Note: Search results may be incomplete. Given $p$-adic completions contain an unramified field and completions are only searched for ramified primes.
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Results (12 matches)
Download displayed columns for results| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 20.0.132...000.1 | $x^{20} + 6 x^{18} - 26 x^{17} + 50 x^{16} - 28 x^{15} + 320 x^{14} - 156 x^{13} + 212 x^{12} - 48 x^{11} - 1560 x^{10} - 3056 x^{9} + 768 x^{8} + 608 x^{7} + 2512 x^{6} + 1984 x^{5} + 5584 x^{4} + 4240 x^{3} + 1600 x^{2} - 320 x + 80$ | $2^{24}\cdot 5^{12}\cdot 37^{7}\cdot 43^{4}$ | $C_5:D_5^3.(C_2\times S_4)$ (as 20T884) | $[2]$ |
| 20.4.261...488.1 | $x^{20} - 2 x^{19} - 5 x^{18} - 8 x^{17} - 183 x^{16} - 640 x^{15} - 876 x^{14} - 3380 x^{13} - 8388 x^{12} - 376 x^{11} - 18600 x^{10} - 34616 x^{9} + 27192 x^{8} - 73984 x^{7} - 53712 x^{6} + 51760 x^{5} - 36192 x^{4} - 23680 x^{3} + 11824 x^{2} - 4960 x + 400$ | $2^{36}\cdot 3^{14}\cdot 7^{17}\cdot 43^{4}$ | $C_5^4:Q_{16}$ (as 20T397) | trivial |
| 20.8.558...592.1 | $x^{20} - 2 x^{19} - 40 x^{18} + 160 x^{17} + 280 x^{16} - 2568 x^{15} + 1558 x^{14} + 11524 x^{13} - 20073 x^{12} - 2834 x^{11} + 9034 x^{10} - 99708 x^{9} + 141906 x^{8} + 177556 x^{7} - 219962 x^{6} + 76168 x^{5} + 127133 x^{4} - 111214 x^{3} + 48492 x^{2} + 1220 x + 2236$ | $2^{36}\cdot 3^{11}\cdot 41^{10}\cdot 43^{4}$ | $D_5^4.S_4$ (as 20T881) | trivial |
| 20.12.272...000.1 | $x^{20} - 4 x^{19} - 50 x^{18} - 118 x^{17} + 180 x^{16} + 2278 x^{15} + 5133 x^{14} + 4652 x^{13} + 5628 x^{12} - 39698 x^{11} - 158379 x^{10} - 91414 x^{9} + 317565 x^{8} + 307162 x^{7} - 371220 x^{6} - 160882 x^{5} + 243288 x^{4} + 53752 x^{3} - 70592 x^{2} - 27248 x - 2495$ | $2^{30}\cdot 3^{16}\cdot 5^{14}\cdot 7^{10}\cdot 43^{4}$ | $C_5^4:D_8:C_4$ (as 20T590) | trivial |
| 20.4.127...984.1 | $x^{20} - 70 x^{18} - 76 x^{17} + 1688 x^{16} + 9484 x^{15} - 16992 x^{14} - 310664 x^{13} - 144053 x^{12} + 4033540 x^{11} + 9121444 x^{10} - 17263124 x^{9} - 105955440 x^{8} - 135238784 x^{7} + 239521094 x^{6} + 1354422944 x^{5} + 2389368401 x^{4} - 159598284 x^{3} - 8304472868 x^{2} - 14428146384 x - 10161127728$ | $2^{36}\cdot 3^{14}\cdot 7^{16}\cdot 43^{8}$ | $C_5^4:Q_{16}$ (as 20T399) | trivial |
| 20.4.893...888.1 | $x^{20} - 2 x^{19} + 35 x^{18} - 22 x^{17} + 329 x^{16} + 244 x^{15} - 4192 x^{14} + 41384 x^{13} - 90776 x^{12} - 489132 x^{11} + 1602720 x^{10} + 2368464 x^{9} - 11881100 x^{8} - 3377864 x^{7} + 43997816 x^{6} - 9037648 x^{5} - 94857196 x^{4} + 29730496 x^{3} + 110096420 x^{2} - 9466648 x - 42641660$ | $2^{36}\cdot 3^{14}\cdot 7^{17}\cdot 43^{8}$ | $C_5^4:Q_{16}$ (as 20T397) | trivial |
| 20.4.119...184.1 | $x^{20} - 8 x^{19} - 60 x^{18} + 364 x^{17} + 616 x^{16} - 5288 x^{15} + 8964 x^{14} + 9196 x^{13} - 19262 x^{12} + 212136 x^{11} - 2765140 x^{10} + 1965292 x^{9} + 15507036 x^{8} - 10383528 x^{7} - 21804844 x^{6} - 241368388 x^{5} + 582931033 x^{4} - 1097861856 x^{3} + 2147934376 x^{2} + 1050891696 x - 125862092$ | $2^{38}\cdot 3^{13}\cdot 7^{17}\cdot 43^{8}$ | $C_5^4:Q_{16}$ (as 20T397) | trivial |
| 20.4.119...184.2 | $x^{20} - 4 x^{19} - 48 x^{18} - 68 x^{17} + 979 x^{16} + 5564 x^{15} + 28576 x^{14} + 108080 x^{13} - 587804 x^{12} - 8017548 x^{11} - 26337108 x^{10} + 46848536 x^{9} + 600983348 x^{8} + 1629063324 x^{7} - 133444512 x^{6} - 11439363888 x^{5} - 26799981633 x^{4} - 8018164584 x^{3} + 72044403660 x^{2} + 130001528844 x + 71108414829$ | $2^{38}\cdot 3^{13}\cdot 7^{17}\cdot 43^{8}$ | $C_5^4:Q_{16}$ (as 20T397) | trivial |
| 20.4.305...288.1 | $x^{20} - 4 x^{19} - 66 x^{18} - 60 x^{17} + 526 x^{16} - 9224 x^{15} - 57544 x^{14} + 2179692 x^{13} - 3704689 x^{12} + 471592 x^{11} + 718378946 x^{10} - 2691043848 x^{9} + 9068782570 x^{8} + 19224504444 x^{7} - 163330561508 x^{6} + 525664159756 x^{5} - 394445612527 x^{4} - 1331407968120 x^{3} + 5531669223274 x^{2} - 862276537812 x + 183142637308$ | $2^{36}\cdot 3^{14}\cdot 7^{17}\cdot 43^{12}$ | $C_5^4:Q_{16}$ (as 20T397) | trivial |
| 20.4.305...288.2 | $x^{20} - 2 x^{19} + 14 x^{18} - 378 x^{17} - 1899 x^{16} + 36072 x^{15} + 10180 x^{14} - 2027996 x^{13} + 1048232 x^{12} + 39348288 x^{11} - 42298536 x^{10} - 301848348 x^{9} - 696238968 x^{8} - 706201464 x^{7} + 22122599340 x^{6} + 30662178116 x^{5} - 164790552325 x^{4} - 299230329734 x^{3} + 761402903306 x^{2} + 2646047590454 x + 711624647647$ | $2^{36}\cdot 3^{14}\cdot 7^{17}\cdot 43^{12}$ | $C_5^4:Q_{16}$ (as 20T397) | trivial |
| 20.4.305...288.3 | $x^{20} - 2 x^{19} + 162 x^{18} - 1128 x^{17} + 11152 x^{16} - 130452 x^{15} + 798352 x^{14} - 6266292 x^{13} + 41078647 x^{12} - 266287410 x^{11} + 914876764 x^{10} - 6305687616 x^{9} + 27239103388 x^{8} + 18836695380 x^{7} + 284971616962 x^{6} + 95129672448 x^{5} - 8217826457291 x^{4} - 2430245568006 x^{3} + 11701329084540 x^{2} - 23321476932628 x + 34453496012860$ | $2^{36}\cdot 3^{14}\cdot 7^{17}\cdot 43^{12}$ | $C_5^4:Q_{16}$ (as 20T397) | trivial |
| 20.4.305...288.4 | $x^{20} - 2 x^{19} + 85 x^{18} + 174 x^{17} + 1023 x^{16} + 54852 x^{15} + 242090 x^{14} - 2100004 x^{13} + 5259458 x^{12} + 143961044 x^{11} - 702709570 x^{10} - 785288200 x^{9} + 13029428062 x^{8} + 42513483088 x^{7} - 306963456152 x^{6} - 2003514721048 x^{5} + 18178752098420 x^{4} - 38007838700584 x^{3} - 19387982060324 x^{2} + 125268852745120 x + 57435551252500$ | $2^{36}\cdot 3^{14}\cdot 7^{17}\cdot 43^{12}$ | $C_5^4:Q_{16}$ (as 20T397) | trivial |