Learn more

Note: Search results may be incomplete. Given $p$-adic completions contain an unramified field and completions are only searched for ramified primes.

Refine search


Results (8 matches)

  displayed columns for results
Label Polynomial Discriminant Galois group Class group Regulator
18.6.319...816.1 $x^{18} - 54 x^{16} - 28 x^{15} + 1125 x^{14} + 924 x^{13} - 11914 x^{12} - 12348 x^{11} + 67638 x^{10} + 81736 x^{9} - 186120 x^{8} - 253200 x^{7} + 129961 x^{6} + 212508 x^{5} + 237480 x^{4} + 303776 x^{3} + 51984 x^{2} + 69312 x - 23104$ $2^{18}\cdot 3^{24}\cdot 19^{2}\cdot 103^{6}$ $C_3\wr A_5$ (as 18T722) trivial $678191205.275$
20.0.104...125.1 $x^{20} - 5 x^{18} + 5 x^{16} - 2 x^{15} + 20 x^{13} + 175 x^{12} + 160 x^{11} - 233 x^{10} - 300 x^{9} + 300 x^{7} + 50 x^{6} - 520 x^{5} + 1025 x^{4} - 1230 x^{3} + 850 x^{2} - 310 x + 47$ $5^{18}\cdot 11^{2}\cdot 19^{2}\cdot 229^{5}$ $D_5^4.(C_2\times S_4)$ (as 20T932) trivial $5588389.68294$
20.4.232...000.1 $x^{20} - 20 x^{18} + 170 x^{16} - 20 x^{15} - 800 x^{14} + 300 x^{13} + 2275 x^{12} - 1800 x^{11} - 3913 x^{10} + 5500 x^{9} + 3380 x^{8} - 9000 x^{7} + 545 x^{6} + 7549 x^{5} - 3725 x^{4} - 2745 x^{3} + 2175 x^{2} + 245 x - 464$ $2^{4}\cdot 3^{10}\cdot 5^{20}\cdot 19^{2}\cdot 61^{10}$ $C_5^4:((C_2^3\times C_4):A_4)$ (as 20T883) trivial $12144160861200$
20.6.259...000.1 $x^{20} - 1548 x^{18} - 12384 x^{17} + 894784 x^{16} + 14688064 x^{15} - 152102736 x^{14} - 5502895488 x^{13} - 35180693648 x^{12} + 384459484928 x^{11} + 8658828603904 x^{10} + 75356261618688 x^{9} + 394246710355456 x^{8} + 1372850751037440 x^{7} + 3312283253698560 x^{6} + 5623477221376000 x^{5} + 6706879612825600 x^{4} + 5506776211456000 x^{3} + 2966874832896000 x^{2} + 945079582720000 x + 135011368960000$ $-\,2^{20}\cdot 5^{8}\cdot 13^{4}\cdot 19^{2}\cdot 23^{4}\cdot 53^{4}\cdot 331^{5}\cdot 26459386451^{2}$ $A_5^4.C_2^3.S_4$ (as 20T1108) trivial $10584225761100000000000000$
21.9.136...489.1 $x^{21} - 7 x^{20} + 7 x^{19} + 55 x^{18} - 132 x^{17} - 112 x^{16} + 589 x^{15} - 188 x^{14} - 1078 x^{13} + 1042 x^{12} + 579 x^{11} - 1297 x^{10} + 411 x^{9} + 431 x^{8} - 127 x^{7} - 455 x^{6} - 126 x^{5} + 888 x^{4} - 460 x^{3} - 146 x^{2} + 127 x - 1$ $17^{10}\cdot 19^{2}\cdot 61^{2}\cdot 131^{6}$ $C_3^7.A_7$ (as 21T132) trivial $39718417.9458$
37.1.106...653.1 $x^{37} + x - 1$ $19\cdot 11323755688122007063\cdot 49\!\cdots\!49$ $S_{37}$ (as 37T11) trivial $232694775426930.7$
37.1.158...693.1 $x^{37} + x - 3$ $3^{36}\cdot 19\cdot 349\cdot 4501649\cdot 1182640248703\cdot 29\!\cdots\!69$ $S_{37}$ (as 37T11) not computed
37.1.498...968.1 $x^{37} + x - 4$ $2^{73}\cdot 19\cdot 311\cdot 20831443951883\cdot 42\!\cdots\!57$ $S_{37}$ (as 37T11) not computed
  displayed columns for results