Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
2.14.12.1 |
$14$ |
$x^{14} + 7 x^{13} + 28 x^{12} + 77 x^{11} + 161 x^{10} + 266 x^{9} + 357 x^{8} + 397 x^{7} + 371 x^{6} + 224 x^{5} + 21 x^{4} + 7 x^{3} + 70 x^{2} + 35 x + 7$ |
$2$ |
$7$ |
$2$ |
$12$ |
$(C_7:C_3) \times C_2$ (as 14T5) |
$6$ |
$7$ |
$[\ ]$ |
$[\ ]_{7}^{6}$ |
$t^{2} + t + 1$ |
$x^{7} + 2$ |
$[0]$ |
$[3]$ |
2.14.20.10 |
$14$ |
$x^{14} + 2 x^{13} + 2 x^{10} + 2 x^{7} + 6$ |
$2$ |
$14$ |
$1$ |
$20$ |
$(C_7:C_3) \times C_2$ (as 14T5) |
$3$ |
$7$ |
$[2]$ |
$[2]_{7}^{3}$ |
$t + 1$ |
$x^{14} + 2 x^{13} + 2 x^{10} + 2 x^{7} + 6$ |
$[7, 0]$ |
$[1, 3]$ |
2.14.20.8 |
$14$ |
$x^{14} + 2 x^{13} + 2 x^{10} + 2 x^{7} + 2$ |
$2$ |
$14$ |
$1$ |
$20$ |
$(C_7:C_3) \times C_2$ (as 14T5) |
$3$ |
$7$ |
$[2]$ |
$[2]_{7}^{3}$ |
$t + 1$ |
$x^{14} + 2 x^{13} + 2 x^{10} + 2 x^{7} + 2$ |
$[7, 0]$ |
$[1, 3]$ |
2.14.27.121 |
$14$ |
$x^{14} + 6 x^{12} + 4 x^{9} + 4 x^{7} + 4 x^{4} + 6$ |
$2$ |
$14$ |
$1$ |
$27$ |
$(C_7:C_3) \times C_2$ (as 14T5) |
$3$ |
$7$ |
$[3]$ |
$[3]_{7}^{3}$ |
$t + 1$ |
$x^{14} + 6 x^{12} + 4 x^{9} + 4 x^{7} + 4 x^{4} + 6$ |
$[14, 0]$ |
$[1, 3]$ |
2.14.27.13 |
$14$ |
$x^{14} + 4 x^{12} + 4 x^{11} + 4 x^{9} + 4 x^{8} + 4 x^{6} + 4 x^{4} + 6$ |
$2$ |
$14$ |
$1$ |
$27$ |
$(C_7:C_3) \times C_2$ (as 14T5) |
$3$ |
$7$ |
$[3]$ |
$[3]_{7}^{3}$ |
$t + 1$ |
$x^{14} + 4 x^{12} + 4 x^{11} + 4 x^{9} + 4 x^{8} + 4 x^{6} + 4 x^{4} + 6$ |
$[14, 0]$ |
$[1, 3]$ |
2.14.27.21 |
$14$ |
$x^{14} + 4 x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 14$ |
$2$ |
$14$ |
$1$ |
$27$ |
$(C_7:C_3) \times C_2$ (as 14T5) |
$3$ |
$7$ |
$[3]$ |
$[3]_{7}^{3}$ |
$t + 1$ |
$x^{14} + 4 x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 14$ |
$[14, 0]$ |
$[1, 3]$ |
2.14.27.213 |
$14$ |
$x^{14} + 4 x^{11} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{4} + 2$ |
$2$ |
$14$ |
$1$ |
$27$ |
$(C_7:C_3) \times C_2$ (as 14T5) |
$3$ |
$7$ |
$[3]$ |
$[3]_{7}^{3}$ |
$t + 1$ |
$x^{14} + 4 x^{11} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{4} + 2$ |
$[14, 0]$ |
$[1, 3]$ |