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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 (32 matches)

  displayed columns for results
Label Polynomial Discriminant Galois group Class group Regulator
17.1.638...280.1 $x^{17} + 4 x^{9} - 18 x^{6} + 12 x^{3} + 4 x - 2$ $2^{16}\cdot 5\cdot 7\cdot 27851834699314662203$ $S_{17}$ (as 17T10) trivial $2034427.1525$
17.1.316...216.1 $x^{17} + 4 x - 2$ $2^{16}\cdot 3\cdot 7\cdot 872441\cdot 263984587017258421$ $S_{17}$ (as 17T10) trivial $169905374.649$
17.1.888...936.1 $x^{17} + 2 x - 4$ $2^{30}\cdot 7\cdot 61\cdot 4567\cdot 424202352194821$ $S_{17}$ (as 17T10) trivial $537738015.354$
17.3.140...383.1 $x^{17} - 5 x - 3$ $-\,7\cdot 618079271321299\cdot 3244645955426531$ $S_{17}$ (as 17T10) trivial $1622430410.88$
17.1.126...217.1 $x^{17} - 3 x - 5$ $7\cdot 29\cdot 621795391062917301569685453139$ $S_{17}$ (as 17T10) trivial $3196340521.35$
17.3.312...199.1 $x^{17} - 6 x - 1$ $-\,7\cdot 41\cdot 40841\cdot 6864777739\cdot 3880487013052123$ $S_{17}$ (as 17T10) trivial $13334665698.3$
17.1.583...832.1 $x^{17} + x - 6$ $2^{14}\cdot 7\cdot 5087140107626907696363832039$ $S_{17}$ (as 17T10) trivial $50678740373.2$
17.1.202...336.1 $x^{17} - 6 x - 6$ $2^{16}\cdot 3^{16}\cdot 7\cdot 11\cdot 359\cdot 80956223\cdot 320196829$ $S_{17}$ (as 17T10) trivial $19635262736.2$
17.1.415...945.1 $x^{17} + 8 x - 1$ $5\cdot 7\cdot 16631\cdot 71361355933032887410783402717$ $S_{17}$ (as 17T10) $[2]$ $35636453391.5$
17.1.438...480.1 $x^{17} + 8 x - 6$ $2^{16}\cdot 5\cdot 7\cdot 19\cdot 1006669595289477854357777017$ $S_{17}$ (as 17T10) trivial $365729183553$
17.1.581...184.1 $x^{17} - 6 x - 8$ $2^{46}\cdot 7\cdot 31\cdot 263\cdot 86695337\cdot 166969703$ $S_{17}$ (as 17T10) trivial $230838251231$
17.1.170...161.1 $x^{17} - 3 x - 9$ $3^{15}\cdot 7\cdot 83\cdot 20430281524984417773058783$ $S_{17}$ (as 17T10) trivial $206622603643$
17.1.232...728.1 $x^{17} + x - 8$ $2^{48}\cdot 3\cdot 7\cdot 13\cdot 107\cdot 131\cdot 1429\cdot 151280069117$ $S_{17}$ (as 17T10) trivial $423742786391$
17.1.307...121.1 $x^{17} + 9 x - 3$ $3^{16}\cdot 7\cdot 11\cdot 13\cdot 23\cdot 227\cdot 1277\cdot 1070837791661177753$ $S_{17}$ (as 17T10) trivial $237490611423$
17.1.153...201.1 $x^{17} + 4 x - 9$ $7\cdot 3167\cdot 69\!\cdots\!29$ $S_{17}$ (as 17T10) $[2]$ $166446792195$
18.18.366...784.1 $x^{18} - 20 x^{16} + 167 x^{14} - 761 x^{12} + 2070 x^{10} - 3445 x^{8} + 3446 x^{6} - 1942 x^{4} + 532 x^{2} - 49$ $2^{18}\cdot 7^{2}\cdot 17^{2}\cdot 994046201^{2}$ $C_2^8.S_9$ (as 18T964) trivial $76610944.3206$
21.7.109...648.1 $x^{21} - 37 x^{19} - 7 x^{18} + 631 x^{17} - 160 x^{16} - 7660 x^{15} + 5137 x^{14} + 56640 x^{13} - 76851 x^{12} - 243751 x^{11} + 479095 x^{10} + 411482 x^{9} - 1347008 x^{8} + 92559 x^{7} + 992616 x^{6} - 416686 x^{5} + 955747 x^{4} + 870892 x^{3} - 1275931 x^{2} - 1256035 x - 284261$ $-\,2^{18}\cdot 7^{12}\cdot 23^{7}\cdot 211^{6}$ $C_7\wr S_3$ (as 21T32) $[7]$ $34482408278.3$
22.6.144...125.1 $x^{22} - 2 x^{21} - x^{20} + 18 x^{19} - 17 x^{18} - 44 x^{17} + 110 x^{16} - 3 x^{15} - 254 x^{14} + 59 x^{13} + 240 x^{12} - 102 x^{11} - 552 x^{10} - 230 x^{9} + 307 x^{8} + 320 x^{7} - 3 x^{6} - 154 x^{5} - 62 x^{4} + 18 x^{3} + 19 x^{2} + 2 x - 1$ $5^{11}\cdot 7^{4}\cdot 83^{4}\cdot 127^{4}$ $C_2\times A_{11}$ (as 22T46) trivial $95631.3345105$
22.4.153...375.1 $x^{22} - 2 x^{21} + 7 x^{20} - 20 x^{19} + 38 x^{18} - 74 x^{17} + 107 x^{16} - 167 x^{15} + 185 x^{14} - 284 x^{13} + 308 x^{12} - 417 x^{11} + 466 x^{10} - 462 x^{9} + 446 x^{8} - 292 x^{7} + 170 x^{6} - 55 x^{5} - 7 x^{4} + 11 x^{3} - 8 x^{2} + x + 1$ $-\,5^{4}\cdot 7^{4}\cdot 83^{5}\cdot 127^{4}\cdot 997$ $C_2^{11}.A_{11}$ (as 22T52) trivial $56909.7191275$
22.14.191...529.1 $x^{22} - 11 x^{21} + 43 x^{20} - 45 x^{19} - 146 x^{18} + 402 x^{17} + 46 x^{16} - 1082 x^{15} + 512 x^{14} + 1700 x^{13} - 1234 x^{12} - 1826 x^{11} + 1419 x^{10} + 1403 x^{9} - 797 x^{8} - 807 x^{7} + 55 x^{6} + 331 x^{5} + 160 x^{4} - 51 x^{3} - 59 x^{2} - 14 x - 1$ $7\cdot 251\cdot 33893\cdot 1792166448977^{2}$ $C_2^{10}.(C_2\times S_{11})$ (as 22T53) trivial $205753246.579$
22.0.101...736.1 $x^{22} + 81 x^{20} + 2082 x^{18} + 19218 x^{16} + 53361 x^{14} + 19161 x^{12} - 39240 x^{10} - 1188 x^{8} + 6588 x^{6} - 11628 x^{4} + 648 x^{2} + 2916$ $-\,2^{32}\cdot 3^{28}\cdot 7^{4}\cdot 23^{4}\cdot 137^{16}$ $C_2\times A_{11}$ (as 22T46) trivial $89738500243100000000000000$
22.14.305...208.1 $x^{22} - 6 x^{21} - 96 x^{20} + 516 x^{19} + 3315 x^{18} - 15678 x^{17} - 58926 x^{16} + 239076 x^{15} + 605475 x^{14} - 2137974 x^{13} - 3792132 x^{12} + 12206088 x^{11} + 14763681 x^{10} - 46019430 x^{9} - 34917642 x^{8} + 112918896 x^{7} + 44592120 x^{6} - 169280496 x^{5} - 19547856 x^{4} + 127652544 x^{3} + 2781648 x^{2} - 33869664 x - 3859488$ $2^{32}\cdot 3^{29}\cdot 7^{4}\cdot 23^{4}\cdot 137^{16}$ $C_2\times A_{11}$ (as 22T46) trivial $852811169305000000000000000$
22.6.624...984.1 $x^{22} + 3 x^{20} - 36 x^{18} - 60 x^{16} + 213 x^{14} + 9 x^{12} - 114 x^{10} + 180 x^{8} - 108 x^{6} - 6 x^{4} + 36 x^{2} - 54$ $2^{43}\cdot 3^{29}\cdot 7^{4}\cdot 23^{4}\cdot 137^{16}$ $C_2^{11}.A_{11}$ (as 22T52) trivial $18112506929300000000000000000$
22.4.666...496.1 $x^{22} + 14 x^{20} + 49 x^{18} - 84 x^{16} - 873 x^{14} - 2112 x^{12} - 2265 x^{10} - 576 x^{8} + 1248 x^{6} + 1432 x^{4} + 632 x^{2} + 64$ $-\,2^{48}\cdot 3^{28}\cdot 7^{4}\cdot 23^{4}\cdot 137^{16}$ $C_2^{11}.A_{11}$ (as 22T52) trivial $13265885053200000000000000000$
22.4.287...640.1 $x^{22} + 30 x^{20} + 369 x^{18} + 2328 x^{16} + 6999 x^{14} - 828 x^{12} - 83625 x^{10} - 301428 x^{8} - 506304 x^{6} - 378264 x^{4} - 11592 x^{2} + 99360$ $-\,2^{45}\cdot 3^{29}\cdot 5\cdot 7^{4}\cdot 23^{5}\cdot 137^{16}$ $C_2^{11}.A_{11}$ (as 22T52) $[2, 2]$ $16360948114200000000000000000$
22.12.149...600.1 $x^{22} - 36 x^{20} + 549 x^{18} - 4638 x^{16} + 23559 x^{14} - 71010 x^{12} + 102675 x^{10} + 60498 x^{8} - 550584 x^{6} + 1014936 x^{4} - 865080 x^{2} + 291600$ $-\,2^{48}\cdot 3^{30}\cdot 5^{2}\cdot 7^{4}\cdot 23^{4}\cdot 137^{16}$ $C_2^{11}.A_{11}$ (as 22T52) trivial $1693786329280000000000000000000$
22.0.233...016.1 $x^{22} + 58 x^{20} + 1489 x^{18} + 22320 x^{16} + 216663 x^{14} + 1424964 x^{12} + 6438231 x^{10} + 19757580 x^{8} + 39484992 x^{6} + 46601624 x^{4} + 25144376 x^{2} + 898976$ $-\,2^{45}\cdot 3^{28}\cdot 7^{4}\cdot 13\cdot 23^{4}\cdot 137^{16}\cdot 2161$ $C_2^{11}.A_{11}$ (as 22T52) not computed
22.14.126...600.1 $x^{22} - 74 x^{20} + 2449 x^{18} - 47772 x^{16} + 608919 x^{14} - 5307720 x^{12} + 32127975 x^{10} - 134044248 x^{8} + 373194336 x^{6} - 645946216 x^{4} + 597000440 x^{2} - 195030400$ $2^{45}\cdot 3^{28}\cdot 5^{2}\cdot 7^{4}\cdot 23^{4}\cdot 59\cdot 137^{16}\cdot 1033$ $C_2^{11}.A_{11}$ (as 22T52) trivial $171825983862000000000000000000000$
41.1.157...441.1 $x^{41} - 3 x - 3$ $3^{40}\cdot 7\cdot 32261\cdot 253464984011\cdot 1238514877771\cdot 76247312349973837\cdot 239507603770962778439$ $S_{41}$ (as 41T10) not computed
41.1.160...816.1 $x^{41} - 3 x - 4$ $2^{80}\cdot 7\cdot 37\cdot 67\cdot 108499\cdot 543997\cdot 270310655161\cdot 312570029227603619\cdot 15379092216330540575461$ $S_{41}$ (as 41T10) not computed
41.3.549...359.1 $x^{41} - 5 x - 1$ $-\,3\cdot 7\cdot 115979\cdot 1907696227638017\cdot 11\!\cdots\!53$ $S_{41}$ (as 41T10) not computed
41.1.121...625.1 $x^{41} + x - 5$ $3\cdot 5^{40}\cdot 7\cdot 11287\cdot 706035413231\cdot 1169722373977559\cdot 67\!\cdots\!99$ $S_{41}$ (as 41T10) not computed
  displayed columns for results