Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)
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Label | Polynomial | Discriminant | Galois group | Class group |
---|---|---|---|---|
8.0.102...744.1 | $x^{8} + 204204 x^{6} + 10424818404 x^{4} + 177399134780868 x^{2} + 754700269141507689$ | $2^{24}\cdot 3^{6}\cdot 7^{4}\cdot 11^{4}\cdot 13^{4}\cdot 17^{4}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 2, 2, 2802, 2802]$ |
8.0.113...921.1 | $x^{8} - 3 x^{7} + 61255 x^{6} + 122679 x^{5} + 501055320 x^{4} + 404247564 x^{3} + 1234857320512 x^{2} + 1655172722880 x + 723936601859584$ | $3^{6}\cdot 11^{6}\cdot 17^{6}\cdot 19^{4}\cdot 23^{4}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 6062, 6062]$ |
8.0.130...961.1 | $x^{8} - x^{7} + 21737 x^{6} + 88265 x^{5} + 173569270 x^{4} + 932586952 x^{3} + 602842775648 x^{2} + 2435623589008 x + 759589912470496$ | $3^{6}\cdot 7^{6}\cdot 13^{6}\cdot 17^{6}\cdot 19^{4}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 2, 2, 1948, 5844]$ |
8.0.133...625.1 | $x^{8} - x^{7} + 63776 x^{6} + 255266 x^{5} + 1219098373 x^{4} + 7778385703 x^{3} + 7439528984474 x^{2} + 29711684041528 x + 13548110758906816$ | $3^{6}\cdot 5^{4}\cdot 7^{4}\cdot 11^{6}\cdot 13^{4}\cdot 17^{6}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 2, 2, 3202, 3202]$ |
8.0.160...944.1 | $x^{8} + 228228 x^{6} + 13022004996 x^{4} + 247665513018924 x^{2} + 1177587598026728889$ | $2^{24}\cdot 3^{6}\cdot 7^{4}\cdot 11^{4}\cdot 13^{4}\cdot 19^{4}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 2, 2, 3322, 3322]$ |
8.0.176...193.1 | $x^{8} - x^{7} + 2122 x^{6} - 39330 x^{5} + 4144821 x^{4} + 24141747 x^{3} + 1540947392 x^{2} - 171927064784 x + 3339224703104$ | $73^{7}\cdot 233^{6}$ | $C_8$ (as 8T1) | $[5513055508]$ |
8.0.237...000.1 | $x^{8} + 251940 x^{6} + 15868440900 x^{4} + 333157916695500 x^{2} + 1748662615255505625$ | $2^{24}\cdot 3^{6}\cdot 5^{4}\cdot 13^{4}\cdot 17^{4}\cdot 19^{4}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 2, 2, 3134, 3134]$ |
8.0.261...000.1 | $x^{8} + 258060 x^{6} + 16648740900 x^{4} + 358031173054500 x^{2} + 1924865094134255625$ | $2^{24}\cdot 3^{6}\cdot 5^{4}\cdot 11^{4}\cdot 17^{4}\cdot 23^{4}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 2, 2, 2, 2, 1546, 1546]$ |
8.0.279...281.2 | $x^{8} - x^{7} + 26378 x^{6} + 86 x^{5} + 260165689 x^{4} + 45371623 x^{3} + 1128045791804 x^{2} + 2837768452 x + 1818890323264576$ | $3^{6}\cdot 7^{6}\cdot 13^{6}\cdot 17^{6}\cdot 23^{4}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 6292, 18876]$ |
8.0.343...224.1 | $x^{8} + 276276 x^{6} + 19082107044 x^{4} + 439327350474012 x^{2} + 2528658397490794569$ | $2^{24}\cdot 3^{6}\cdot 7^{4}\cdot 11^{4}\cdot 13^{4}\cdot 23^{4}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 2, 2, 2, 2, 1604, 1604]$ |
8.0.467...784.1 | $x^{8} + 298452 x^{6} + 22268399076 x^{4} + 553837353419196 x^{2} + 3443622204222205929$ | $2^{24}\cdot 3^{6}\cdot 7^{4}\cdot 11^{4}\cdot 17^{4}\cdot 19^{4}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 2, 2, 3674, 3674]$ |
8.0.533...584.6 | $x^{8} + 29716 x^{6} + 220760164 x^{4} + 594065601324 x^{2} + 532088565032025$ | $2^{24}\cdot 17^{6}\cdot 19^{6}\cdot 23^{4}$ | $Q_8$ (as 8T5) | $[2, 4, 4, 4, 4, 1236, 4944]$ |
8.0.761...000.1 | $x^{8} + 213180 x^{6} + 10225285290 x^{4} + 80734308078600 x^{2} + 143424498301632900$ | $2^{22}\cdot 3^{6}\cdot 5^{6}\cdot 11^{4}\cdot 17^{4}\cdot 19^{4}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 2, 2, 2, 2, 1430, 1430]$ |
8.0.785...625.4 | $x^{8} - 3 x^{7} + 18055 x^{6} - 111621 x^{5} + 101515224 x^{4} - 1596051000 x^{3} + 149120229520 x^{2} - 6942078570000 x + 75452224163200$ | $3^{6}\cdot 5^{4}\cdot 13^{6}\cdot 17^{6}\cdot 23^{6}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 4, 4, 1020, 4080]$ |
8.0.823...056.1 | $x^{8} + 204204 x^{6} + 8891756874 x^{4} + 125222918668848 x^{2} + 376044424762550544$ | $2^{22}\cdot 3^{4}\cdot 7^{4}\cdot 11^{4}\cdot 13^{4}\cdot 17^{6}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 2, 2, 2, 2, 1494, 1494]$ |
8.0.865...209.1 | $x^{8} - 3 x^{7} + 8468 x^{6} - 150738 x^{5} + 22418861 x^{4} + 396498613 x^{3} - 32011251778 x^{2} - 848649683424 x + 28742837126528$ | $113^{6}\cdot 401^{6}$ | $Q_8$ (as 8T5) | $[2, 4522, 203490]$ |
8.0.912...864.1 | $x^{8} + 352716 x^{6} + 31102144164 x^{4} + 914185323412452 x^{2} + 6717662302765550409$ | $2^{24}\cdot 3^{6}\cdot 7^{4}\cdot 13^{4}\cdot 17^{4}\cdot 19^{4}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 2, 2, 5198, 5198]$ |
8.0.923...376.1 | $x^{8} + 184756 x^{6} + 5430533108 x^{4} + 35832984817916 x^{2} + 37615675812607321$ | $2^{24}\cdot 11^{6}\cdot 13^{4}\cdot 17^{4}\cdot 19^{4}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 5970, 5970]$ |
8.0.978...000.2 | $x^{8} + 135660 x^{6} + 5915454300 x^{4} + 81735146608500 x^{2} + 3000051403925625$ | $2^{24}\cdot 3^{6}\cdot 5^{4}\cdot 7^{6}\cdot 17^{4}\cdot 19^{4}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 2, 2, 2190, 4380]$ |
8.0.100...864.1 | $x^{8} + 361284 x^{6} + 32631532164 x^{4} + 982437538861548 x^{2} + 7394561745626156409$ | $2^{24}\cdot 3^{6}\cdot 7^{4}\cdot 11^{4}\cdot 17^{4}\cdot 23^{4}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 2, 2, 2, 2, 2286, 2286]$ |
8.0.120...000.1 | $x^{8} + 197340 x^{6} + 6195489300 x^{4} + 43664923516500 x^{2} + 48959295492875625$ | $2^{24}\cdot 3^{4}\cdot 5^{4}\cdot 11^{6}\cdot 13^{4}\cdot 23^{4}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 2, 2, 2954, 2954]$ |
8.0.124...000.3 | $x^{8} + 30940 x^{6} + 229853260 x^{4} + 183080488500 x^{2} + 35014143425625$ | $2^{24}\cdot 5^{6}\cdot 7^{6}\cdot 13^{6}\cdot 17^{4}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 2, 2, 3816, 3816]$ |
8.0.124...000.4 | $x^{8} + 30940 x^{6} + 248788540 x^{4} + 183080488500 x^{2} + 35014143425625$ | $2^{24}\cdot 5^{6}\cdot 7^{6}\cdot 13^{6}\cdot 17^{4}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 2, 2, 3288, 3288]$ |
8.0.125...864.2 | $x^{8} + 204204 x^{6} + 14147967834 x^{4} + 354798269561736 x^{2} + 1540204630901036100$ | $2^{22}\cdot 3^{6}\cdot 7^{6}\cdot 11^{4}\cdot 13^{4}\cdot 17^{4}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 2, 2, 4122, 4122]$ |
8.0.148...000.1 | $x^{8} + 251940 x^{6} + 14281596810 x^{4} + 133263166678200 x^{2} + 279786018440880900$ | $2^{22}\cdot 3^{6}\cdot 5^{6}\cdot 13^{4}\cdot 17^{4}\cdot 19^{4}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 2, 2, 6, 6, 492, 492]$ |
8.0.148...000.2 | $x^{8} + 251940 x^{6} + 20628973170 x^{4} + 666315833391000 x^{2} + 6994650461022022500$ | $2^{22}\cdot 3^{6}\cdot 5^{6}\cdot 13^{4}\cdot 17^{4}\cdot 19^{4}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 2, 2, 2, 2, 1826, 1826]$ |
8.0.151...625.4 | $x^{8} - 3 x^{7} + 20148 x^{6} + 88150 x^{5} + 107098581 x^{4} - 1425481315 x^{3} + 153676038518 x^{2} - 6526881311472 x + 123445713318656$ | $5^{4}\cdot 7^{6}\cdot 11^{6}\cdot 13^{6}\cdot 17^{6}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 2, 2, 1988, 3976]$ |
8.0.163...000.1 | $x^{8} + 258060 x^{6} + 14983866810 x^{4} + 143212469221800 x^{2} + 307978415061480900$ | $2^{22}\cdot 3^{6}\cdot 5^{6}\cdot 11^{4}\cdot 17^{4}\cdot 23^{4}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 2, 2, 3546, 3546]$ |
8.0.172...000.1 | $x^{8} + 125580 x^{6} + 2699153730 x^{4} + 7617072481200 x^{2} + 3679046008419600$ | $2^{22}\cdot 3^{4}\cdot 5^{6}\cdot 7^{4}\cdot 13^{6}\cdot 23^{4}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 2, 2, 2, 2, 814, 3256]$ |
8.0.194...000.1 | $x^{8} + 34580 x^{6} + 61102860 x^{4} + 28399689500 x^{2} + 674492625625$ | $2^{24}\cdot 5^{6}\cdot 7^{6}\cdot 13^{6}\cdot 19^{4}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 2, 2, 3976, 3976]$ |
8.0.194...000.8 | $x^{8} + 34580 x^{6} + 431662140 x^{4} + 2300374849500 x^{2} + 4425346116725625$ | $2^{24}\cdot 5^{6}\cdot 7^{6}\cdot 13^{6}\cdot 19^{4}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 2, 2, 3880, 3880]$ |
8.0.196...544.1 | $x^{8} + 426972 x^{6} + 45576272196 x^{4} + 1621649341005876 x^{2} + 14424976300582518489$ | $2^{24}\cdot 3^{6}\cdot 7^{4}\cdot 13^{4}\cdot 17^{4}\cdot 23^{4}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 2, 2, 2, 4, 1324, 2648]$ |
8.0.196...064.1 | $x^{8} + 228228 x^{6} + 13952148210 x^{4} + 212284725444792 x^{2} + 96129599838916644$ | $2^{22}\cdot 3^{6}\cdot 7^{6}\cdot 11^{4}\cdot 13^{4}\cdot 19^{4}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 2, 2, 3934, 3934]$ |
8.0.210...000.1 | $x^{8} + 164220 x^{6} + 4815751500 x^{4} + 39542135566500 x^{2} + 6442072919375625$ | $2^{24}\cdot 3^{6}\cdot 5^{4}\cdot 7^{6}\cdot 17^{4}\cdot 23^{4}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 2, 2, 3070, 6140]$ |
8.0.212...000.3 | $x^{8} + 30940 x^{6} + 282760660 x^{4} + 812015813700 x^{2} + 66340291952025$ | $2^{24}\cdot 5^{6}\cdot 7^{6}\cdot 13^{4}\cdot 17^{6}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 4348, 8696]$ |
8.0.225...504.5 | $x^{8} + 42636 x^{6} + 482596884 x^{4} + 1814647296132 x^{2} + 1811471663363769$ | $2^{24}\cdot 3^{4}\cdot 11^{4}\cdot 17^{6}\cdot 19^{6}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 2, 2, 1460, 5840]$ |
8.0.225...504.6 | $x^{8} + 42636 x^{6} + 454457124 x^{4} + 1754658955764 x^{2} + 2254905475364025$ | $2^{24}\cdot 3^{4}\cdot 11^{4}\cdot 17^{6}\cdot 19^{6}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 2, 2, 1596, 6384]$ |
8.0.226...536.2 | $x^{8} + 201894 x^{6} + 13234151700 x^{4} + 285002221154112 x^{2} + 498183882577387776$ | $2^{12}\cdot 3^{6}\cdot 7^{6}\cdot 11^{6}\cdot 19^{4}\cdot 23^{4}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 2, 2, 2838, 2838]$ |
8.0.247...000.1 | $x^{8} + 125580 x^{6} + 3336032700 x^{4} + 28564021804500 x^{2} + 77285515107425625$ | $2^{24}\cdot 3^{6}\cdot 5^{4}\cdot 7^{4}\cdot 13^{6}\cdot 23^{4}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 2, 2, 2, 2, 1014, 2028]$ |
8.0.255...000.1 | $x^{8} + 288420 x^{6} + 18716871690 x^{4} + 199937782697400 x^{2} + 480550460713200900$ | $2^{22}\cdot 3^{6}\cdot 5^{6}\cdot 11^{4}\cdot 19^{4}\cdot 23^{4}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 2, 2, 2, 2, 1854, 1854]$ |
8.0.255...000.2 | $x^{8} + 288420 x^{6} + 27035481330 x^{4} + 999688913487000 x^{2} + 12013761517830022500$ | $2^{22}\cdot 3^{6}\cdot 5^{6}\cdot 11^{4}\cdot 19^{4}\cdot 23^{4}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 2, 2, 2, 2, 1812, 1812]$ |
8.0.270...000.1 | $x^{8} + 197340 x^{6} + 6638024250 x^{4} + 58219898022000 x^{2} + 87038747542890000$ | $2^{22}\cdot 3^{6}\cdot 5^{4}\cdot 11^{6}\cdot 13^{4}\cdot 23^{4}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 2, 2, 3182, 3182]$ |
8.0.271...000.2 | $x^{8} + 135660 x^{6} + 4863817980 x^{4} + 40124526516900 x^{2} + 87481498938471225$ | $2^{24}\cdot 3^{4}\cdot 5^{6}\cdot 7^{6}\cdot 17^{4}\cdot 19^{4}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 6, 6, 702, 1404]$ |
8.0.285...000.6 | $x^{8} + 45220 x^{6} + 511212100 x^{4} + 2093413549500 x^{2} + 2853282410015625$ | $2^{24}\cdot 5^{4}\cdot 7^{4}\cdot 17^{6}\cdot 19^{6}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 2, 2, 2620, 10480]$ |
8.0.294...000.2 | $x^{8} + 83980 x^{6} + 2097232540 x^{4} + 17534627194500 x^{2} + 43595466862325625$ | $2^{24}\cdot 5^{6}\cdot 13^{4}\cdot 17^{4}\cdot 19^{6}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 4318, 8636]$ |
8.0.297...264.1 | $x^{8} + 51612 x^{6} + 723858300 x^{4} + 2139696180468 x^{2} + 35075733815529$ | $2^{24}\cdot 3^{4}\cdot 11^{6}\cdot 17^{4}\cdot 23^{6}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 2494, 14964]$ |
8.0.301...401.4 | $x^{8} - x^{7} + 25676 x^{6} + 320510 x^{5} + 192919861 x^{4} + 2035118239 x^{3} + 309836432486 x^{2} - 439505901212 x + 242465027917336$ | $3^{6}\cdot 7^{4}\cdot 13^{6}\cdot 17^{6}\cdot 23^{6}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 2, 2, 2380, 9520]$ |
8.0.327...000.1 | $x^{8} + 183540 x^{6} + 6015523500 x^{4} + 55204459159500 x^{2} + 10051811938625625$ | $2^{24}\cdot 3^{6}\cdot 5^{4}\cdot 7^{6}\cdot 19^{4}\cdot 23^{4}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 2, 2, 2370, 4740]$ |
8.0.327...000.2 | $x^{8} + 183540 x^{6} + 10827942300 x^{4} + 202416350251500 x^{2} + 10051811938625625$ | $2^{24}\cdot 3^{6}\cdot 5^{4}\cdot 7^{6}\cdot 19^{4}\cdot 23^{4}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 2, 2, 2594, 5188]$ |
8.0.342...625.1 | $x^{8} - x^{7} + 64822 x^{6} + 260066 x^{5} + 1492497601 x^{4} + 8160572815 x^{3} + 14520370974600 x^{2} + 58168038790800 x + 50003470008515200$ | $5^{4}\cdot 7^{6}\cdot 17^{6}\cdot 19^{4}\cdot 23^{6}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 2, 2, 3078, 3078]$ |