Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)
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Results (18 matches)
Download displayed columns for results| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 20.0.146...000.1 | $x^{20} + 1244 x^{18} + 664827 x^{16} + 200221838 x^{14} + 37413894201 x^{12} + 4495384753024 x^{10} + 347651176196668 x^{8} + 16802127274725302 x^{6} + 473166172952080318 x^{4} + 6673646740206221537 x^{2} + 31142373916142055599$ | $2^{20}\cdot 5^{10}\cdot 11^{16}\cdot 7919^{5}$ | $C_2^6:C_{10}$ (as 20T130) | $[2, 2, 2, 2, 6069812336]$ |
| 20.0.989...256.1 | $x^{20} + 1604 x^{18} + 1057838 x^{16} + 378364753 x^{14} + 80925997668 x^{12} + 10700977711955 x^{10} + 870171034803357 x^{8} + 41765095228552836 x^{6} + 1076119346023005367 x^{4} + 11444522960549429763 x^{2} + 878026939499046681$ | $2^{20}\cdot 3^{2}\cdot 97^{2}\cdot 401^{15}$ | $C_2^9.D_5$ (as 20T350) | $[2, 2, 2, 2, 2, 2, 4, 258041912]$ |
| 20.0.143...000.1 | $x^{20} + 410 x^{18} + 61500 x^{16} + 4510000 x^{14} + 177726800 x^{12} + 3804144000 x^{10} + 41636320000 x^{8} + 201697040000 x^{6} + 427036320000 x^{4} + 350697600000 x^{2} + 95644800000$ | $2^{30}\cdot 5^{15}\cdot 41^{19}$ | $C_{20}$ (as 20T1) | $[2, 2, 6653372708]$ |
| 20.0.894...000.2 | $x^{20} + 680 x^{18} + 181560 x^{16} + 24969600 x^{14} + 1951674800 x^{12} + 89321484320 x^{10} + 2339342636800 x^{8} + 31990547504000 x^{6} + 183353317216000 x^{4} + 332169297779200 x^{2} + 17454472483840$ | $2^{30}\cdot 5^{35}\cdot 17^{15}$ | $C_{20}$ (as 20T1) | $[2, 7684068100]$ |
| 20.0.679...000.5 | $x^{20} + 820 x^{18} + 214225 x^{16} + 24743500 x^{14} + 1372885000 x^{12} + 37375600000 x^{10} + 491561171875 x^{8} + 3135590312500 x^{6} + 9074116796875 x^{4} + 9810210937500 x^{2} + 1329697265625$ | $2^{40}\cdot 3^{10}\cdot 5^{10}\cdot 41^{18}$ | $C_2\times C_{10}$ (as 20T3) | $[2, 2, 2, 2, 2, 2, 397410288]$ |
| 20.0.701...000.2 | $x^{20} - 4 x^{19} + 42 x^{18} - 192 x^{17} + 1959 x^{16} - 4884 x^{15} + 57274 x^{14} - 122536 x^{13} + 1213272 x^{12} - 1901616 x^{11} + 24013092 x^{10} - 5463084 x^{9} + 433071955 x^{8} + 329523584 x^{7} + 5662159086 x^{6} + 5435837856 x^{5} + 46311595263 x^{4} + 38060451720 x^{3} + 221685746346 x^{2} + 115448641956 x + 465058055151$ | $2^{55}\cdot 5^{15}\cdot 41^{16}$ | $C_{20}$ (as 20T1) | $[24298398100]$ |
| 20.0.213...000.3 | $x^{20} + 620 x^{18} + 163370 x^{16} + 23832800 x^{14} + 2101010275 x^{12} + 114636279655 x^{10} + 3808990097300 x^{8} + 72806825933425 x^{6} + 711319770305875 x^{4} + 2763074514531375 x^{2} + 1976877420853005$ | $2^{20}\cdot 5^{35}\cdot 31^{18}$ | $C_{20}$ (as 20T1) | $[2, 10, 979089050]$ |
| 20.0.466...000.2 | $x^{20} - 220 x^{18} - 2420 x^{17} + 21450 x^{16} + 583836 x^{15} + 3502950 x^{14} - 33013640 x^{13} - 752736160 x^{12} - 5543554500 x^{11} + 2279418570 x^{10} + 495397268300 x^{9} + 6227682310245 x^{8} + 48294891164740 x^{7} + 272661356669900 x^{6} + 1169108267232268 x^{5} + 3836312578497410 x^{4} + 9520797872018840 x^{3} + 17430947729479900 x^{2} + 21572531775270080 x + 15613369350198257$ | $2^{55}\cdot 5^{32}\cdot 11^{18}$ | $C_{20}$ (as 20T1) | $[5, 2621610050]$ |
| 20.0.483...000.3 | $x^{20} + 820 x^{18} + 256250 x^{16} + 39237000 x^{14} + 3199197200 x^{12} + 143862932000 x^{10} + 3577377715000 x^{8} + 47512954140000 x^{6} + 312165040270000 x^{4} + 857751578200000 x^{2} + 787722016100000$ | $2^{55}\cdot 5^{15}\cdot 41^{19}$ | $C_{20}$ (as 20T1) | $[2, 4, 2907751652]$ |
| 20.0.654...000.2 | $x^{20} + 820 x^{18} + 271420 x^{16} + 47070050 x^{14} + 4657110050 x^{12} + 267724300303 x^{10} + 8608657192805 x^{8} + 136377368788730 x^{6} + 743596568481275 x^{4} + 876479585827850 x^{2} + 71877073801$ | $2^{20}\cdot 5^{34}\cdot 41^{18}$ | $C_2\times C_{10}$ (as 20T3) | $[5, 10, 278966420]$ |
| 20.0.654...000.12 | $x^{20} + 820 x^{18} + 277570 x^{16} + 50790800 x^{14} + 5529189275 x^{12} + 370384365328 x^{10} + 15206844638930 x^{8} + 367779268319780 x^{6} + 4775088327115025 x^{4} + 26398034793363200 x^{2} + 17023928122802176$ | $2^{20}\cdot 5^{34}\cdot 41^{18}$ | $C_2\times C_{10}$ (as 20T3) | $[2, 4, 40, 40, 40, 31240]$ |
| 20.0.654...000.13 | $x^{20} + 820 x^{18} + 285770 x^{16} + 55136800 x^{14} + 6428606275 x^{12} + 463900095803 x^{10} + 20382812663480 x^{8} + 514849477932005 x^{6} + 6628457585928775 x^{4} + 33576526013427075 x^{2} + 21574938539041801$ | $2^{20}\cdot 5^{34}\cdot 41^{18}$ | $C_2\times C_{10}$ (as 20T3) | $[10, 1360841680]$ |
| 20.0.654...000.15 | $x^{20} + 820 x^{18} + 285770 x^{16} + 55136800 x^{14} + 6428606275 x^{12} + 464056945403 x^{10} + 20447120999480 x^{8} + 524077724148005 x^{6} + 7168969150008775 x^{4} + 44657013077067075 x^{2} + 78262133223197401$ | $2^{20}\cdot 5^{34}\cdot 41^{18}$ | $C_2\times C_{10}$ (as 20T3) | $[110, 603188080]$ |
| 20.0.116...000.4 | $x^{20} + 880 x^{18} + 202400 x^{16} + 20823000 x^{14} + 1127002800 x^{12} + 34241740720 x^{10} + 601169648200 x^{8} + 6083933240000 x^{6} + 34121257060000 x^{4} + 95835622256000 x^{2} + 103893806112800$ | $2^{55}\cdot 5^{34}\cdot 11^{18}$ | $C_{20}$ (as 20T1) | $[6, 8243193030]$ |
| 20.0.582...000.1 | $x^{20} + 880 x^{18} + 306240 x^{16} + 54245400 x^{14} + 5249103200 x^{12} + 278566111120 x^{10} + 7831272677800 x^{8} + 103761119545600 x^{6} + 446208997828000 x^{4} + 9488880790400 x^{2} + 3596332960$ | $2^{55}\cdot 5^{35}\cdot 11^{18}$ | $C_{20}$ (as 20T1) | $[2, 48365690180]$ |
| 20.0.582...000.2 | $x^{20} + 880 x^{18} + 296560 x^{16} + 46800600 x^{14} + 3314018400 x^{12} + 79169797520 x^{10} + 802430109800 x^{8} + 3803674688000 x^{6} + 8121911556000 x^{4} + 6279892643200 x^{2} + 1417582740640$ | $2^{55}\cdot 5^{35}\cdot 11^{18}$ | $C_{20}$ (as 20T1) | $[10, 5043150100]$ |
| 20.0.582...000.4 | $x^{20} + 880 x^{18} + 332640 x^{16} + 70613400 x^{14} + 9223517600 x^{12} + 761619477520 x^{10} + 39102956021800 x^{8} + 1163689163929600 x^{6} + 16694916231268000 x^{4} + 59652203230294400 x^{2} + 29061634614163360$ | $2^{55}\cdot 5^{35}\cdot 11^{18}$ | $C_{20}$ (as 20T1) | $[3, 3, 6, 1198931340]$ |
| 20.0.268...000.3 | $x^{20} + 820 x^{18} + 243950 x^{16} + 33107500 x^{14} + 2274853225 x^{12} + 81706435080 x^{10} + 1515651542800 x^{8} + 14458216384000 x^{6} + 66066967040000 x^{4} + 116659093504000 x^{2} + 66103908761600$ | $2^{20}\cdot 5^{34}\cdot 41^{19}$ | $C_{20}$ (as 20T1) | $[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 15580820]$ |