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Label Polynomial $p$ $f$ $e$ $c$ Galois group $u$ $t$ Visible Artin slopes Visible Swan slopes Artin slope content Swan slope content Hidden Artin slopes Hidden Swan slopes Unram. Ext. Eisen. Poly. Ind. of Insep. Assoc. Inertia Resid. Poly Jump Set
5.1.15.21a1.2 $x^{15} + 5 x^{8} + 5 x^{7} + 5$ $5$ $1$ $15$ $21$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{19}{12}]$ $[\frac{7}{12}]$ $[\frac{5}{4}, \frac{19}{12}, \frac{19}{12}]_{12}^{2}$ $[\frac{1}{4},\frac{7}{12},\frac{7}{12}]_{12}^{2}$ $[\frac{5}{4},\frac{19}{12}]^{2}_{4}$ $[\frac{1}{4},\frac{7}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 5 x^{8} + 5 x^{7} + 5$ $[7, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 3$ undefined
5.1.15.21a1.3 $x^{15} + 10 x^{8} + 5 x^{7} + 5$ $5$ $1$ $15$ $21$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{19}{12}]$ $[\frac{7}{12}]$ $[\frac{5}{4}, \frac{19}{12}, \frac{19}{12}]_{12}^{2}$ $[\frac{1}{4},\frac{7}{12},\frac{7}{12}]_{12}^{2}$ $[\frac{5}{4},\frac{19}{12}]^{2}_{4}$ $[\frac{1}{4},\frac{7}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 10 x^{8} + 5 x^{7} + 5$ $[7, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 3$ undefined
5.1.15.21a1.4 $x^{15} + 15 x^{8} + 5 x^{7} + 5$ $5$ $1$ $15$ $21$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{19}{12}]$ $[\frac{7}{12}]$ $[\frac{5}{4}, \frac{19}{12}, \frac{19}{12}]_{12}^{2}$ $[\frac{1}{4},\frac{7}{12},\frac{7}{12}]_{12}^{2}$ $[\frac{5}{4},\frac{19}{12}]^{2}_{4}$ $[\frac{1}{4},\frac{7}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 15 x^{8} + 5 x^{7} + 5$ $[7, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 3$ undefined
5.1.15.21a1.5 $x^{15} + 20 x^{8} + 5 x^{7} + 5$ $5$ $1$ $15$ $21$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{19}{12}]$ $[\frac{7}{12}]$ $[\frac{5}{4}, \frac{19}{12}, \frac{19}{12}]_{12}^{2}$ $[\frac{1}{4},\frac{7}{12},\frac{7}{12}]_{12}^{2}$ $[\frac{5}{4},\frac{19}{12}]^{2}_{4}$ $[\frac{1}{4},\frac{7}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 20 x^{8} + 5 x^{7} + 5$ $[7, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 3$ undefined
5.1.15.21a1.7 $x^{15} + 5 x^{8} + 10 x^{7} + 5$ $5$ $1$ $15$ $21$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{19}{12}]$ $[\frac{7}{12}]$ $[\frac{5}{4}, \frac{19}{12}, \frac{19}{12}]_{12}^{2}$ $[\frac{1}{4},\frac{7}{12},\frac{7}{12}]_{12}^{2}$ $[\frac{5}{4},\frac{19}{12}]^{2}_{4}$ $[\frac{1}{4},\frac{7}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 5 x^{8} + 10 x^{7} + 5$ $[7, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 1$ undefined
5.1.15.21a1.8 $x^{15} + 10 x^{8} + 10 x^{7} + 5$ $5$ $1$ $15$ $21$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{19}{12}]$ $[\frac{7}{12}]$ $[\frac{5}{4}, \frac{19}{12}, \frac{19}{12}]_{12}^{2}$ $[\frac{1}{4},\frac{7}{12},\frac{7}{12}]_{12}^{2}$ $[\frac{5}{4},\frac{19}{12}]^{2}_{4}$ $[\frac{1}{4},\frac{7}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 10 x^{8} + 10 x^{7} + 5$ $[7, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 1$ undefined
5.1.15.21a1.9 $x^{15} + 15 x^{8} + 10 x^{7} + 5$ $5$ $1$ $15$ $21$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{19}{12}]$ $[\frac{7}{12}]$ $[\frac{5}{4}, \frac{19}{12}, \frac{19}{12}]_{12}^{2}$ $[\frac{1}{4},\frac{7}{12},\frac{7}{12}]_{12}^{2}$ $[\frac{5}{4},\frac{19}{12}]^{2}_{4}$ $[\frac{1}{4},\frac{7}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 15 x^{8} + 10 x^{7} + 5$ $[7, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 1$ undefined
5.1.15.21a1.10 $x^{15} + 20 x^{8} + 10 x^{7} + 5$ $5$ $1$ $15$ $21$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{19}{12}]$ $[\frac{7}{12}]$ $[\frac{5}{4}, \frac{19}{12}, \frac{19}{12}]_{12}^{2}$ $[\frac{1}{4},\frac{7}{12},\frac{7}{12}]_{12}^{2}$ $[\frac{5}{4},\frac{19}{12}]^{2}_{4}$ $[\frac{1}{4},\frac{7}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 20 x^{8} + 10 x^{7} + 5$ $[7, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 1$ undefined
5.1.15.21a1.12 $x^{15} + 5 x^{8} + 15 x^{7} + 5$ $5$ $1$ $15$ $21$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{19}{12}]$ $[\frac{7}{12}]$ $[\frac{5}{4}, \frac{19}{12}, \frac{19}{12}]_{12}^{2}$ $[\frac{1}{4},\frac{7}{12},\frac{7}{12}]_{12}^{2}$ $[\frac{5}{4},\frac{19}{12}]^{2}_{4}$ $[\frac{1}{4},\frac{7}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 5 x^{8} + 15 x^{7} + 5$ $[7, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 4$ undefined
5.1.15.21a1.13 $x^{15} + 10 x^{8} + 15 x^{7} + 5$ $5$ $1$ $15$ $21$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{19}{12}]$ $[\frac{7}{12}]$ $[\frac{5}{4}, \frac{19}{12}, \frac{19}{12}]_{12}^{2}$ $[\frac{1}{4},\frac{7}{12},\frac{7}{12}]_{12}^{2}$ $[\frac{5}{4},\frac{19}{12}]^{2}_{4}$ $[\frac{1}{4},\frac{7}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 10 x^{8} + 15 x^{7} + 5$ $[7, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 4$ undefined
5.1.15.21a1.14 $x^{15} + 15 x^{8} + 15 x^{7} + 5$ $5$ $1$ $15$ $21$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{19}{12}]$ $[\frac{7}{12}]$ $[\frac{5}{4}, \frac{19}{12}, \frac{19}{12}]_{12}^{2}$ $[\frac{1}{4},\frac{7}{12},\frac{7}{12}]_{12}^{2}$ $[\frac{5}{4},\frac{19}{12}]^{2}_{4}$ $[\frac{1}{4},\frac{7}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 15 x^{8} + 15 x^{7} + 5$ $[7, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 4$ undefined
5.1.15.21a1.15 $x^{15} + 20 x^{8} + 15 x^{7} + 5$ $5$ $1$ $15$ $21$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{19}{12}]$ $[\frac{7}{12}]$ $[\frac{5}{4}, \frac{19}{12}, \frac{19}{12}]_{12}^{2}$ $[\frac{1}{4},\frac{7}{12},\frac{7}{12}]_{12}^{2}$ $[\frac{5}{4},\frac{19}{12}]^{2}_{4}$ $[\frac{1}{4},\frac{7}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 20 x^{8} + 15 x^{7} + 5$ $[7, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 4$ undefined
5.1.15.21a1.17 $x^{15} + 5 x^{8} + 20 x^{7} + 5$ $5$ $1$ $15$ $21$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{19}{12}]$ $[\frac{7}{12}]$ $[\frac{5}{4}, \frac{19}{12}, \frac{19}{12}]_{12}^{2}$ $[\frac{1}{4},\frac{7}{12},\frac{7}{12}]_{12}^{2}$ $[\frac{5}{4},\frac{19}{12}]^{2}_{4}$ $[\frac{1}{4},\frac{7}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 5 x^{8} + 20 x^{7} + 5$ $[7, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 2$ undefined
5.1.15.21a1.18 $x^{15} + 10 x^{8} + 20 x^{7} + 5$ $5$ $1$ $15$ $21$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{19}{12}]$ $[\frac{7}{12}]$ $[\frac{5}{4}, \frac{19}{12}, \frac{19}{12}]_{12}^{2}$ $[\frac{1}{4},\frac{7}{12},\frac{7}{12}]_{12}^{2}$ $[\frac{5}{4},\frac{19}{12}]^{2}_{4}$ $[\frac{1}{4},\frac{7}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 10 x^{8} + 20 x^{7} + 5$ $[7, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 2$ undefined
5.1.15.21a1.19 $x^{15} + 15 x^{8} + 20 x^{7} + 5$ $5$ $1$ $15$ $21$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{19}{12}]$ $[\frac{7}{12}]$ $[\frac{5}{4}, \frac{19}{12}, \frac{19}{12}]_{12}^{2}$ $[\frac{1}{4},\frac{7}{12},\frac{7}{12}]_{12}^{2}$ $[\frac{5}{4},\frac{19}{12}]^{2}_{4}$ $[\frac{1}{4},\frac{7}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 15 x^{8} + 20 x^{7} + 5$ $[7, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 2$ undefined
5.1.15.21a1.20 $x^{15} + 20 x^{8} + 20 x^{7} + 5$ $5$ $1$ $15$ $21$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{19}{12}]$ $[\frac{7}{12}]$ $[\frac{5}{4}, \frac{19}{12}, \frac{19}{12}]_{12}^{2}$ $[\frac{1}{4},\frac{7}{12},\frac{7}{12}]_{12}^{2}$ $[\frac{5}{4},\frac{19}{12}]^{2}_{4}$ $[\frac{1}{4},\frac{7}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 20 x^{8} + 20 x^{7} + 5$ $[7, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 2$ undefined
5.1.15.23a1.2 $x^{15} + 5 x^{11} + 5 x^{9} + 5$ $5$ $1$ $15$ $23$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{7}{4}]$ $[\frac{3}{4}]$ $[\frac{13}{12}, \frac{13}{12}, \frac{7}{4}]_{12}^{2}$ $[\frac{1}{12},\frac{1}{12},\frac{3}{4}]_{12}^{2}$ $[\frac{13}{12},\frac{13}{12}]^{2}_{4}$ $[\frac{1}{12},\frac{1}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 5 x^{11} + 5 x^{9} + 5$ $[9, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 1$ undefined
5.1.15.23a1.3 $x^{15} + 10 x^{11} + 5 x^{9} + 5$ $5$ $1$ $15$ $23$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{7}{4}]$ $[\frac{3}{4}]$ $[\frac{13}{12}, \frac{13}{12}, \frac{7}{4}]_{12}^{2}$ $[\frac{1}{12},\frac{1}{12},\frac{3}{4}]_{12}^{2}$ $[\frac{13}{12},\frac{13}{12}]^{2}_{4}$ $[\frac{1}{12},\frac{1}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 10 x^{11} + 5 x^{9} + 5$ $[9, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 1$ undefined
5.1.15.23a1.4 $x^{15} + 15 x^{11} + 5 x^{9} + 5$ $5$ $1$ $15$ $23$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{7}{4}]$ $[\frac{3}{4}]$ $[\frac{13}{12}, \frac{13}{12}, \frac{7}{4}]_{12}^{2}$ $[\frac{1}{12},\frac{1}{12},\frac{3}{4}]_{12}^{2}$ $[\frac{13}{12},\frac{13}{12}]^{2}_{4}$ $[\frac{1}{12},\frac{1}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 15 x^{11} + 5 x^{9} + 5$ $[9, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 1$ undefined
5.1.15.23a1.5 $x^{15} + 20 x^{11} + 5 x^{9} + 5$ $5$ $1$ $15$ $23$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{7}{4}]$ $[\frac{3}{4}]$ $[\frac{13}{12}, \frac{13}{12}, \frac{7}{4}]_{12}^{2}$ $[\frac{1}{12},\frac{1}{12},\frac{3}{4}]_{12}^{2}$ $[\frac{13}{12},\frac{13}{12}]^{2}_{4}$ $[\frac{1}{12},\frac{1}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 20 x^{11} + 5 x^{9} + 5$ $[9, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 1$ undefined
5.1.15.23a1.7 $x^{15} + 5 x^{11} + 10 x^{9} + 5$ $5$ $1$ $15$ $23$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{7}{4}]$ $[\frac{3}{4}]$ $[\frac{13}{12}, \frac{13}{12}, \frac{7}{4}]_{12}^{2}$ $[\frac{1}{12},\frac{1}{12},\frac{3}{4}]_{12}^{2}$ $[\frac{13}{12},\frac{13}{12}]^{2}_{4}$ $[\frac{1}{12},\frac{1}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 5 x^{11} + 10 x^{9} + 5$ $[9, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 2$ undefined
5.1.15.23a1.8 $x^{15} + 10 x^{11} + 10 x^{9} + 5$ $5$ $1$ $15$ $23$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{7}{4}]$ $[\frac{3}{4}]$ $[\frac{13}{12}, \frac{13}{12}, \frac{7}{4}]_{12}^{2}$ $[\frac{1}{12},\frac{1}{12},\frac{3}{4}]_{12}^{2}$ $[\frac{13}{12},\frac{13}{12}]^{2}_{4}$ $[\frac{1}{12},\frac{1}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 10 x^{11} + 10 x^{9} + 5$ $[9, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 2$ undefined
5.1.15.23a1.9 $x^{15} + 15 x^{11} + 10 x^{9} + 5$ $5$ $1$ $15$ $23$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{7}{4}]$ $[\frac{3}{4}]$ $[\frac{13}{12}, \frac{13}{12}, \frac{7}{4}]_{12}^{2}$ $[\frac{1}{12},\frac{1}{12},\frac{3}{4}]_{12}^{2}$ $[\frac{13}{12},\frac{13}{12}]^{2}_{4}$ $[\frac{1}{12},\frac{1}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 15 x^{11} + 10 x^{9} + 5$ $[9, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 2$ undefined
5.1.15.23a1.10 $x^{15} + 20 x^{11} + 10 x^{9} + 5$ $5$ $1$ $15$ $23$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{7}{4}]$ $[\frac{3}{4}]$ $[\frac{13}{12}, \frac{13}{12}, \frac{7}{4}]_{12}^{2}$ $[\frac{1}{12},\frac{1}{12},\frac{3}{4}]_{12}^{2}$ $[\frac{13}{12},\frac{13}{12}]^{2}_{4}$ $[\frac{1}{12},\frac{1}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 20 x^{11} + 10 x^{9} + 5$ $[9, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 2$ undefined
5.1.15.23a1.12 $x^{15} + 5 x^{11} + 15 x^{9} + 5$ $5$ $1$ $15$ $23$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{7}{4}]$ $[\frac{3}{4}]$ $[\frac{13}{12}, \frac{13}{12}, \frac{7}{4}]_{12}^{2}$ $[\frac{1}{12},\frac{1}{12},\frac{3}{4}]_{12}^{2}$ $[\frac{13}{12},\frac{13}{12}]^{2}_{4}$ $[\frac{1}{12},\frac{1}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 5 x^{11} + 15 x^{9} + 5$ $[9, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 3$ undefined
5.1.15.23a1.13 $x^{15} + 10 x^{11} + 15 x^{9} + 5$ $5$ $1$ $15$ $23$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{7}{4}]$ $[\frac{3}{4}]$ $[\frac{13}{12}, \frac{13}{12}, \frac{7}{4}]_{12}^{2}$ $[\frac{1}{12},\frac{1}{12},\frac{3}{4}]_{12}^{2}$ $[\frac{13}{12},\frac{13}{12}]^{2}_{4}$ $[\frac{1}{12},\frac{1}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 10 x^{11} + 15 x^{9} + 5$ $[9, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 3$ undefined
5.1.15.23a1.14 $x^{15} + 15 x^{11} + 15 x^{9} + 5$ $5$ $1$ $15$ $23$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{7}{4}]$ $[\frac{3}{4}]$ $[\frac{13}{12}, \frac{13}{12}, \frac{7}{4}]_{12}^{2}$ $[\frac{1}{12},\frac{1}{12},\frac{3}{4}]_{12}^{2}$ $[\frac{13}{12},\frac{13}{12}]^{2}_{4}$ $[\frac{1}{12},\frac{1}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 15 x^{11} + 15 x^{9} + 5$ $[9, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 3$ undefined
5.1.15.23a1.15 $x^{15} + 20 x^{11} + 15 x^{9} + 5$ $5$ $1$ $15$ $23$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{7}{4}]$ $[\frac{3}{4}]$ $[\frac{13}{12}, \frac{13}{12}, \frac{7}{4}]_{12}^{2}$ $[\frac{1}{12},\frac{1}{12},\frac{3}{4}]_{12}^{2}$ $[\frac{13}{12},\frac{13}{12}]^{2}_{4}$ $[\frac{1}{12},\frac{1}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 20 x^{11} + 15 x^{9} + 5$ $[9, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 3$ undefined
5.1.15.23a1.17 $x^{15} + 5 x^{11} + 20 x^{9} + 5$ $5$ $1$ $15$ $23$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{7}{4}]$ $[\frac{3}{4}]$ $[\frac{13}{12}, \frac{13}{12}, \frac{7}{4}]_{12}^{2}$ $[\frac{1}{12},\frac{1}{12},\frac{3}{4}]_{12}^{2}$ $[\frac{13}{12},\frac{13}{12}]^{2}_{4}$ $[\frac{1}{12},\frac{1}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 5 x^{11} + 20 x^{9} + 5$ $[9, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 4$ undefined
5.1.15.23a1.18 $x^{15} + 10 x^{11} + 20 x^{9} + 5$ $5$ $1$ $15$ $23$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{7}{4}]$ $[\frac{3}{4}]$ $[\frac{13}{12}, \frac{13}{12}, \frac{7}{4}]_{12}^{2}$ $[\frac{1}{12},\frac{1}{12},\frac{3}{4}]_{12}^{2}$ $[\frac{13}{12},\frac{13}{12}]^{2}_{4}$ $[\frac{1}{12},\frac{1}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 10 x^{11} + 20 x^{9} + 5$ $[9, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 4$ undefined
5.1.15.23a1.19 $x^{15} + 15 x^{11} + 20 x^{9} + 5$ $5$ $1$ $15$ $23$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{7}{4}]$ $[\frac{3}{4}]$ $[\frac{13}{12}, \frac{13}{12}, \frac{7}{4}]_{12}^{2}$ $[\frac{1}{12},\frac{1}{12},\frac{3}{4}]_{12}^{2}$ $[\frac{13}{12},\frac{13}{12}]^{2}_{4}$ $[\frac{1}{12},\frac{1}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 15 x^{11} + 20 x^{9} + 5$ $[9, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 4$ undefined
5.1.15.23a1.20 $x^{15} + 20 x^{11} + 20 x^{9} + 5$ $5$ $1$ $15$ $23$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{7}{4}]$ $[\frac{3}{4}]$ $[\frac{13}{12}, \frac{13}{12}, \frac{7}{4}]_{12}^{2}$ $[\frac{1}{12},\frac{1}{12},\frac{3}{4}]_{12}^{2}$ $[\frac{13}{12},\frac{13}{12}]^{2}_{4}$ $[\frac{1}{12},\frac{1}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 20 x^{11} + 20 x^{9} + 5$ $[9, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 4$ undefined
5.1.15.25a1.2 $x^{15} + 5 x^{13} + 5 x^{11} + 5$ $5$ $1$ $15$ $25$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{23}{12}]$ $[\frac{11}{12}]$ $[\frac{5}{4}, \frac{23}{12}, \frac{23}{12}]_{12}^{2}$ $[\frac{1}{4},\frac{11}{12},\frac{11}{12}]_{12}^{2}$ $[\frac{5}{4},\frac{23}{12}]^{2}_{4}$ $[\frac{1}{4},\frac{11}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 5 x^{13} + 5 x^{11} + 5$ $[11, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 4$ undefined
5.1.15.25a1.3 $x^{15} + 10 x^{13} + 5 x^{11} + 5$ $5$ $1$ $15$ $25$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{23}{12}]$ $[\frac{11}{12}]$ $[\frac{5}{4}, \frac{23}{12}, \frac{23}{12}]_{12}^{2}$ $[\frac{1}{4},\frac{11}{12},\frac{11}{12}]_{12}^{2}$ $[\frac{5}{4},\frac{23}{12}]^{2}_{4}$ $[\frac{1}{4},\frac{11}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 10 x^{13} + 5 x^{11} + 5$ $[11, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 4$ undefined
5.1.15.25a1.4 $x^{15} + 15 x^{13} + 5 x^{11} + 5$ $5$ $1$ $15$ $25$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{23}{12}]$ $[\frac{11}{12}]$ $[\frac{5}{4}, \frac{23}{12}, \frac{23}{12}]_{12}^{2}$ $[\frac{1}{4},\frac{11}{12},\frac{11}{12}]_{12}^{2}$ $[\frac{5}{4},\frac{23}{12}]^{2}_{4}$ $[\frac{1}{4},\frac{11}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 15 x^{13} + 5 x^{11} + 5$ $[11, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 4$ undefined
5.1.15.25a1.5 $x^{15} + 20 x^{13} + 5 x^{11} + 5$ $5$ $1$ $15$ $25$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{23}{12}]$ $[\frac{11}{12}]$ $[\frac{5}{4}, \frac{23}{12}, \frac{23}{12}]_{12}^{2}$ $[\frac{1}{4},\frac{11}{12},\frac{11}{12}]_{12}^{2}$ $[\frac{5}{4},\frac{23}{12}]^{2}_{4}$ $[\frac{1}{4},\frac{11}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 20 x^{13} + 5 x^{11} + 5$ $[11, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 4$ undefined
5.1.15.25a1.7 $x^{15} + 5 x^{13} + 5 x^{12} + 5 x^{11} + 5$ $5$ $1$ $15$ $25$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{23}{12}]$ $[\frac{11}{12}]$ $[\frac{5}{4}, \frac{23}{12}, \frac{23}{12}]_{12}^{2}$ $[\frac{1}{4},\frac{11}{12},\frac{11}{12}]_{12}^{2}$ $[\frac{5}{4},\frac{23}{12}]^{2}_{4}$ $[\frac{1}{4},\frac{11}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 5 x^{13} + 5 x^{12} + 5 x^{11} + 5$ $[11, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 4$ undefined
5.1.15.25a1.8 $x^{15} + 10 x^{13} + 5 x^{12} + 5 x^{11} + 5$ $5$ $1$ $15$ $25$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{23}{12}]$ $[\frac{11}{12}]$ $[\frac{5}{4}, \frac{23}{12}, \frac{23}{12}]_{12}^{2}$ $[\frac{1}{4},\frac{11}{12},\frac{11}{12}]_{12}^{2}$ $[\frac{5}{4},\frac{23}{12}]^{2}_{4}$ $[\frac{1}{4},\frac{11}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 10 x^{13} + 5 x^{12} + 5 x^{11} + 5$ $[11, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 4$ undefined
5.1.15.25a1.9 $x^{15} + 15 x^{13} + 5 x^{12} + 5 x^{11} + 5$ $5$ $1$ $15$ $25$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{23}{12}]$ $[\frac{11}{12}]$ $[\frac{5}{4}, \frac{23}{12}, \frac{23}{12}]_{12}^{2}$ $[\frac{1}{4},\frac{11}{12},\frac{11}{12}]_{12}^{2}$ $[\frac{5}{4},\frac{23}{12}]^{2}_{4}$ $[\frac{1}{4},\frac{11}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 15 x^{13} + 5 x^{12} + 5 x^{11} + 5$ $[11, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 4$ undefined
5.1.15.25a1.10 $x^{15} + 20 x^{13} + 5 x^{12} + 5 x^{11} + 5$ $5$ $1$ $15$ $25$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{23}{12}]$ $[\frac{11}{12}]$ $[\frac{5}{4}, \frac{23}{12}, \frac{23}{12}]_{12}^{2}$ $[\frac{1}{4},\frac{11}{12},\frac{11}{12}]_{12}^{2}$ $[\frac{5}{4},\frac{23}{12}]^{2}_{4}$ $[\frac{1}{4},\frac{11}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 20 x^{13} + 5 x^{12} + 5 x^{11} + 5$ $[11, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 4$ undefined
5.1.15.25a1.12 $x^{15} + 5 x^{13} + 10 x^{12} + 5 x^{11} + 5$ $5$ $1$ $15$ $25$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{23}{12}]$ $[\frac{11}{12}]$ $[\frac{5}{4}, \frac{23}{12}, \frac{23}{12}]_{12}^{2}$ $[\frac{1}{4},\frac{11}{12},\frac{11}{12}]_{12}^{2}$ $[\frac{5}{4},\frac{23}{12}]^{2}_{4}$ $[\frac{1}{4},\frac{11}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 5 x^{13} + 10 x^{12} + 5 x^{11} + 5$ $[11, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 4$ undefined
5.1.15.25a1.13 $x^{15} + 10 x^{13} + 10 x^{12} + 5 x^{11} + 5$ $5$ $1$ $15$ $25$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{23}{12}]$ $[\frac{11}{12}]$ $[\frac{5}{4}, \frac{23}{12}, \frac{23}{12}]_{12}^{2}$ $[\frac{1}{4},\frac{11}{12},\frac{11}{12}]_{12}^{2}$ $[\frac{5}{4},\frac{23}{12}]^{2}_{4}$ $[\frac{1}{4},\frac{11}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 10 x^{13} + 10 x^{12} + 5 x^{11} + 5$ $[11, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 4$ undefined
5.1.15.25a1.14 $x^{15} + 15 x^{13} + 10 x^{12} + 5 x^{11} + 5$ $5$ $1$ $15$ $25$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{23}{12}]$ $[\frac{11}{12}]$ $[\frac{5}{4}, \frac{23}{12}, \frac{23}{12}]_{12}^{2}$ $[\frac{1}{4},\frac{11}{12},\frac{11}{12}]_{12}^{2}$ $[\frac{5}{4},\frac{23}{12}]^{2}_{4}$ $[\frac{1}{4},\frac{11}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 15 x^{13} + 10 x^{12} + 5 x^{11} + 5$ $[11, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 4$ undefined
5.1.15.25a1.15 $x^{15} + 20 x^{13} + 10 x^{12} + 5 x^{11} + 5$ $5$ $1$ $15$ $25$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{23}{12}]$ $[\frac{11}{12}]$ $[\frac{5}{4}, \frac{23}{12}, \frac{23}{12}]_{12}^{2}$ $[\frac{1}{4},\frac{11}{12},\frac{11}{12}]_{12}^{2}$ $[\frac{5}{4},\frac{23}{12}]^{2}_{4}$ $[\frac{1}{4},\frac{11}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 20 x^{13} + 10 x^{12} + 5 x^{11} + 5$ $[11, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 4$ undefined
5.1.15.25a1.17 $x^{15} + 5 x^{13} + 15 x^{12} + 5 x^{11} + 5$ $5$ $1$ $15$ $25$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{23}{12}]$ $[\frac{11}{12}]$ $[\frac{5}{4}, \frac{23}{12}, \frac{23}{12}]_{12}^{2}$ $[\frac{1}{4},\frac{11}{12},\frac{11}{12}]_{12}^{2}$ $[\frac{5}{4},\frac{23}{12}]^{2}_{4}$ $[\frac{1}{4},\frac{11}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 5 x^{13} + 15 x^{12} + 5 x^{11} + 5$ $[11, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 4$ undefined
5.1.15.25a1.18 $x^{15} + 10 x^{13} + 15 x^{12} + 5 x^{11} + 5$ $5$ $1$ $15$ $25$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{23}{12}]$ $[\frac{11}{12}]$ $[\frac{5}{4}, \frac{23}{12}, \frac{23}{12}]_{12}^{2}$ $[\frac{1}{4},\frac{11}{12},\frac{11}{12}]_{12}^{2}$ $[\frac{5}{4},\frac{23}{12}]^{2}_{4}$ $[\frac{1}{4},\frac{11}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 10 x^{13} + 15 x^{12} + 5 x^{11} + 5$ $[11, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 4$ undefined
5.1.15.25a1.19 $x^{15} + 15 x^{13} + 15 x^{12} + 5 x^{11} + 5$ $5$ $1$ $15$ $25$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{23}{12}]$ $[\frac{11}{12}]$ $[\frac{5}{4}, \frac{23}{12}, \frac{23}{12}]_{12}^{2}$ $[\frac{1}{4},\frac{11}{12},\frac{11}{12}]_{12}^{2}$ $[\frac{5}{4},\frac{23}{12}]^{2}_{4}$ $[\frac{1}{4},\frac{11}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 15 x^{13} + 15 x^{12} + 5 x^{11} + 5$ $[11, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 4$ undefined
5.1.15.25a1.20 $x^{15} + 20 x^{13} + 15 x^{12} + 5 x^{11} + 5$ $5$ $1$ $15$ $25$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{23}{12}]$ $[\frac{11}{12}]$ $[\frac{5}{4}, \frac{23}{12}, \frac{23}{12}]_{12}^{2}$ $[\frac{1}{4},\frac{11}{12},\frac{11}{12}]_{12}^{2}$ $[\frac{5}{4},\frac{23}{12}]^{2}_{4}$ $[\frac{1}{4},\frac{11}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 20 x^{13} + 15 x^{12} + 5 x^{11} + 5$ $[11, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 4$ undefined
5.1.15.25a1.22 $x^{15} + 5 x^{13} + 20 x^{12} + 5 x^{11} + 5$ $5$ $1$ $15$ $25$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{23}{12}]$ $[\frac{11}{12}]$ $[\frac{5}{4}, \frac{23}{12}, \frac{23}{12}]_{12}^{2}$ $[\frac{1}{4},\frac{11}{12},\frac{11}{12}]_{12}^{2}$ $[\frac{5}{4},\frac{23}{12}]^{2}_{4}$ $[\frac{1}{4},\frac{11}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 5 x^{13} + 20 x^{12} + 5 x^{11} + 5$ $[11, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 4$ undefined
5.1.15.25a1.23 $x^{15} + 10 x^{13} + 20 x^{12} + 5 x^{11} + 5$ $5$ $1$ $15$ $25$ $C_5^3:(C_4\times S_3)$ (as 15T49) $2$ $12$ $[\frac{23}{12}]$ $[\frac{11}{12}]$ $[\frac{5}{4}, \frac{23}{12}, \frac{23}{12}]_{12}^{2}$ $[\frac{1}{4},\frac{11}{12},\frac{11}{12}]_{12}^{2}$ $[\frac{5}{4},\frac{23}{12}]^{2}_{4}$ $[\frac{1}{4},\frac{11}{12}]^{2}_{4}$ $t + 3$ $x^{15} + 10 x^{13} + 20 x^{12} + 5 x^{11} + 5$ $[11, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z + 4$ undefined
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