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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
2.12.30.314 $x^{12} + 4 x^{10} + 4 x^{7} + 4 x^{4} + 8 x^{2} + 2$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{10} + 4 x^{7} + 4 x^{4} + 8 x^{2} + 2$
2.12.30.321 $x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 8 x^{2} + 14$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 8 x^{2} + 14$
2.12.30.322 $x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 8 x^{2} + 2$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 8 x^{2} + 2$
2.12.30.326 $x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{9} + 4 x^{7} + 4 x^{6} + 8 x^{2} + 6$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{9} + 4 x^{7} + 4 x^{6} + 8 x^{2} + 6$
2.12.30.329 $x^{12} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 8 x^{2} + 2$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 8 x^{2} + 2$
2.12.30.334 $x^{12} + 4 x^{9} + 4 x^{7} + 2$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{9} + 4 x^{7} + 2$
2.12.30.335 $x^{12} + 4 x^{10} + 4 x^{7} + 4 x^{4} + 6$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{10} + 4 x^{7} + 4 x^{4} + 6$
2.12.30.337 $x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 10$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 10$
2.12.30.341 $x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 10$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 10$
2.12.30.342 $x^{12} + 4 x^{9} + 4 x^{7} + 8 x^{2} + 2$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{9} + 4 x^{7} + 8 x^{2} + 2$
2.12.30.347 $x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{7} + 8 x^{2} + 2$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{7} + 8 x^{2} + 2$
2.12.30.352 $x^{12} + 4 x^{11} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 8 x^{2} + 10$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 8 x^{2} + 10$
2.12.30.354 $x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{7} + 14$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{7} + 14$
2.12.30.355 $x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 10$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 10$
2.12.30.370 $x^{12} + 4 x^{11} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 2$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 2$
2.12.30.372 $x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 14$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 14$
2.12.30.373 $x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 8 x^{2} + 6$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 8 x^{2} + 6$
2.12.30.374 $x^{12} + 4 x^{9} + 4 x^{7} + 10$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{9} + 4 x^{7} + 10$
2.12.30.375 $x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{7} + 4 x^{4} + 6$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{7} + 4 x^{4} + 6$
2.12.30.376 $x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{7} + 8 x^{2} + 6$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{7} + 8 x^{2} + 6$
2.12.30.380 $x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 10$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 10$
2.12.30.383 $x^{12} + 4 x^{11} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 8 x^{2} + 14$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 8 x^{2} + 14$
2.12.30.388 $x^{12} + 4 x^{10} + 4 x^{7} + 4 x^{6} + 8 x^{2} + 2$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{10} + 4 x^{7} + 4 x^{6} + 8 x^{2} + 2$
2.12.30.391 $x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 2$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 2$
2.12.30.394 $x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{8} + 4 x^{7} + 14$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{8} + 4 x^{7} + 14$
2.12.30.403 $x^{12} + 4 x^{10} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 8 x^{2} + 6$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{10} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 8 x^{2} + 6$
2.12.30.404 $x^{12} + 4 x^{10} + 4 x^{7} + 4 x^{4} + 2$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{10} + 4 x^{7} + 4 x^{4} + 2$
2.12.30.408 $x^{12} + 4 x^{11} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 8 x^{2} + 2$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 8 x^{2} + 2$
2.12.30.411 $x^{12} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 14$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 14$
2.12.30.416 $x^{12} + 4 x^{10} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 8 x^{2} + 2$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{10} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 8 x^{2} + 2$
2.12.30.418 $x^{12} + 4 x^{11} + 4 x^{7} + 4 x^{4} + 8 x^{2} + 2$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{7} + 4 x^{4} + 8 x^{2} + 2$
2.12.30.433 $x^{12} + 4 x^{9} + 4 x^{7} + 4 x^{4} + 6$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{9} + 4 x^{7} + 4 x^{4} + 6$
2.12.30.434 $x^{12} + 4 x^{8} + 4 x^{7} + 8 x^{2} + 14$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{8} + 4 x^{7} + 8 x^{2} + 14$
2.12.30.435 $x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{7} + 4 x^{6} + 10$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{7} + 4 x^{6} + 10$
2.12.30.436 $x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 8 x^{2} + 10$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 8 x^{2} + 10$
2.12.30.438 $x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 8 x^{2} + 14$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 8 x^{2} + 14$
2.12.30.441 $x^{12} + 4 x^{11} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 10$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 10$
2.12.30.444 $x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{7} + 4 x^{4} + 8 x^{2} + 2$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{7} + 4 x^{4} + 8 x^{2} + 2$
2.12.30.449 $x^{12} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 8 x^{2} + 2$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 8 x^{2} + 2$
2.12.30.453 $x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 8 x^{2} + 10$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 8 x^{2} + 10$
2.12.30.455 $x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 8 x^{2} + 14$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 8 x^{2} + 14$
2.12.30.456 $x^{12} + 4 x^{8} + 4 x^{7} + 6$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{8} + 4 x^{7} + 6$
2.12.30.459 $x^{12} + 4 x^{9} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 8 x^{2} + 10$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{9} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 8 x^{2} + 10$
2.12.30.460 $x^{12} + 4 x^{10} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 8 x^{2} + 14$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{10} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 8 x^{2} + 14$
2.12.30.473 $x^{12} + 4 x^{11} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 8 x^{2} + 10$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 8 x^{2} + 10$
2.12.30.477 $x^{12} + 4 x^{7} + 4 x^{4} + 8 x^{2} + 10$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{7} + 4 x^{4} + 8 x^{2} + 10$
2.12.30.482 $x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 8 x^{2} + 10$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 8 x^{2} + 10$
2.12.30.492 $x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{7} + 10$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{7} + 10$
2.12.30.503 $x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 8 x^{2} + 10$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 8 x^{2} + 10$
2.12.30.508 $x^{12} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{4} + 8 x^{2} + 6$ $2$ $12$ $1$ $30$ $C_2\wr S_4$ (as 12T223) $[3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{4} + 8 x^{2} + 6$
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