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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
13.13.0.1 $x^{13} + 12 x + 11$ $13$ $1$ $13$ $0$ $C_{13}$ (as 13T1) $[\ ]$ $[\ ]^{13}$ $t^{13} + 12 t + 11$ $x - 13$
13.13.13.1 $x^{13} + 13 x + 13$ $13$ $13$ $1$ $13$ $F_{13}$ (as 13T6) $[13/12]$ $[13/12]_{12}$ $t + 11$ $x^{13} + 13 x + 13$
13.13.13.2 $x^{13} + 39 x + 13$ $13$ $13$ $1$ $13$ $F_{13}$ (as 13T6) $[13/12]$ $[13/12]_{12}$ $t + 11$ $x^{13} + 39 x + 13$
13.13.13.3 $x^{13} + 52 x + 13$ $13$ $13$ $1$ $13$ $F_{13}$ (as 13T6) $[13/12]$ $[13/12]_{12}$ $t + 11$ $x^{13} + 52 x + 13$
13.13.13.4 $x^{13} + 117 x + 13$ $13$ $13$ $1$ $13$ $F_{13}$ (as 13T6) $[13/12]$ $[13/12]_{12}$ $t + 11$ $x^{13} + 117 x + 13$
13.13.13.5 $x^{13} + 130 x + 13$ $13$ $13$ $1$ $13$ $F_{13}$ (as 13T6) $[13/12]$ $[13/12]_{12}$ $t + 11$ $x^{13} + 130 x + 13$
13.13.13.6 $x^{13} + 156 x + 13$ $13$ $13$ $1$ $13$ $F_{13}$ (as 13T6) $[13/12]$ $[13/12]_{12}$ $t + 11$ $x^{13} + 156 x + 13$
13.13.13.7 $x^{13} + 26 x + 13$ $13$ $13$ $1$ $13$ $F_{13}$ (as 13T6) $[13/12]$ $[13/12]_{12}$ $t + 11$ $x^{13} + 26 x + 13$
13.13.13.8 $x^{13} + 65 x + 13$ $13$ $13$ $1$ $13$ $F_{13}$ (as 13T6) $[13/12]$ $[13/12]_{12}$ $t + 11$ $x^{13} + 65 x + 13$
13.13.13.9 $x^{13} + 78 x + 13$ $13$ $13$ $1$ $13$ $F_{13}$ (as 13T6) $[13/12]$ $[13/12]_{12}$ $t + 11$ $x^{13} + 78 x + 13$
13.13.13.10 $x^{13} + 91 x + 13$ $13$ $13$ $1$ $13$ $F_{13}$ (as 13T6) $[13/12]$ $[13/12]_{12}$ $t + 11$ $x^{13} + 91 x + 13$
13.13.13.11 $x^{13} + 104 x + 13$ $13$ $13$ $1$ $13$ $F_{13}$ (as 13T6) $[13/12]$ $[13/12]_{12}$ $t + 11$ $x^{13} + 104 x + 13$
13.13.13.12 $x^{13} + 143 x + 13$ $13$ $13$ $1$ $13$ $F_{13}$ (as 13T6) $[13/12]$ $[13/12]_{12}$ $t + 11$ $x^{13} + 143 x + 13$
13.13.14.1 $x^{13} + 26 x^{2} + 13$ $13$ $13$ $1$ $14$ $C_{13}:C_6$ (as 13T5) $[7/6]$ $[7/6]_{6}$ $t + 11$ $x^{13} + 26 x^{2} + 13$
13.13.14.2 $x^{13} + 65 x^{2} + 13$ $13$ $13$ $1$ $14$ $C_{13}:C_6$ (as 13T5) $[7/6]$ $[7/6]_{6}$ $t + 11$ $x^{13} + 65 x^{2} + 13$
13.13.14.3 $x^{13} + 78 x^{2} + 13$ $13$ $13$ $1$ $14$ $C_{13}:C_6$ (as 13T5) $[7/6]$ $[7/6]_{6}$ $t + 11$ $x^{13} + 78 x^{2} + 13$
13.13.14.4 $x^{13} + 91 x^{2} + 13$ $13$ $13$ $1$ $14$ $C_{13}:C_6$ (as 13T5) $[7/6]$ $[7/6]_{6}$ $t + 11$ $x^{13} + 91 x^{2} + 13$
13.13.14.5 $x^{13} + 104 x^{2} + 13$ $13$ $13$ $1$ $14$ $C_{13}:C_6$ (as 13T5) $[7/6]$ $[7/6]_{6}$ $t + 11$ $x^{13} + 104 x^{2} + 13$
13.13.14.6 $x^{13} + 143 x^{2} + 13$ $13$ $13$ $1$ $14$ $C_{13}:C_6$ (as 13T5) $[7/6]$ $[7/6]_{6}$ $t + 11$ $x^{13} + 143 x^{2} + 13$
13.13.14.7 $x^{13} + 13 x^{2} + 13$ $13$ $13$ $1$ $14$ $F_{13}$ (as 13T6) $[7/6]$ $[7/6]_{6}^{2}$ $t + 11$ $x^{13} + 13 x^{2} + 13$
13.13.14.8 $x^{13} + 39 x^{2} + 13$ $13$ $13$ $1$ $14$ $F_{13}$ (as 13T6) $[7/6]$ $[7/6]_{6}^{2}$ $t + 11$ $x^{13} + 39 x^{2} + 13$
13.13.14.9 $x^{13} + 52 x^{2} + 13$ $13$ $13$ $1$ $14$ $F_{13}$ (as 13T6) $[7/6]$ $[7/6]_{6}^{2}$ $t + 11$ $x^{13} + 52 x^{2} + 13$
13.13.14.10 $x^{13} + 117 x^{2} + 13$ $13$ $13$ $1$ $14$ $F_{13}$ (as 13T6) $[7/6]$ $[7/6]_{6}^{2}$ $t + 11$ $x^{13} + 117 x^{2} + 13$
13.13.14.11 $x^{13} + 130 x^{2} + 13$ $13$ $13$ $1$ $14$ $F_{13}$ (as 13T6) $[7/6]$ $[7/6]_{6}^{2}$ $t + 11$ $x^{13} + 130 x^{2} + 13$
13.13.14.12 $x^{13} + 156 x^{2} + 13$ $13$ $13$ $1$ $14$ $F_{13}$ (as 13T6) $[7/6]$ $[7/6]_{6}^{2}$ $t + 11$ $x^{13} + 156 x^{2} + 13$
13.13.15.1 $x^{13} + 52 x^{3} + 13$ $13$ $13$ $1$ $15$ $C_{13}:C_4$ (as 13T4) $[5/4]$ $[5/4]_{4}$ $t + 11$ $x^{13} + 52 x^{3} + 13$
13.13.15.2 $x^{13} + 117 x^{3} + 13$ $13$ $13$ $1$ $15$ $C_{13}:C_4$ (as 13T4) $[5/4]$ $[5/4]_{4}$ $t + 11$ $x^{13} + 117 x^{3} + 13$
13.13.15.3 $x^{13} + 13 x^{3} + 13$ $13$ $13$ $1$ $15$ $F_{13}$ (as 13T6) $[5/4]$ $[5/4]_{4}^{3}$ $t + 11$ $x^{13} + 13 x^{3} + 13$
13.13.15.4 $x^{13} + 39 x^{3} + 13$ $13$ $13$ $1$ $15$ $F_{13}$ (as 13T6) $[5/4]$ $[5/4]_{4}^{3}$ $t + 11$ $x^{13} + 39 x^{3} + 13$
13.13.15.5 $x^{13} + 130 x^{3} + 13$ $13$ $13$ $1$ $15$ $F_{13}$ (as 13T6) $[5/4]$ $[5/4]_{4}^{3}$ $t + 11$ $x^{13} + 130 x^{3} + 13$
13.13.15.6 $x^{13} + 156 x^{3} + 13$ $13$ $13$ $1$ $15$ $F_{13}$ (as 13T6) $[5/4]$ $[5/4]_{4}^{3}$ $t + 11$ $x^{13} + 156 x^{3} + 13$
13.13.15.7 $x^{13} + 78 x^{3} + 13$ $13$ $13$ $1$ $15$ $C_{13}:C_4$ (as 13T4) $[5/4]$ $[5/4]_{4}$ $t + 11$ $x^{13} + 78 x^{3} + 13$
13.13.15.8 $x^{13} + 91 x^{3} + 13$ $13$ $13$ $1$ $15$ $C_{13}:C_4$ (as 13T4) $[5/4]$ $[5/4]_{4}$ $t + 11$ $x^{13} + 91 x^{3} + 13$
13.13.15.9 $x^{13} + 26 x^{3} + 13$ $13$ $13$ $1$ $15$ $F_{13}$ (as 13T6) $[5/4]$ $[5/4]_{4}^{3}$ $t + 11$ $x^{13} + 26 x^{3} + 13$
13.13.15.10 $x^{13} + 65 x^{3} + 13$ $13$ $13$ $1$ $15$ $F_{13}$ (as 13T6) $[5/4]$ $[5/4]_{4}^{3}$ $t + 11$ $x^{13} + 65 x^{3} + 13$
13.13.15.11 $x^{13} + 104 x^{3} + 13$ $13$ $13$ $1$ $15$ $F_{13}$ (as 13T6) $[5/4]$ $[5/4]_{4}^{3}$ $t + 11$ $x^{13} + 104 x^{3} + 13$
13.13.15.12 $x^{13} + 143 x^{3} + 13$ $13$ $13$ $1$ $15$ $F_{13}$ (as 13T6) $[5/4]$ $[5/4]_{4}^{3}$ $t + 11$ $x^{13} + 143 x^{3} + 13$
13.13.16.1 $x^{13} + 52 x^{4} + 13$ $13$ $13$ $1$ $16$ $C_{13}:C_3$ (as 13T3) $[4/3]$ $[4/3]_{3}$ $t + 11$ $x^{13} + 52 x^{4} + 13$
13.13.16.2 $x^{13} + 130 x^{4} + 13$ $13$ $13$ $1$ $16$ $C_{13}:C_3$ (as 13T3) $[4/3]$ $[4/3]_{3}$ $t + 11$ $x^{13} + 130 x^{4} + 13$
13.13.16.3 $x^{13} + 156 x^{4} + 13$ $13$ $13$ $1$ $16$ $C_{13}:C_3$ (as 13T3) $[4/3]$ $[4/3]_{3}$ $t + 11$ $x^{13} + 156 x^{4} + 13$
13.13.16.4 $x^{13} + 13 x^{4} + 13$ $13$ $13$ $1$ $16$ $C_{13}:C_6$ (as 13T5) $[4/3]$ $[4/3]_{3}^{2}$ $t + 11$ $x^{13} + 13 x^{4} + 13$
13.13.16.5 $x^{13} + 39 x^{4} + 13$ $13$ $13$ $1$ $16$ $C_{13}:C_6$ (as 13T5) $[4/3]$ $[4/3]_{3}^{2}$ $t + 11$ $x^{13} + 39 x^{4} + 13$
13.13.16.6 $x^{13} + 117 x^{4} + 13$ $13$ $13$ $1$ $16$ $C_{13}:C_6$ (as 13T5) $[4/3]$ $[4/3]_{3}^{2}$ $t + 11$ $x^{13} + 117 x^{4} + 13$
13.13.16.7 $x^{13} + 26 x^{4} + 13$ $13$ $13$ $1$ $16$ $F_{13}$ (as 13T6) $[4/3]$ $[4/3]_{3}^{4}$ $t + 11$ $x^{13} + 26 x^{4} + 13$
13.13.16.8 $x^{13} + 65 x^{4} + 13$ $13$ $13$ $1$ $16$ $F_{13}$ (as 13T6) $[4/3]$ $[4/3]_{3}^{4}$ $t + 11$ $x^{13} + 65 x^{4} + 13$
13.13.16.9 $x^{13} + 78 x^{4} + 13$ $13$ $13$ $1$ $16$ $F_{13}$ (as 13T6) $[4/3]$ $[4/3]_{3}^{4}$ $t + 11$ $x^{13} + 78 x^{4} + 13$
13.13.16.10 $x^{13} + 91 x^{4} + 13$ $13$ $13$ $1$ $16$ $F_{13}$ (as 13T6) $[4/3]$ $[4/3]_{3}^{4}$ $t + 11$ $x^{13} + 91 x^{4} + 13$
13.13.16.11 $x^{13} + 104 x^{4} + 13$ $13$ $13$ $1$ $16$ $F_{13}$ (as 13T6) $[4/3]$ $[4/3]_{3}^{4}$ $t + 11$ $x^{13} + 104 x^{4} + 13$
13.13.16.12 $x^{13} + 143 x^{4} + 13$ $13$ $13$ $1$ $16$ $F_{13}$ (as 13T6) $[4/3]$ $[4/3]_{3}^{4}$ $t + 11$ $x^{13} + 143 x^{4} + 13$
13.13.17.1 $x^{13} + 26 x^{5} + 13$ $13$ $13$ $1$ $17$ $F_{13}$ (as 13T6) $[17/12]$ $[17/12]_{12}$ $t + 11$ $x^{13} + 26 x^{5} + 13$
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