( -\,2^{12}\cdot 3^{27}\cdot 17^{5} \)	18T400	Trivial
18.8.51624178951832860036871.1	x^18 - x^17 - 9x^16 + 12x^15 + 18x^14 - 58x^13 + 15x^12 + 122x^11 - 38x^10 - 31x^9 + 54x^8 - 37x^7 - 15x^6 + 9x^5 + 2x^4 + 8x^3 + 7x^2 + 4x + 1	\( -\,37^{4}\cdot 191\cdot 229^{6} \)	18T764	Trivial (GRH)
18.8.53977668015744910360576.1	x^18 - 4x^16 + 5x^14 - 6x^12 + 12x^10 - x^8 - 23x^6 + 22x^4 - 8x^2 + 1	\( -\,2^{18}\cdot 453771377^{2} \)	18T968	Trivial
18.8.55092309991415643027071.1	x^18 - 2x^17 - 4x^16 + 21x^15 - 42x^14 + 47x^13 - 17x^12 - 45x^11 + 110x^10 - 137x^9 + 110x^8 - 45x^7 - 17x^6 + 47x^5 - 42x^4 + 21x^3 - 4x^2 - 2x + 1	\( -\,19^{16}\cdot 191 \)	18T460	Trivial
18.8.57388858189268996325376.1	x^18 - 10x^16 + 39x^14 - 75x^12 + 66x^10 + x^8 - 52x^6 + 42x^4 - 12x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 41^{2}\cdot 97^{2} \)	18T879	Trivial (GRH)
18.8.57388858189268996325376.2	x^18 - 6x^16 + 16x^14 - 12x^12 - 15x^10 + 4x^8 + 18x^6 - 6x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 41^{2}\cdot 97^{2} \)	18T879	Trivial (GRH)
18.8.57388858189268996325376.3	x^18 - 3x^14 - x^12 - 4x^10 + 2x^8 + 11x^6 - x^4 - 5x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 41^{2}\cdot 97^{2} \)	18T879	Trivial (GRH)
18.8.57388858189268996325376.4	x^18 - 9x^16 + 34x^14 - 73x^12 + 101x^10 - 106x^8 + 73x^6 - 23x^4 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 41^{2}\cdot 97^{2} \)	18T879	Trivial (GRH)
18.8.58115525246155509346123.1	x^18 - 4x^17 + 6x^16 + 5x^15 - 35x^14 + 77x^13 - 114x^12 + 119x^11 - 52x^10 - 90x^9 + 173x^8 - 163x^7 + 142x^6 - 187x^5 + 147x^4 + 13x^3 - 50x^2 + 14x - 1	\( -\,7^{12}\cdot 13^{4}\cdot 43^{5} \)	18T696	Trivial (GRH)
18.8.66852546470398177734375.1	x^18 - 3x^17 + x^15 + 3x^14 + 3x^13 + 3x^12 + 6x^11 - 15x^10 - 3x^9 - 15x^8 + 6x^7 + 3x^6 + 3x^5 + 3x^4 + x^3 - 3x + 1	\( -\,3^{15}\cdot 5^{9}\cdot 13^{4}\cdot 17^{4} \)	18T966	Trivial
18.8.75954541386658254041088.1	x^18 - 4x^17 + 2x^16 + 7x^15 - 12x^14 + 12x^13 + 6x^12 - 8x^11 + 10x^10 - x^9 + 10x^8 - 8x^7 + 6x^6 + 12x^5 - 12x^4 + 7x^3 + 2x^2 - 4x + 1	\( -\,2^{12}\cdot 3^{3}\cdot 37^{6}\cdot 16361^{2} \)	18T836	Trivial (GRH)
18.8.75954541386658254041088.2	x^18 - 2x^17 - 9x^16 + 19x^15 + 29x^14 - 55x^13 - 81x^12 + 101x^11 + 145x^10 - 94x^9 - 152x^8 - 13x^7 + 99x^6 + 89x^5 - 33x^4 - 52x^3 + 3x^2 + 7x - 1	\( -\,2^{12}\cdot 3^{3}\cdot 37^{6}\cdot 16361^{2} \)	18T836	Trivial (GRH)
18.8.120964639986159441620992.1	x^18 - 3x^17 - x^16 + 10x^15 - 10x^14 + 4x^13 - 8x^11 + 21x^10 - 27x^9 + 21x^8 - 8x^7 + 4x^5 - 10x^4 + 10x^3 - x^2 - 3x + 1	\( -\,2^{12}\cdot 37^{6}\cdot 43\cdot 16361^{2} \)	18T912	Trivial (GRH)
18.8.126696010133518717775872.1	x^18 - 3x^17 - 4x^16 + 8x^15 + 27x^14 - 39x^13 - 18x^12 + 39x^11 - 56x^10 + 91x^9 - 109x^7 + 94x^6 - 13x^5 - 49x^4 + 34x^3 - 5x + 1	\( -\,2^{12}\cdot 101^{6}\cdot 127\cdot 479^{2} \)	18T912	Trivial
18.8.147324066234986659840000.1	x^18 + x^16 - 12x^14 + 24x^12 - 6x^10 - 66x^8 + 44x^6 + 44x^4 - 27x^2 + 1	\( -\,2^{26}\cdot 5^{4}\cdot 37^{8} \)	18T485	Trivial
18.8.162609839777665755885568.1	x^18 - 4x^17 - x^16 + 28x^15 - 53x^14 + 32x^13 + 22x^12 - 72x^11 + 174x^10 - 456x^9 + 817x^8 - 696x^7 - 177x^6 + 1028x^5 - 1053x^4 + 540x^3 - 148x^2 + 20x - 1	\( -\,2^{12}\cdot 101^{6}\cdot 163\cdot 479^{2} \)	18T912	Trivial
18.8.165974738585660629200896.1	x^18 - 8x^17 + 23x^16 - 17x^15 - 59x^14 + 169x^13 - 149x^12 - 99x^11 + 385x^10 - 386x^9 + 64x^8 + 275x^7 - 347x^6 + 189x^5 - 19x^4 - 44x^3 + 31x^2 - 9x + 1	\( -\,2^{12}\cdot 37^{6}\cdot 59\cdot 16361^{2} \)	18T912	Trivial
18.8.171643528052598829929247.1	x^18 - 5x^17 - x^16 + 46x^15 - 73x^14 - 72x^13 + 294x^12 - 197x^11 - 206x^10 + 343x^9 - 52x^8 - 160x^7 + 82x^6 + 3x^5 - 4x^4 - x^3 + 2x^2 + 2x - 1	\( -\,7^{12}\cdot 13^{4}\cdot 43^{4}\cdot 127 \)	18T696	Trivial (GRH)
18.8.173017860931893910933504.1	x^18 - 4x^16 + 4x^14 + x^12 - 12x^10 + 18x^8 + 6x^6 - 16x^4 + 2x^2 + 1	\( -\,2^{12}\cdot 7^{12}\cdot 55243^{2} \)	18T768	Trivial (GRH)
18.8.178571541841731106156544.1	x^18 - x^17 - 11x^16 + 13x^15 + 40x^14 - 68x^13 - 75x^12 + 176x^11 + 99x^10 - 296x^9 - 132x^8 + 398x^7 + 155x^6 - 413x^5 - 96x^4 + 312x^3 + 50x^2 - 140x - 49	\( -\,2^{12}\cdot 101^{6}\cdot 179\cdot 479^{2} \)	18T912	Trivial
18.8.178571541841731106156544.2	x^18 - 3x^17 - 3x^16 + 13x^15 - 7x^14 + 7x^13 + 20x^12 - 103x^11 + 42x^10 + 171x^9 - 53x^8 - 251x^7 - 138x^6 + 436x^5 + 30x^4 - 175x^3 + 68x^2 - 13x + 1	\( -\,2^{12}\cdot 101^{6}\cdot 179\cdot 479^{2} \)	18T912	Trivial
18.8.188479787885411222990848.1	x^18 - 2x^17 - 8x^16 + 27x^15 - 26x^14 - 18x^13 + 66x^12 - 52x^11 - 16x^10 + 57x^9 - 16x^8 - 52x^7 + 66x^6 - 18x^5 - 26x^4 + 27x^3 - 8x^2 - 2x + 1	\( -\,2^{12}\cdot 37^{6}\cdot 67\cdot 16361^{2} \)	18T912	Trivial
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
18.8.256106564050292863664128.1	x^18 + 3x^16 - 13x^14 - 48x^12 + 38x^10 + 163x^8 + 23x^6 - 161x^4 - 56x^2 + 37	\( -\,2^{24}\cdot 37^{7}\cdot 401^{2} \)	18T912	Trivial
18.8.256106564050292863664128.2	x^18 - 4x^16 + 21x^14 - 45x^12 + 55x^10 - 174x^8 + 274x^6 - 53x^4 - 111x^2 + 37	\( -\,2^{24}\cdot 37^{7}\cdot 401^{2} \)	18T912	Trivial
18.8.256106564050292863664128.3	x^18 - 3x^16 - 9x^14 + 46x^12 - 38x^10 - 209x^8 + 599x^6 - 343x^4 - 148x^2 + 37	\( -\,2^{24}\cdot 37^{7}\cdot 401^{2} \)	18T912	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
18.8.395754347757959764770816.1	x^18 - 9x^16 + 24x^14 - 31x^12 + 39x^10 - 9x^8 - 9x^6 - 24x^4 + 1	\( -\,2^{24}\cdot 3^{24}\cdot 17^{4} \)	18T199	Trivial (GRH)
18.8.395754347757959764770816.2	x^18 - 3x^16 - 6x^14 + 41x^12 - 93x^10 + 105x^8 - 99x^6 + 90x^4 - 18x^2 + 1	\( -\,2^{24}\cdot 3^{24}\cdot 17^{4} \)	18T199	Trivial (GRH)
18.8.395754347757959764770816.3	x^18 - 6x^16 + 9x^14 - 11x^12 + 33x^10 - 36x^8 + 14x^6 + 69x^4 - 21x^2 + 1	\( -\,2^{24}\cdot 3^{24}\cdot 17^{4} \)	18T705	Trivial (GRH)
18.8.395754347757959764770816.4	x^18 - 6x^16 - 6x^14 + 29x^12 + 21x^10 - 45x^8 - 17x^6 + 30x^4 - 9x^2 + 1	\( -\,2^{24}\cdot 3^{24}\cdot 17^{4} \)	18T705	Trivial (GRH)