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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
3.15.16.2 $x^{15} + 3 x^{3} + 3 x^{2} + 3$ $3$ $15$ $1$ $16$ $C_3\wr F_5$ (as 15T56) $[6/5]$ $[6/5, 6/5, 6/5, 6/5]_{5}^{12}$ $t + 1$ $x^{15} + 3 x^{3} + 3 x^{2} + 3$
3.15.16.3 $x^{15} + 6 x^{3} + 3 x^{2} + 3$ $3$ $15$ $1$ $16$ $C_3\wr F_5$ (as 15T56) $[6/5]$ $[6/5, 6/5, 6/5, 6/5]_{5}^{12}$ $t + 1$ $x^{15} + 6 x^{3} + 3 x^{2} + 3$
3.15.18.1 $x^{15} + 3 x^{6} + 6 x^{5} + 6 x^{4} + 3 x^{3} + 3$ $3$ $15$ $1$ $18$ $C_3\wr F_5$ (as 15T56) $[7/5]$ $[7/5, 7/5, 7/5, 7/5]_{5}^{12}$ $t + 1$ $x^{15} + 3 x^{6} + 6 x^{5} + 6 x^{4} + 3 x^{3} + 3$
3.15.18.10 $x^{15} + 6 x^{6} + 6 x^{5} + 6 x^{4} + 3$ $3$ $15$ $1$ $18$ $C_3\wr F_5$ (as 15T56) $[7/5]$ $[7/5, 7/5, 7/5, 7/5]_{5}^{12}$ $t + 1$ $x^{15} + 6 x^{6} + 6 x^{5} + 6 x^{4} + 3$
3.15.18.11 $x^{15} + 3 x^{6} + 6 x^{5} + 6 x^{4} + 3$ $3$ $15$ $1$ $18$ $C_3\wr F_5$ (as 15T56) $[7/5]$ $[7/5, 7/5, 7/5, 7/5]_{5}^{12}$ $t + 1$ $x^{15} + 3 x^{6} + 6 x^{5} + 6 x^{4} + 3$
3.15.18.12 $x^{15} + 6 x^{6} + 3 x^{5} + 6 x^{4} + 3$ $3$ $15$ $1$ $18$ $C_3\wr F_5$ (as 15T56) $[7/5]$ $[7/5, 7/5, 7/5, 7/5]_{5}^{12}$ $t + 1$ $x^{15} + 6 x^{6} + 3 x^{5} + 6 x^{4} + 3$
3.15.18.3 $x^{15} + 6 x^{6} + 6 x^{4} + 3$ $3$ $15$ $1$ $18$ $C_3\wr F_5$ (as 15T56) $[7/5]$ $[7/5, 7/5, 7/5, 7/5]_{5}^{12}$ $t + 1$ $x^{15} + 6 x^{6} + 6 x^{4} + 3$
3.15.18.9 $x^{15} + 3 x^{6} + 3 x^{5} + 6 x^{4} + 3$ $3$ $15$ $1$ $18$ $C_3\wr F_5$ (as 15T56) $[7/5]$ $[7/5, 7/5, 7/5, 7/5]_{5}^{12}$ $t + 1$ $x^{15} + 3 x^{6} + 3 x^{5} + 6 x^{4} + 3$
3.15.22.10 $x^{15} + 6 x^{12} + 6 x^{11} + 3 x^{9} + 3 x^{8} + 3 x^{6} + 3 x^{3} + 3$ $3$ $15$ $1$ $22$ $C_3\wr F_5$ (as 15T56) $[9/5]$ $[9/5, 9/5, 9/5, 9/5]_{5}^{12}$ $t + 1$ $x^{15} + 6 x^{12} + 6 x^{11} + 3 x^{9} + 3 x^{8} + 3 x^{6} + 3 x^{3} + 3$
3.15.22.12 $x^{15} + 6 x^{12} + 3 x^{11} + 6 x^{10} + 3 x^{8} + 3$ $3$ $15$ $1$ $22$ $C_3\wr F_5$ (as 15T56) $[9/5]$ $[9/5, 9/5, 9/5, 9/5]_{5}^{12}$ $t + 1$ $x^{15} + 6 x^{12} + 3 x^{11} + 6 x^{10} + 3 x^{8} + 3$
3.15.22.13 $x^{15} + 6 x^{12} + 3 x^{8} + 3$ $3$ $15$ $1$ $22$ $C_3\wr F_5$ (as 15T56) $[9/5]$ $[9/5, 9/5, 9/5, 9/5]_{5}^{12}$ $t + 1$ $x^{15} + 6 x^{12} + 3 x^{8} + 3$
3.15.22.14 $x^{15} + 6 x^{12} + 6 x^{11} + 3 x^{8} + 3$ $3$ $15$ $1$ $22$ $C_3\wr F_5$ (as 15T56) $[9/5]$ $[9/5, 9/5, 9/5, 9/5]_{5}^{12}$ $t + 1$ $x^{15} + 6 x^{12} + 6 x^{11} + 3 x^{8} + 3$
3.15.22.18 $x^{15} + 6 x^{12} + 6 x^{11} + 6 x^{10} + 3 x^{9} + 3 x^{8} + 3$ $3$ $15$ $1$ $22$ $C_3\wr F_5$ (as 15T56) $[9/5]$ $[9/5, 9/5, 9/5, 9/5]_{5}^{12}$ $t + 1$ $x^{15} + 6 x^{12} + 6 x^{11} + 6 x^{10} + 3 x^{9} + 3 x^{8} + 3$
3.15.22.22 $x^{15} + 3 x^{12} + 3 x^{10} + 3 x^{8} + 3$ $3$ $15$ $1$ $22$ $C_3\wr F_5$ (as 15T56) $[9/5]$ $[9/5, 9/5, 9/5, 9/5]_{5}^{12}$ $t + 1$ $x^{15} + 3 x^{12} + 3 x^{10} + 3 x^{8} + 3$
3.15.22.23 $x^{15} + 3 x^{12} + 3 x^{8} + 3$ $3$ $15$ $1$ $22$ $C_3\wr F_5$ (as 15T56) $[9/5]$ $[9/5, 9/5, 9/5, 9/5]_{5}^{12}$ $t + 1$ $x^{15} + 3 x^{12} + 3 x^{8} + 3$
3.15.22.27 $x^{15} + 6 x^{12} + 6 x^{11} + 6 x^{10} + 3 x^{8} + 3$ $3$ $15$ $1$ $22$ $C_3\wr F_5$ (as 15T56) $[9/5]$ $[9/5, 9/5, 9/5, 9/5]_{5}^{12}$ $t + 1$ $x^{15} + 6 x^{12} + 6 x^{11} + 6 x^{10} + 3 x^{8} + 3$
3.15.22.29 $x^{15} + 3 x^{11} + 6 x^{9} + 3 x^{8} + 3 x^{6} + 3 x^{3} + 3$ $3$ $15$ $1$ $22$ $C_3\wr F_5$ (as 15T56) $[9/5]$ $[9/5, 9/5, 9/5, 9/5]_{5}^{12}$ $t + 1$ $x^{15} + 3 x^{11} + 6 x^{9} + 3 x^{8} + 3 x^{6} + 3 x^{3} + 3$
3.15.22.30 $x^{15} + 3 x^{12} + 3 x^{11} + 3 x^{9} + 3 x^{8} + 3$ $3$ $15$ $1$ $22$ $C_3\wr F_5$ (as 15T56) $[9/5]$ $[9/5, 9/5, 9/5, 9/5]_{5}^{12}$ $t + 1$ $x^{15} + 3 x^{12} + 3 x^{11} + 3 x^{9} + 3 x^{8} + 3$
3.15.22.31 $x^{15} + 3 x^{12} + 6 x^{11} + 3 x^{10} + 6 x^{9} + 3 x^{8} + 3$ $3$ $15$ $1$ $22$ $C_3\wr F_5$ (as 15T56) $[9/5]$ $[9/5, 9/5, 9/5, 9/5]_{5}^{12}$ $t + 1$ $x^{15} + 3 x^{12} + 6 x^{11} + 3 x^{10} + 6 x^{9} + 3 x^{8} + 3$
3.15.22.32 $x^{15} + 6 x^{12} + 3 x^{11} + 3 x^{10} + 3 x^{8} + 3$ $3$ $15$ $1$ $22$ $C_3\wr F_5$ (as 15T56) $[9/5]$ $[9/5, 9/5, 9/5, 9/5]_{5}^{12}$ $t + 1$ $x^{15} + 6 x^{12} + 3 x^{11} + 3 x^{10} + 3 x^{8} + 3$
3.15.22.34 $x^{15} + 6 x^{12} + 6 x^{11} + 3 x^{10} + 3 x^{8} + 3$ $3$ $15$ $1$ $22$ $C_3\wr F_5$ (as 15T56) $[9/5]$ $[9/5, 9/5, 9/5, 9/5]_{5}^{12}$ $t + 1$ $x^{15} + 6 x^{12} + 6 x^{11} + 3 x^{10} + 3 x^{8} + 3$
3.15.22.35 $x^{15} + 6 x^{12} + 6 x^{11} + 3 x^{10} + 3 x^{9} + 3 x^{8} + 3$ $3$ $15$ $1$ $22$ $C_3\wr F_5$ (as 15T56) $[9/5]$ $[9/5, 9/5, 9/5, 9/5]_{5}^{12}$ $t + 1$ $x^{15} + 6 x^{12} + 6 x^{11} + 3 x^{10} + 3 x^{9} + 3 x^{8} + 3$
3.15.22.36 $x^{15} + 3 x^{12} + 6 x^{10} + 3 x^{8} + 3$ $3$ $15$ $1$ $22$ $C_3\wr F_5$ (as 15T56) $[9/5]$ $[9/5, 9/5, 9/5, 9/5]_{5}^{12}$ $t + 1$ $x^{15} + 3 x^{12} + 6 x^{10} + 3 x^{8} + 3$
3.15.22.5 $x^{15} + 6 x^{10} + 3 x^{8} + 3 x^{6} + 6 x^{3} + 3$ $3$ $15$ $1$ $22$ $C_3\wr F_5$ (as 15T56) $[9/5]$ $[9/5, 9/5, 9/5, 9/5]_{5}^{12}$ $t + 1$ $x^{15} + 6 x^{10} + 3 x^{8} + 3 x^{6} + 6 x^{3} + 3$
3.15.22.6 $x^{15} + 3 x^{12} + 6 x^{11} + 6 x^{10} + 3 x^{8} + 3$ $3$ $15$ $1$ $22$ $C_3\wr F_5$ (as 15T56) $[9/5]$ $[9/5, 9/5, 9/5, 9/5]_{5}^{12}$ $t + 1$ $x^{15} + 3 x^{12} + 6 x^{11} + 6 x^{10} + 3 x^{8} + 3$
3.15.22.8 $x^{15} + 3 x^{12} + 6 x^{11} + 3 x^{10} + 3 x^{8} + 3$ $3$ $15$ $1$ $22$ $C_3\wr F_5$ (as 15T56) $[9/5]$ $[9/5, 9/5, 9/5, 9/5]_{5}^{12}$ $t + 1$ $x^{15} + 3 x^{12} + 6 x^{11} + 3 x^{10} + 3 x^{8} + 3$
3.15.24.1 $x^{15} + 6 x^{14} + 6 x^{13} + 6 x^{12} + 6 x^{10} + 3 x^{6} + 3 x^{3} + 12$ $3$ $15$ $1$ $24$ $C_3\wr F_5$ (as 15T56) $[2]$ $[9/5, 9/5, 9/5, 9/5, 2]_{5}^{4}$ $t + 1$ $x^{15} + 6 x^{14} + 6 x^{13} + 6 x^{12} + 6 x^{10} + 3 x^{6} + 3 x^{3} + 12$
3.15.24.100 $x^{15} + 3 x^{11} + 6 x^{10} + 3 x^{9} + 21$ $3$ $15$ $1$ $24$ $C_3\wr F_5$ (as 15T56) $[2]$ $[9/5, 9/5, 9/5, 9/5, 2]_{5}^{4}$ $t + 1$ $x^{15} + 3 x^{11} + 6 x^{10} + 3 x^{9} + 21$
3.15.24.101 $x^{15} + 6 x^{14} + 6 x^{13} + 3 x^{12} + 6 x^{11} + 6 x^{10} + 3$ $3$ $15$ $1$ $24$ $C_3\wr F_5$ (as 15T56) $[2]$ $[9/5, 9/5, 9/5, 9/5, 2]_{5}^{4}$ $t + 1$ $x^{15} + 6 x^{14} + 6 x^{13} + 3 x^{12} + 6 x^{11} + 6 x^{10} + 3$
3.15.24.102 $x^{15} + 6 x^{14} + 6 x^{13} + 3 x^{12} + 3 x^{11} + 6 x^{10} + 3 x^{6} + 6 x^{3} + 3$ $3$ $15$ $1$ $24$ $C_3\wr F_5$ (as 15T56) $[2]$ $[7/5, 7/5, 7/5, 7/5, 2]_{5}^{4}$ $t + 1$ $x^{15} + 6 x^{14} + 6 x^{13} + 3 x^{12} + 3 x^{11} + 6 x^{10} + 3 x^{6} + 6 x^{3} + 3$
3.15.24.103 $x^{15} + 3 x^{14} + 3 x^{11} + 6 x^{10} + 6 x^{9} + 3$ $3$ $15$ $1$ $24$ $C_3\wr F_5$ (as 15T56) $[2]$ $[9/5, 9/5, 9/5, 9/5, 2]_{5}^{4}$ $t + 1$ $x^{15} + 3 x^{14} + 3 x^{11} + 6 x^{10} + 6 x^{9} + 3$
3.15.24.104 $x^{15} + 6 x^{13} + 3 x^{12} + 6 x^{11} + 6 x^{10} + 3 x^{9} + 3$ $3$ $15$ $1$ $24$ $C_3\wr F_5$ (as 15T56) $[2]$ $[9/5, 9/5, 9/5, 9/5, 2]_{5}^{4}$ $t + 1$ $x^{15} + 6 x^{13} + 3 x^{12} + 6 x^{11} + 6 x^{10} + 3 x^{9} + 3$
3.15.24.105 $x^{15} + 3 x^{14} + 3 x^{12} + 6 x^{10} + 3 x^{9} + 3 x^{6} + 3 x^{3} + 12$ $3$ $15$ $1$ $24$ $C_3\wr F_5$ (as 15T56) $[2]$ $[9/5, 9/5, 9/5, 9/5, 2]_{5}^{4}$ $t + 1$ $x^{15} + 3 x^{14} + 3 x^{12} + 6 x^{10} + 3 x^{9} + 3 x^{6} + 3 x^{3} + 12$
3.15.24.106 $x^{15} + 6 x^{14} + 6 x^{13} + 6 x^{10} + 6 x^{9} + 12$ $3$ $15$ $1$ $24$ $C_3\wr F_5$ (as 15T56) $[2]$ $[7/5, 7/5, 7/5, 7/5, 2]_{5}^{4}$ $t + 1$ $x^{15} + 6 x^{14} + 6 x^{13} + 6 x^{10} + 6 x^{9} + 12$
3.15.24.107 $x^{15} + 3 x^{14} + 6 x^{13} + 6 x^{12} + 3 x^{11} + 6 x^{10} + 3 x^{9} + 21$ $3$ $15$ $1$ $24$ $C_3\wr F_5$ (as 15T56) $[2]$ $[9/5, 9/5, 9/5, 9/5, 2]_{5}^{4}$ $t + 1$ $x^{15} + 3 x^{14} + 6 x^{13} + 6 x^{12} + 3 x^{11} + 6 x^{10} + 3 x^{9} + 21$
3.15.24.108 $x^{15} + 6 x^{10} + 3 x^{9} + 3 x^{6} + 6 x^{3} + 12$ $3$ $15$ $1$ $24$ $C_3\wr F_5$ (as 15T56) $[2]$ $[9/5, 9/5, 9/5, 9/5, 2]_{5}^{4}$ $t + 1$ $x^{15} + 6 x^{10} + 3 x^{9} + 3 x^{6} + 6 x^{3} + 12$
3.15.24.11 $x^{15} + 3 x^{14} + 3 x^{12} + 3 x^{11} + 6 x^{10} + 3 x^{9} + 3 x^{6} + 6 x^{3} + 3$ $3$ $15$ $1$ $24$ $C_3\wr F_5$ (as 15T56) $[2]$ $[7/5, 7/5, 7/5, 7/5, 2]_{5}^{4}$ $t + 1$ $x^{15} + 3 x^{14} + 3 x^{12} + 3 x^{11} + 6 x^{10} + 3 x^{9} + 3 x^{6} + 6 x^{3} + 3$
3.15.24.12 $x^{15} + 3 x^{13} + 6 x^{12} + 6 x^{10} + 6 x^{9} + 3 x^{6} + 3 x^{3} + 3$ $3$ $15$ $1$ $24$ $C_3\wr F_5$ (as 15T56) $[2]$ $[9/5, 9/5, 9/5, 9/5, 2]_{5}^{4}$ $t + 1$ $x^{15} + 3 x^{13} + 6 x^{12} + 6 x^{10} + 6 x^{9} + 3 x^{6} + 3 x^{3} + 3$
3.15.24.13 $x^{15} + 6 x^{14} + 3 x^{13} + 3 x^{12} + 6 x^{10} + 12$ $3$ $15$ $1$ $24$ $C_3\wr F_5$ (as 15T56) $[2]$ $[7/5, 7/5, 7/5, 7/5, 2]_{5}^{4}$ $t + 1$ $x^{15} + 6 x^{14} + 3 x^{13} + 3 x^{12} + 6 x^{10} + 12$
3.15.24.14 $x^{15} + 6 x^{14} + 6 x^{13} + 6 x^{12} + 3 x^{11} + 6 x^{10} + 6 x^{9} + 3 x^{6} + 6 x^{3} + 21$ $3$ $15$ $1$ $24$ $C_3\wr F_5$ (as 15T56) $[2]$ $[7/5, 7/5, 7/5, 7/5, 2]_{5}^{4}$ $t + 1$ $x^{15} + 6 x^{14} + 6 x^{13} + 6 x^{12} + 3 x^{11} + 6 x^{10} + 6 x^{9} + 3 x^{6} + 6 x^{3} + 21$
3.15.24.15 $x^{15} + 6 x^{13} + 6 x^{12} + 6 x^{10} + 3 x^{6} + 6 x^{3} + 3$ $3$ $15$ $1$ $24$ $C_3\wr F_5$ (as 15T56) $[2]$ $[9/5, 9/5, 9/5, 9/5, 2]_{5}^{4}$ $t + 1$ $x^{15} + 6 x^{13} + 6 x^{12} + 6 x^{10} + 3 x^{6} + 6 x^{3} + 3$
3.15.24.16 $x^{15} + 6 x^{13} + 3 x^{12} + 3 x^{11} + 6 x^{10} + 6 x^{9} + 3$ $3$ $15$ $1$ $24$ $C_3\wr F_5$ (as 15T56) $[2]$ $[9/5, 9/5, 9/5, 9/5, 2]_{5}^{4}$ $t + 1$ $x^{15} + 6 x^{13} + 3 x^{12} + 3 x^{11} + 6 x^{10} + 6 x^{9} + 3$
3.15.24.20 $x^{15} + 3 x^{12} + 3 x^{11} + 6 x^{10} + 6 x^{9} + 3$ $3$ $15$ $1$ $24$ $C_3\wr F_5$ (as 15T56) $[2]$ $[9/5, 9/5, 9/5, 9/5, 2]_{5}^{4}$ $t + 1$ $x^{15} + 3 x^{12} + 3 x^{11} + 6 x^{10} + 6 x^{9} + 3$
3.15.24.23 $x^{15} + 6 x^{13} + 6 x^{12} + 3 x^{11} + 6 x^{10} + 6 x^{9} + 3 x^{6} + 3 x^{3} + 21$ $3$ $15$ $1$ $24$ $C_3\wr F_5$ (as 15T56) $[2]$ $[9/5, 9/5, 9/5, 9/5, 2]_{5}^{4}$ $t + 1$ $x^{15} + 6 x^{13} + 6 x^{12} + 3 x^{11} + 6 x^{10} + 6 x^{9} + 3 x^{6} + 3 x^{3} + 21$
3.15.24.24 $x^{15} + 6 x^{13} + 3 x^{12} + 3 x^{11} + 6 x^{10} + 3 x^{9} + 3 x^{6} + 3 x^{3} + 12$ $3$ $15$ $1$ $24$ $C_3\wr F_5$ (as 15T56) $[2]$ $[9/5, 9/5, 9/5, 9/5, 2]_{5}^{4}$ $t + 1$ $x^{15} + 6 x^{13} + 3 x^{12} + 3 x^{11} + 6 x^{10} + 3 x^{9} + 3 x^{6} + 3 x^{3} + 12$
3.15.24.27 $x^{15} + 6 x^{13} + 6 x^{12} + 6 x^{10} + 3$ $3$ $15$ $1$ $24$ $C_3\wr F_5$ (as 15T56) $[2]$ $[7/5, 7/5, 7/5, 7/5, 2]_{5}^{4}$ $t + 1$ $x^{15} + 6 x^{13} + 6 x^{12} + 6 x^{10} + 3$
3.15.24.29 $x^{15} + 3 x^{11} + 6 x^{10} + 3 x^{9} + 3 x^{6} + 3 x^{3} + 3$ $3$ $15$ $1$ $24$ $C_3\wr F_5$ (as 15T56) $[2]$ $[9/5, 9/5, 9/5, 9/5, 2]_{5}^{4}$ $t + 1$ $x^{15} + 3 x^{11} + 6 x^{10} + 3 x^{9} + 3 x^{6} + 3 x^{3} + 3$
3.15.24.3 $x^{15} + 3 x^{13} + 3 x^{12} + 6 x^{11} + 6 x^{10} + 3 x^{6} + 3 x^{3} + 12$ $3$ $15$ $1$ $24$ $C_3\wr F_5$ (as 15T56) $[2]$ $[7/5, 7/5, 7/5, 7/5, 2]_{5}^{4}$ $t + 1$ $x^{15} + 3 x^{13} + 3 x^{12} + 6 x^{11} + 6 x^{10} + 3 x^{6} + 3 x^{3} + 12$
3.15.24.30 $x^{15} + 6 x^{14} + 6 x^{13} + 3 x^{12} + 6 x^{11} + 6 x^{10} + 6 x^{9} + 3 x^{6} + 6 x^{3} + 12$ $3$ $15$ $1$ $24$ $C_3\wr F_5$ (as 15T56) $[2]$ $[9/5, 9/5, 9/5, 9/5, 2]_{5}^{4}$ $t + 1$ $x^{15} + 6 x^{14} + 6 x^{13} + 3 x^{12} + 6 x^{11} + 6 x^{10} + 6 x^{9} + 3 x^{6} + 6 x^{3} + 12$
3.15.24.31 $x^{15} + 3 x^{11} + 6 x^{10} + 12$ $3$ $15$ $1$ $24$ $C_3\wr F_5$ (as 15T56) $[2]$ $[9/5, 9/5, 9/5, 9/5, 2]_{5}^{4}$ $t + 1$ $x^{15} + 3 x^{11} + 6 x^{10} + 12$
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