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Results (1-50 of 3536 matches)

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Label Polynomial Discriminant Galois group Class group Regulator
8.0.624...625.2 $x^{8} - 3 x^{7} + 5497 x^{6} + 35643 x^{5} + 5272038 x^{4} - 20736792 x^{3} + 1848968032 x^{2} - 11739093888 x + 453733866496$ $3^{6}\cdot 5^{4}\cdot 7^{6}\cdot 13^{6}\cdot 17^{6}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 1132, 3396]$ $1706.950274733737$
8.0.106...625.1 $x^{8} - x^{7} + 18008 x^{6} + 36086 x^{5} + 23114233 x^{4} + 6421627 x^{3} + 9443753102 x^{2} - 56498768 x + 1102555134976$ $3^{6}\cdot 5^{4}\cdot 11^{6}\cdot 19^{6}\cdot 23^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 1774, 1774]$ $2000.9207292969234$
8.0.224...000.1 $x^{8} + 78540 x^{6} + 1542132900 x^{4} + 10093259830500 x^{2} + 16515096397655625$ $2^{24}\cdot 3^{6}\cdot 5^{4}\cdot 7^{4}\cdot 11^{4}\cdot 17^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 982, 982]$ $21.287188641522963$
8.0.255...313.1 $x^{8} - x^{7} + 881 x^{6} + 20093 x^{5} + 1109222 x^{4} - 5894476 x^{3} + 95433112 x^{2} + 5333705760 x + 33591285504$ $37^{6}\cdot 193^{7}$ $C_8$ (as 8T1) $[11, 21919612]$ $92656.6271982$
8.0.350...000.1 $x^{8} + 87780 x^{6} + 1926332100 x^{4} + 14091119311500 x^{2} + 25769134440905625$ $2^{24}\cdot 3^{6}\cdot 5^{4}\cdot 7^{4}\cdot 11^{4}\cdot 19^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 946, 946]$ $21.287188641522963$
8.0.372...984.1 $x^{8} + 89148 x^{6} + 1986841476 x^{4} + 14760245325204 x^{2} + 27413465630235129$ $2^{24}\cdot 3^{6}\cdot 17^{4}\cdot 19^{4}\cdot 23^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 1116, 1116]$ $21.287188641522963$
8.0.384...593.1 $x^{8} - x^{7} + 9654 x^{6} - 77586 x^{5} + 14786073 x^{4} - 99617681 x^{3} + 3903207296 x^{2} + 399712164 x + 148887867824$ $151^{4}\cdot 257^{7}$ $C_8$ (as 8T1) $[120043158]$ $6320.84371215$
8.0.408...049.1 $x^{8} - 3 x^{7} + 25222 x^{6} - 50454 x^{5} + 182638449 x^{4} - 129817803 x^{3} + 410660572648 x^{2} + 823303138788 x + 66858343242784$ $3^{6}\cdot 7^{4}\cdot 11^{6}\cdot 19^{6}\cdot 23^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 6, 6, 762, 762]$ $2000.9207292969234$
8.0.437...000.1 $x^{8} + 92820 x^{6} + 2153888100 x^{4} + 16660324453500 x^{2} + 32216902411955625$ $2^{24}\cdot 3^{6}\cdot 5^{4}\cdot 7^{4}\cdot 13^{4}\cdot 17^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 1278, 1278]$ $21.287188641522963$
8.0.516...424.2 $x^{8} + 29172 x^{6} + 290115540 x^{4} + 1081415345868 x^{2} + 937786931616249$ $2^{24}\cdot 3^{6}\cdot 11^{6}\cdot 13^{4}\cdot 17^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 1318, 2636]$ $267.19553215080305$
8.0.579...193.1 $x^{8} - 3 x^{7} + 12376 x^{6} - 24734 x^{5} + 22720489 x^{4} + 32175201 x^{3} + 11819644958 x^{2} + 63691264512 x + 944227994976$ $193^{6}\cdot 257^{5}$ $C_4\wr C_2$ (as 8T17) $[2, 2, 4, 7602920]$ $24150.6330833$
8.0.683...000.1 $x^{8} + 103740 x^{6} + 2690496900 x^{4} + 23259345700500 x^{2} + 50269260895205625$ $2^{24}\cdot 3^{6}\cdot 5^{4}\cdot 7^{4}\cdot 13^{4}\cdot 19^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 1354, 1354]$ $21.287188641522963$
8.0.751...000.1 $x^{8} + 106260 x^{6} + 2822796900 x^{4} + 24995866549500 x^{2} + 55334599573955625$ $2^{24}\cdot 3^{6}\cdot 5^{4}\cdot 7^{4}\cdot 11^{4}\cdot 23^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 2, 2, 678, 678]$ $21.287188641522963$
8.0.111...625.2 $x^{8} - 3 x^{7} + 4099 x^{6} + 135483 x^{5} + 7704396 x^{4} + 277892280 x^{3} + 12251958160 x^{2} + 272654257200 x + 3998388846400$ $3^{6}\cdot 5^{6}\cdot 7^{6}\cdot 11^{6}\cdot 19^{6}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 4, 1292, 1292]$ $18163.67450497027$
8.0.116...241.1 $x^{8} - x^{7} + 34604 x^{6} + 138578 x^{5} + 359166157 x^{4} + 2291482567 x^{3} + 1193941213766 x^{2} + 4762087747048 x + 1180931781336256$ $3^{6}\cdot 11^{6}\cdot 13^{4}\cdot 17^{6}\cdot 19^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 3294, 3294]$ $1778.2833765514763$
8.0.120...641.3 $x^{8} - x^{7} + 333 x^{6} - 30679 x^{5} - 287030 x^{4} - 9799184 x^{3} + 278703872 x^{2} + 4915236864 x + 58573389824$ $17^{7}\cdot 313^{7}$ $C_8$ (as 8T1) $[89, 2011400]$ $31027.5883758$
8.0.128...000.1 $x^{8} + 82110 x^{6} + 2118930660 x^{4} + 21089138968800 x^{2} + 65966826694406400$ $2^{12}\cdot 3^{6}\cdot 5^{6}\cdot 7^{6}\cdot 17^{4}\cdot 23^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 1098, 1098]$ $53.158209818210345$
8.0.128...000.2 $x^{8} + 82110 x^{6} + 2311560720 x^{4} + 26361423711000 x^{2} + 103073166710010000$ $2^{12}\cdot 3^{6}\cdot 5^{6}\cdot 7^{6}\cdot 17^{4}\cdot 23^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 986, 986]$ $53.158209818210345$
8.0.140...000.1 $x^{8} + 78540 x^{6} + 1387919610 x^{4} + 4037303932200 x^{2} + 2642415423624900$ $2^{22}\cdot 3^{6}\cdot 5^{6}\cdot 7^{4}\cdot 11^{4}\cdot 17^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 926, 926]$ $54.52131853640607$
8.0.140...000.2 $x^{8} + 78540 x^{6} + 2004772770 x^{4} + 20186519661000 x^{2} + 66060385590622500$ $2^{22}\cdot 3^{6}\cdot 5^{6}\cdot 7^{4}\cdot 11^{4}\cdot 17^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 950, 950]$ $54.52131853640607$
8.0.146...081.1 $x^{8} - x^{7} + 12455 x^{6} + 51137 x^{5} + 57924832 x^{4} + 310395928 x^{3} + 118644572432 x^{2} + 482903755216 x + 88804805801728$ $3^{6}\cdot 7^{6}\cdot 11^{4}\cdot 13^{6}\cdot 17^{6}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2380, 7140]$ $1706.950274733737$
8.0.146...000.1 $x^{8} + 125580 x^{6} + 3942584100 x^{4} + 41259142606500 x^{2} + 107944231844255625$ $2^{24}\cdot 3^{6}\cdot 5^{4}\cdot 7^{4}\cdot 13^{4}\cdot 23^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 2, 2, 764, 764]$ $21.287188641522963$
8.0.173...504.2 $x^{8} + 39468 x^{6} + 531041940 x^{4} + 2678115309012 x^{2} + 3142098786298329$ $2^{24}\cdot 3^{6}\cdot 11^{6}\cdot 13^{4}\cdot 23^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 1966, 3932]$ $267.19553215080305$
8.0.180...000.1 $x^{8} + 78540 x^{6} + 1315348650 x^{4} + 7124653998000 x^{2} + 8228975367690000$ $2^{22}\cdot 3^{4}\cdot 5^{4}\cdot 7^{4}\cdot 11^{4}\cdot 17^{6}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 2, 2, 470, 470]$ $125.49277292047219$
8.0.199...000.1 $x^{8} + 135660 x^{6} + 4600908900 x^{4} + 52013275114500 x^{2} + 147002518792355625$ $2^{24}\cdot 3^{6}\cdot 5^{4}\cdot 7^{4}\cdot 17^{4}\cdot 19^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 1538, 1538]$ $21.287188641522963$
8.0.200...000.1 $x^{8} + 91770 x^{6} + 2646830340 x^{4} + 29442378218400 x^{2} + 102930554251526400$ $2^{12}\cdot 3^{6}\cdot 5^{6}\cdot 7^{6}\cdot 19^{4}\cdot 23^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 1210, 1210]$ $53.158209818210345$
8.0.200...000.2 $x^{8} + 91770 x^{6} + 2887451280 x^{4} + 36802972773000 x^{2} + 160828991018010000$ $2^{12}\cdot 3^{6}\cdot 5^{6}\cdot 7^{6}\cdot 19^{4}\cdot 23^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 1078, 1078]$ $53.158209818210345$
8.0.202...000.1 $x^{8} + 71060 x^{6} + 803333300 x^{4} + 2038745153500 x^{2} + 823143355725625$ $2^{24}\cdot 5^{4}\cdot 11^{6}\cdot 17^{4}\cdot 19^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2066, 2066]$ $126.1318284350999$
8.0.212...000.1 $x^{8} + 41860 x^{6} + 299905970 x^{4} + 282113795600 x^{2} + 45420321091600$ $2^{22}\cdot 5^{6}\cdot 7^{4}\cdot 13^{6}\cdot 23^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 4, 4, 4, 276, 552]$ $186.8030680507958$
8.0.212...000.2 $x^{8} + 41860 x^{6} + 542526530 x^{4} + 2539024160400 x^{2} + 3679046008419600$ $2^{22}\cdot 5^{6}\cdot 7^{4}\cdot 13^{6}\cdot 23^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 446, 1784]$ $186.8030680507958$
8.0.218...000.1 $x^{8} + 87780 x^{6} + 1733698890 x^{4} + 5636447724600 x^{2} + 4123061510544900$ $2^{22}\cdot 3^{6}\cdot 5^{6}\cdot 7^{4}\cdot 11^{4}\cdot 19^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 2, 2, 514, 514]$ $54.52131853640607$
8.0.218...000.2 $x^{8} + 87780 x^{6} + 2504231730 x^{4} + 28182238623000 x^{2} + 103076537763622500$ $2^{22}\cdot 3^{6}\cdot 5^{6}\cdot 7^{4}\cdot 11^{4}\cdot 19^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 2, 4, 332, 664]$ $54.52131853640607$
8.0.235...264.1 $x^{8} + 42636 x^{6} + 454457124 x^{4} + 1027527557364 x^{2} + 296331608061225$ $2^{24}\cdot 3^{6}\cdot 11^{6}\cdot 17^{4}\cdot 19^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 1636, 1636]$ $267.19553215080305$
8.0.236...000.1 $x^{8} + 15980 x^{6} + 8964780 x^{4} + 1085281700 x^{2} + 4612447225$ $2^{24}\cdot 5^{6}\cdot 17^{4}\cdot 47^{6}$ $Q_8$ (as 8T5) $[2, 2, 6, 1602, 3204]$ $2009.0324011375665$
8.0.259...000.1 $x^{8} + 86020 x^{6} + 1577821850 x^{4} + 9360292106000 x^{2} + 11840769514090000$ $2^{22}\cdot 5^{4}\cdot 11^{4}\cdot 17^{6}\cdot 23^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 994, 994]$ $125.49277292047219$
8.0.266...000.1 $x^{8} + 145860 x^{6} + 5318784900 x^{4} + 64649830459500 x^{2} + 196454672308805625$ $2^{24}\cdot 3^{6}\cdot 5^{4}\cdot 11^{4}\cdot 13^{4}\cdot 17^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 1902, 1902]$ $21.287188641522963$
8.0.273...000.1 $x^{8} + 92820 x^{6} + 1938499290 x^{4} + 6664129781400 x^{2} + 5154704385912900$ $2^{22}\cdot 3^{6}\cdot 5^{6}\cdot 7^{4}\cdot 13^{4}\cdot 17^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 1122, 1122]$ $54.52131853640607$
8.0.273...000.2 $x^{8} + 92820 x^{6} + 2800054530 x^{4} + 33320648907000 x^{2} + 128867609647822500$ $2^{22}\cdot 3^{6}\cdot 5^{6}\cdot 7^{4}\cdot 13^{4}\cdot 17^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 1278, 1278]$ $54.52131853640607$
8.0.274...000.1 $x^{8} + 78540 x^{6} + 1652285250 x^{4} + 8651365569000 x^{2} + 1348171134502500$ $2^{22}\cdot 3^{6}\cdot 5^{4}\cdot 7^{6}\cdot 11^{4}\cdot 17^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 2, 482, 964]$ $97.6988467620126$
8.0.274...000.2 $x^{8} + 78540 x^{6} + 2092894650 x^{4} + 20186519661000 x^{2} + 33704278362562500$ $2^{22}\cdot 3^{6}\cdot 5^{4}\cdot 7^{6}\cdot 11^{4}\cdot 17^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 2, 514, 1028]$ $97.6988467620126$
8.0.278...784.6 $x^{8} + 14212 x^{6} + 50495236 x^{4} + 64987368732 x^{2} + 27838339202025$ $2^{24}\cdot 11^{4}\cdot 17^{6}\cdot 19^{6}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 1020, 4080]$ $1270.5324197061695$
8.0.280...744.2 $x^{8} + 12236 x^{6} + 48564684 x^{4} + 63668300724 x^{2} + 8356464470025$ $2^{24}\cdot 7^{4}\cdot 19^{6}\cdot 23^{6}$ $Q_8$ (as 8T5) $[2, 2, 2, 2458, 14748]$ $4487.275846567552$
8.0.299...816.1 $x^{8} + 89148 x^{6} + 1694658906 x^{4} + 10418996700144 x^{2} + 13659304673888784$ $2^{22}\cdot 3^{4}\cdot 17^{6}\cdot 19^{4}\cdot 23^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 1106, 1106]$ $125.49277292047219$
8.0.301...000.1 $x^{8} + 78540 x^{6} + 981357300 x^{4} + 2752707226500 x^{2} + 1228395599825625$ $2^{24}\cdot 3^{4}\cdot 5^{4}\cdot 7^{4}\cdot 11^{6}\cdot 17^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 2, 2, 462, 462]$ $126.1318284350999$
8.0.343...576.1 $x^{8} + 50388 x^{6} + 384183306 x^{4} + 561108070224 x^{2} + 124004883519504$ $2^{22}\cdot 3^{6}\cdot 13^{4}\cdot 17^{4}\cdot 19^{6}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 1850, 1850]$ $614.0751062361139$
8.0.351...000.1 $x^{8} + 92820 x^{6} + 1837139850 x^{4} + 11760229026000 x^{2} + 16052712620490000$ $2^{22}\cdot 3^{4}\cdot 5^{4}\cdot 7^{4}\cdot 13^{4}\cdot 17^{6}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 2, 2, 606, 606]$ $125.49277292047219$
8.0.376...000.1 $x^{8} + 60060 x^{6} + 644143500 x^{4} + 1934362930500 x^{2} + 115255791275625$ $2^{24}\cdot 3^{6}\cdot 5^{4}\cdot 7^{6}\cdot 11^{4}\cdot 13^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 188, 188]$ $116.6588945460986$
8.0.376...000.2 $x^{8} + 60060 x^{6} + 1159458300 x^{4} + 7092664078500 x^{2} + 115255791275625$ $2^{24}\cdot 3^{6}\cdot 5^{4}\cdot 7^{6}\cdot 11^{4}\cdot 13^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 396, 396]$ $116.6588945460986$
8.0.386...000.1 $x^{8} + 48620 x^{6} + 404591330 x^{4} + 442050122800 x^{2} + 82663372963600$ $2^{22}\cdot 5^{6}\cdot 11^{4}\cdot 13^{6}\cdot 17^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 4, 4, 4, 324, 648]$ $186.8030680507958$
8.0.386...000.2 $x^{8} + 48620 x^{6} + 731901170 x^{4} + 3978451105200 x^{2} + 6695733210051600$ $2^{22}\cdot 5^{6}\cdot 11^{4}\cdot 13^{6}\cdot 17^{4}$ $Q_8$ (as 8T5) $[2, 2, 2, 2, 2, 2, 2, 502, 2008]$ $186.8030680507958$
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