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 502)

Label	Polynomial	Discriminant	Galois group	Class group
18.12.51624178951832860036871.1	x^18 - 2x^17 - 8x^16 + 24x^15 - 8x^14 - 8x^13 - 30x^12 - 9x^11 + 103x^10 - 10x^9 - 41x^8 - 96x^7 + 41x^6 + 99x^5 - 44x^4 - 27x^3 + 13x^2 + 2x - 1	\( -\,37^{4}\cdot 191\cdot 229^{6} \)	18T764	Trivial (GRH)
18.12.58115525246155509346123.1	x^18 - 6x^17 + 4x^16 + 30x^15 - 31x^14 - 62x^13 + 33x^12 + 91x^11 + 4x^10 - 85x^9 + 4x^8 + 91x^7 + 33x^6 - 62x^5 - 31x^4 + 30x^3 + 4x^2 - 6x + 1	\( -\,7^{12}\cdot 13^{4}\cdot 43^{5} \)	18T188	Trivial (GRH)
18.12.90466292782051905202183.1	x^18 - 7x^17 + 9x^16 + 44x^15 - 129x^14 - 27x^13 + 439x^12 - 291x^11 - 576x^10 + 632x^9 + 345x^8 - 462x^7 - 230x^6 + 207x^5 + 126x^4 - 60x^3 - 27x^2 + 6x + 1	\( -\,7^{15}\cdot 138041^{2} \)	18T768	Trivial (GRH)
18.12.95958192848303282873831.1	x^18 - 3x^17 - 7x^16 + 34x^15 - 34x^14 - 21x^13 + 134x^12 - 245x^11 + 115x^10 + 105x^9 - 10x^8 - 106x^7 + 17x^6 + 82x^5 - 131x^4 + 66x^3 + 14x^2 - 11x - 1	\( -\,7^{12}\cdot 13^{4}\cdot 43^{4}\cdot 71 \)	18T696	Trivial (GRH)
18.12.105226667788517176205647.1	x^18 - 8x^17 + 21x^16 - 15x^15 - 25x^14 + 82x^13 - 132x^12 + 80x^11 + 56x^10 - 131x^9 + 153x^8 - 99x^7 + 61x^6 - 93x^5 + 21x^4 + 62x^3 - 37x^2 + 3x + 1	\( -\,7^{15}\cdot 53^{6} \)	$C_6\times S_4$ (as 18T61)	Trivial
18.12.136329432645150668523607.1	x^18 - 8x^17 + 19x^16 - 45x^14 + 6x^13 + 59x^12 + 58x^11 - 104x^10 - 155x^9 + 212x^8 + 122x^7 - 270x^6 + 20x^5 + 169x^4 - 62x^3 - 41x^2 + 19x + 1	\( -\,7^{15}\cdot 169457^{2} \)	18T768	Trivial (GRH)
18.12.153849444412406174216731.1	x^18 - 9x^17 + 27x^16 - 12x^15 - 94x^14 + 154x^13 + 70x^12 - 316x^11 + 80x^10 + 304x^9 - 188x^8 - 154x^7 + 168x^6 + 28x^5 - 78x^4 + 5x^3 + 15x^2 - x - 1	\( -\,167\cdot 173\cdot 2307632671^{2} \)	18T968	Trivial (GRH)
18.12.161453767328118264113639.1	x^18 - 9x^17 + 24x^16 + 9x^15 - 141x^14 + 170x^13 + 115x^12 - 266x^11 + 55x^10 - 308x^9 + 704x^8 + 18x^7 - 980x^6 + 858x^5 - 242x^4 - 41x^3 + 44x^2 - 11x + 1	\( -\,7^{12}\cdot 22679^{3} \)	18T207	Trivial
18.12.165974738585660629200896.1	x^18 - 4x^17 + x^16 + 20x^15 - 42x^14 + 7x^13 + 114x^12 - 130x^11 - 66x^10 + 203x^9 - 109x^8 - 134x^7 + 169x^6 + 49x^5 - 83x^4 - 11x^3 + 16x^2 + x - 1	\( -\,2^{12}\cdot 37^{6}\cdot 59\cdot 16361^{2} \)	18T912	Trivial
18.12.221475861541215709988399.1	x^18 - 6x^17 + 4x^16 + 33x^15 - 60x^14 + 17x^13 + 44x^12 - 240x^11 + 290x^10 + 272x^9 - 41x^8 - 992x^7 - 415x^6 + 2830x^5 - 1547x^4 - 1504x^3 + 2040x^2 - 850x + 125	\( -\,7^{12}\cdot 113^{3}\cdot 223^{3} \)	18T207	Trivial
18.12.244708287054102675846827.1	x^18 - 10x^16 - 8x^15 + 28x^14 + 52x^13 - 82x^12 - 73x^11 + 312x^10 - 112x^9 - 460x^8 + 429x^7 + 171x^6 - 365x^5 + 62x^4 + 91x^3 - 36x^2 + 1	\( -\,257^{6}\cdot 947^{3} \)	18T314	Trivial
18.12.250188053022644984299584.1	x^18 - 3x^16 - 27x^14 + 113x^12 + 15x^10 - 465x^8 + 366x^6 + 102x^4 - 39x^2 + 1	\( -\,2^{6}\cdot 3^{24}\cdot 7^{12} \)	$C_6\times A_4$ (as 18T25)	Trivial (GRH)
18.12.264502279525614257635328.1	x^18 - 4x^17 - 3x^16 + 40x^15 - 54x^14 - 116x^13 + 358x^12 + 8x^11 - 904x^10 + 556x^9 + 1244x^8 - 1152x^7 - 1146x^6 + 1076x^5 + 690x^4 - 512x^3 - 169x^2 + 104x - 1	\( -\,2^{16}\cdot 37^{6}\cdot 1163^{3} \)	18T314	Trivial
18.12.301005034384164191940608.1	x^18 - 6x^17 + 8x^16 + 16x^15 - 65x^14 + 90x^13 + 17x^12 - 278x^11 + 321x^10 + 90x^9 - 394x^8 + 194x^7 + 108x^6 - 154x^5 + 31x^4 + 36x^3 - 15x^2 - 2x + 1	\( -\,2^{12}\cdot 37^{6}\cdot 107\cdot 16361^{2} \)	18T912	Trivial
18.12.429456733437258587406367.1	x^18 - 3x^17 - 7x^16 + 34x^15 - 35x^14 - 42x^13 + 146x^12 + 32x^11 - 240x^10 - 164x^9 + 112x^8 + 146x^7 + 105x^6 + 174x^5 + 108x^4 - 27x^3 - 45x^2 - 13x - 1	\( -\,7^{15}\cdot 67^{6} \)	$C_6\times S_4$ (as 18T61)	Trivial (GRH)
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)
18.12.640031705538953992499008.1	x^18 - 6x^17 + 3x^16 + 34x^15 - 74x^14 + 68x^13 - 8x^12 - 160x^11 + 395x^10 - 474x^9 + 187x^8 + 270x^7 - 312x^6 + 6x^5 + 101x^4 - 24x^3 - 13x^2 + 4x + 1	\( -\,2^{6}\cdot 37^{5}\cdot 229^{6} \)	18T284	Trivial
18.12.640031705538953992499008.2	x^18 - 9x^17 + 30x^16 - 22x^15 - 145x^14 + 446x^13 - 269x^12 - 972x^11 + 1981x^10 - 378x^9 - 2497x^8 + 2227x^7 + 548x^6 - 1285x^5 + 199x^4 + 193x^3 - 43x^2 - 5x + 1	\( -\,2^{6}\cdot 37^{5}\cdot 229^{6} \)	18T284	Trivial
18.12.755501828200021621499599.1	x^18 - 6x^16 - 2x^15 - 5x^14 + 50x^13 + 48x^12 - 137x^11 - 110x^10 - 151x^9 + 393x^8 + 748x^7 - 519x^6 - 661x^5 + 256x^4 + 180x^3 - 38x^2 - 7x + 1	\( -\,7^{12}\cdot 13^{5}\cdot 43^{5} \)	18T188	Trivial (GRH)
18.12.755501828200021621499599.2	x^18 - 3x^17 - 4x^16 + 26x^15 - 38x^14 + 14x^13 + 29x^12 - 84x^11 + 246x^10 - 483x^9 + 496x^8 - 218x^7 - 122x^6 + 284x^5 - 162x^4 - 2x^3 + 24x^2 - 2x - 1	\( -\,7^{12}\cdot 13^{5}\cdot 43^{5} \)	18T696	Trivial (GRH)
18.12.987629569339089510074691.1	x^18 - 3x^17 - 12x^16 + 46x^15 + 15x^14 - 165x^13 + 11x^12 + 321x^11 - 9x^10 - 405x^9 - 60x^8 + 297x^7 + 126x^6 - 90x^5 - 93x^4 - 10x^3 + 21x^2 + 9x + 1	\( -\,3^{27}\cdot 73^{3}\cdot 577^{2} \)	18T472	Trivial
18.12.987629569339089510074691.2	x^18 - 6x^17 + 3x^16 + 41x^15 - 48x^14 - 153x^13 + 249x^12 + 276x^11 - 624x^10 - 165x^9 + 774x^8 - 90x^7 - 472x^6 + 132x^5 + 135x^4 - 38x^3 - 18x^2 + 3x + 1	\( -\,3^{27}\cdot 73^{3}\cdot 577^{2} \)	18T879	Trivial
18.12.987629569339089510074691.3	x^18 - 6x^16 - 4x^15 - 6x^14 + 51x^13 + 105x^12 - 186x^11 - 318x^10 + 237x^9 + 552x^8 + 18x^7 - 613x^6 - 237x^5 + 384x^4 + 112x^3 - 99x^2 + 9x + 1	\( -\,3^{27}\cdot 73^{3}\cdot 577^{2} \)	18T879	Trivial
18.12.1000242318837874626994967.1	x^18 - 4x^17 - 12x^16 + 54x^15 + 63x^14 - 307x^13 - 186x^12 + 961x^11 + 307x^10 - 1779x^9 - 187x^8 + 1893x^7 - 151x^6 - 988x^5 + 200x^4 + 161x^3 - 13x^2 - 11x - 1	\( -\,23^{3}\cdot 5569^{3}\cdot 21817^{2} \)	18T968	Trivial (GRH)
18.12.1107081869040352851890176.1	x^18 - 10x^16 + 26x^14 + 29x^12 - 188x^10 + 125x^8 + 158x^6 - 81x^4 + 3x^2 + 1	\( -\,2^{12}\cdot 37^{4}\cdot 229^{6} \)	18T764	Trivial (GRH)
18.12.1107081869040352851890176.2	x^18 - 10x^16 + 32x^14 - 18x^12 - 92x^10 + 150x^8 + 13x^6 - 150x^4 + 72x^2 + 1	\( -\,2^{12}\cdot 37^{4}\cdot 229^{6} \)	18T764	Trivial (GRH)
18.12.1107081869040352851890176.3	x^18 - 6x^16 + 4x^14 + 43x^12 - 114x^10 + 96x^8 - 6x^6 - 22x^4 + 4x^2 + 1	\( -\,2^{12}\cdot 37^{4}\cdot 229^{6} \)	18T764	Trivial (GRH)
18.12.1256584347701942722269184.1	x^18 - x^16 - 25x^14 + 90x^12 - 97x^10 - 14x^8 + 81x^6 - 34x^4 - x^2 + 1	\( -\,2^{12}\cdot 7^{12}\cdot 53^{6} \)	18T544	Trivial (GRH)
18.12.1256584347701942722269184.2	x^18 + 7x^16 - 16x^14 - 74x^12 + 230x^10 - 172x^8 - 45x^6 + 97x^4 - 30x^2 + 1	\( -\,2^{12}\cdot 7^{12}\cdot 53^{6} \)	18T544	Trivial (GRH)
18.12.1256584347701942722269184.3	x^18 - 6x^16 - 3x^14 + 50x^12 - 12x^10 - 89x^8 + 58x^6 + 8x^4 - 9x^2 + 1	\( -\,2^{12}\cdot 7^{12}\cdot 53^{6} \)	18T544	Trivial (GRH)
18.12.1256584347701942722269184.4	x^18 - 6x^16 - 3x^14 + 62x^12 - 60x^10 - 119x^8 + 218x^6 - 106x^4 + 13x^2 + 1	\( -\,2^{12}\cdot 7^{12}\cdot 53^{6} \)	18T544	Trivial (GRH)
18.12.1327814090454436325666816.1	x^18 - 13x^16 - 5x^15 + 71x^14 + 33x^13 - 193x^12 - 65x^11 + 247x^10 + 50x^9 - 114x^8 - 53x^7 - x^6 + 69x^5 + 7x^4 - 34x^3 + 3x^2 + 5x - 1	\( -\,2^{12}\cdot 11^{3}\cdot 101^{6}\cdot 479^{2} \)	18T556	Trivial (GRH)
18.12.2095795683329361973048159.1	x^18 - 2x^17 - 6x^16 + 14x^15 - 3x^14 - 32x^13 + 34x^12 + 19x^11 - 10x^10 - 51x^9 + 15x^8 + 90x^7 - 57x^6 - 57x^5 + 44x^4 + 14x^3 - 12x^2 - x + 1	\( -\,7^{12}\cdot 4591\cdot 181607^{2} \)	18T879	Trivial (GRH)
18.12.2466930139718004361521211.1	x^18 - 3x^17 - 15x^16 + 32x^15 + 78x^14 - 133x^13 - 147x^12 + 275x^11 - 27x^10 - 233x^9 + 400x^8 - 152x^7 - 378x^6 + 406x^5 - 6x^4 - 171x^3 + 90x^2 - 17x + 1	\( -\,7^{17}\cdot 13^{9} \)	$C_2\times C_3^2.A_4$ (as 18T92)	Trivial (GRH)
18.12.2466930139718004361521211.2	x^18 - 3x^17 - 8x^16 + 11x^15 + 36x^14 + 21x^13 - 56x^12 - 369x^11 - 20x^10 + 1104x^9 + 92x^8 - 1279x^7 - 70x^6 + 651x^5 + 29x^4 - 143x^3 - 8x^2 + 11x + 1	\( -\,7^{17}\cdot 13^{9} \)	$C_2\times C_3^2.A_4$ (as 18T92)	Trivial (GRH)
18.12.2518170116818978404827136.1	x^18 - 9x^16 - 18x^13 + 138x^12 + 144x^11 - 207x^10 - 324x^9 - 99x^8 + 450x^7 + 369x^6 - 432x^5 - 351x^4 + 162x^3 + 153x^2 + 18x - 3	\( -\,2^{24}\cdot 3^{36} \)	$C_3\times S_3\wr C_2$ (as 18T93)	Trivial
18.12.2889069193792436475743559.1	x^18 - 3x^17 - 3x^16 + 29x^15 - 26x^14 - 87x^13 + 156x^12 + 36x^11 - 300x^10 + 229x^9 + 15x^8 - 525x^7 + 630x^6 + 677x^5 - 678x^4 - 533x^3 + 175x^2 + 177x + 29	\( -\,3^{9}\cdot 7^{12}\cdot 13^{9} \)	$C_3\times S_3\wr C_2$ (as 18T93)	Trivial (GRH)
18.12.3007309704449688000000000.1	x^18 - 6x^17 + 9x^16 + 14x^15 - 93x^14 + 246x^13 - 139x^12 - 840x^11 + 1350x^10 + 902x^9 - 2604x^8 - 276x^7 + 2352x^6 - 72x^5 - 1104x^4 + 32x^3 + 240x^2 - 16	\( -\,2^{12}\cdot 3^{24}\cdot 5^{9}\cdot 11^{3} \)	18T189	Trivial (GRH)
18.12.4086195728400729669369856.1	x^18 - 9x^16 + 33x^14 - 44x^12 - 48x^10 + 211x^8 - 229x^6 + 103x^4 - 18x^2 + 1	\( -\,2^{24}\cdot 101^{6}\cdot 479^{2} \)	18T556	Trivial (GRH)
18.12.5852021141154776996728512.1	x^18 - 3x^17 - 6x^16 + 24x^15 - 15x^14 + 27x^13 - 12x^12 - 261x^11 + 222x^10 + 508x^9 - 384x^8 - 534x^7 + 258x^6 + 330x^5 - 63x^4 - 102x^3 + 12x + 1	\( -\,2^{6}\cdot 3^{31}\cdot 23^{6} \)	18T366	Trivial (GRH)
18.12.6734506738465099277161408.1	x^18 - 7x^17 + 11x^16 + 30x^15 - 110x^14 + 58x^13 + 159x^12 - 212x^11 + 115x^10 - 264x^9 + 351x^8 + 98x^7 - 587x^6 + 506x^5 - 98x^4 - 109x^3 + 74x^2 - 16x + 1	\( -\,2^{6}\cdot 7^{15}\cdot 53^{6} \)	18T366	Trivial (GRH)
18.12.6755077431611414576088768.1	x^18 - 15x^16 + 72x^14 - 93x^12 - 225x^10 + 675x^8 - 297x^6 - 378x^4 + 162x^2 + 27	\( -\,2^{6}\cdot 3^{27}\cdot 7^{12} \)	18T263	Trivial (GRH)
18.12.7806332349433625305658859.1	x^18 - 15x^16 - x^15 + 60x^14 + 48x^13 - 40x^12 - 375x^11 + 87x^10 + 729x^9 - 756x^8 + 336x^7 + 108x^6 - 279x^5 + 108x^4 + 28x^3 - 21x^2 + 1	\( -\,3^{27}\cdot 73^{2}\cdot 577^{3} \)	18T472	Trivial
18.12.10145719923049728269615104.1	x^18 - 3x^16 - 4x^14 - 23x^12 + 79x^10 + 139x^8 - 303x^6 + 135x^4 - 21x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 52879^{2} \)	18T472	Trivial (GRH)
18.12.10145719923049728269615104.2	x^18 - 8x^16 + 17x^14 + 12x^12 - 87x^10 + 121x^8 - 88x^6 + 43x^4 - 11x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 52879^{2} \)	18T879	Trivial (GRH)
18.12.10145719923049728269615104.3	x^18 - 11x^16 + 43x^14 - 74x^12 + 58x^10 - 24x^8 - 9x^6 + 45x^4 - 29x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 52879^{2} \)	18T879	Trivial (GRH)
18.12.10161075065555921079107584.1	x^18 - 10x^16 + 36x^14 - 48x^12 - 27x^10 + 158x^8 - 180x^6 + 88x^4 - 18x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 52919^{2} \)	18T472	Trivial (GRH)
18.12.10161075065555921079107584.2	x^18 - 14x^16 + 76x^14 - 200x^12 + 257x^10 - 128x^8 - 38x^6 + 96x^4 - 50x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 52919^{2} \)	18T879	Trivial (GRH)
18.12.11054154796697849551765939.1	x^18 - x^17 - 12x^16 + 15x^15 + 40x^14 - 82x^13 - 61x^12 + 200x^11 + 174x^10 - 275x^9 - 352x^8 + 317x^7 + 198x^6 - 178x^5 - 15x^4 + 43x^3 - 10x^2 - 4x + 1	\( -\,7^{12}\cdot 92779^{3} \)	18T362	Trivial (GRH)
18.12.11522585241472304020455424.1	x^18 - 13x^16 + 53x^14 - 48x^12 - 144x^10 + 279x^8 - 33x^6 - 129x^4 + 14x^2 + 1	\( -\,2^{24}\cdot 37^{6}\cdot 16361^{2} \)	18T556	Trivial (GRH)