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Degree Residue characteristic Galois group Galois unramified degree Assoc. Inertia
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Residue field degree Top slope Wild Visible Wild inertia subgroup
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Results (28 matches)

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Label Polynomial $p$ $e$ $f$ $c$ Galois group $u$ $t$ Visible slopes Slope content Unram. Ext. Eisen. Poly. Ind. of Insep. Assoc. Inertia
13.12.0.1 $x^{12} + x^{8} + 5 x^{7} + 8 x^{6} + 11 x^{5} + 3 x^{4} + x^{3} + x^{2} + 4 x + 2$ $13$ $1$ $12$ $0$ $C_{12}$ (as 12T1) $12$ $1$ $[\ ]$ $[\ ]^{12}$ $t^{12} + t^{8} + 5 t^{7} + 8 t^{6} + 11 t^{5} + 3 t^{4} + t^{3} + t^{2} + 4 t + 2$ $x - 13$ $[0]$ $[\ ]$
13.12.6.1 $x^{12} + 780 x^{11} + 253578 x^{10} + 43990720 x^{9} + 4297346257 x^{8} + 224493831662 x^{7} + 4938918346310 x^{6} + 2961720498866 x^{5} + 3005850529646 x^{4} + 51307643736852 x^{3} + 70292613843513 x^{2} + 65587287977710 x + 15475747398037$ $13$ $2$ $6$ $6$ $C_6\times C_2$ (as 12T2) $6$ $2$ $[\ ]$ $[\ ]_{2}^{6}$ $t^{6} + 10 t^{3} + 11 t^{2} + 11 t + 2$ $x^{2} + 130 x + 13$ $[0]$ $[1]$
13.12.6.2 $x^{12} - 21970 x^{6} + 314171 x^{4} - 4084223 x^{2} + 9653618$ $13$ $2$ $6$ $6$ $C_{12}$ (as 12T1) $6$ $2$ $[\ ]$ $[\ ]_{2}^{6}$ $t^{6} + 10 t^{3} + 11 t^{2} + 11 t + 2$ $x^{2} + 13 t$ $[0]$ $[1]$
13.12.8.1 $x^{12} + 9 x^{10} + 88 x^{9} + 33 x^{8} + 216 x^{7} - 1299 x^{6} - 78 x^{5} - 1797 x^{4} - 15494 x^{3} + 21687 x^{2} - 41586 x + 201846$ $13$ $3$ $4$ $8$ $C_{12}$ (as 12T1) $4$ $3$ $[\ ]$ $[\ ]_{3}^{4}$ $t^{4} + 3 t^{2} + 12 t + 2$ $x^{3} + 13$ $[0]$ $[1]$
13.12.8.2 $x^{12} + 507 x^{6} - 26364 x^{3} + 57122$ $13$ $3$ $4$ $8$ $C_{12}$ (as 12T1) $4$ $3$ $[\ ]$ $[\ ]_{3}^{4}$ $t^{4} + 3 t^{2} + 12 t + 2$ $x^{3} + 13 t$ $[0]$ $[1]$
13.12.8.3 $x^{12} - 78 x^{9} + 2197 x^{6} + 290004 x^{3} + 114244$ $13$ $3$ $4$ $8$ $C_{12}$ (as 12T1) $4$ $3$ $[\ ]$ $[\ ]_{3}^{4}$ $t^{4} + 3 t^{2} + 12 t + 2$ $x^{3} + 13 t^{2}$ $[0]$ $[1]$
13.12.9.1 $x^{12} - 52 x^{8} + 676 x^{4} + 265837$ $13$ $4$ $3$ $9$ $C_{12}$ (as 12T1) $3$ $4$ $[\ ]$ $[\ ]_{4}^{3}$ $t^{3} + 2 t + 11$ $x^{4} + 13 t^{2}$ $[0]$ $[1]$
13.12.9.2 $x^{12} + 8 x^{10} + 44 x^{9} + 63 x^{8} + 264 x^{7} + 550 x^{6} - 6336 x^{5} + 3843 x^{4} + 4532 x^{3} + 46454 x^{2} + 30668 x + 30982$ $13$ $4$ $3$ $9$ $C_{12}$ (as 12T1) $3$ $4$ $[\ ]$ $[\ ]_{4}^{3}$ $t^{3} + 2 t + 11$ $x^{4} + 13$ $[0]$ $[1]$
13.12.9.3 $x^{12} + 338 x^{4} - 24167$ $13$ $4$ $3$ $9$ $C_{12}$ (as 12T1) $3$ $4$ $[\ ]$ $[\ ]_{4}^{3}$ $t^{3} + 2 t + 11$ $x^{4} + 13 t$ $[0]$ $[1]$
13.12.9.4 $x^{12} + 78 x^{8} + 42926 x^{4} - 31085353$ $13$ $4$ $3$ $9$ $C_{12}$ (as 12T1) $3$ $4$ $[\ ]$ $[\ ]_{4}^{3}$ $t^{3} + 2 t + 11$ $x^{4} + 143 t + 26$ $[0]$ $[1]$
13.12.10.1 $x^{12} + 72 x^{11} + 2172 x^{10} + 35280 x^{9} + 328380 x^{8} + 1703232 x^{7} + 4282170 x^{6} + 3407400 x^{5} + 1340820 x^{4} + 712800 x^{3} + 3855192 x^{2} + 18082080 x + 35650393$ $13$ $6$ $2$ $10$ $C_6\times C_2$ (as 12T2) $2$ $6$ $[\ ]$ $[\ ]_{6}^{2}$ $t^{2} + 12 t + 2$ $x^{6} + 13$ $[0]$ $[1]$
13.12.10.2 $x^{12} + 130 x^{6} - 1521$ $13$ $6$ $2$ $10$ $C_6\times C_2$ (as 12T2) $2$ $6$ $[\ ]$ $[\ ]_{6}^{2}$ $t^{2} + 12 t + 2$ $x^{6} + 13 t + 143$ $[0]$ $[1]$
13.12.10.3 $x^{12} - 1508 x^{6} - 6084$ $13$ $6$ $2$ $10$ $C_6\times C_2$ (as 12T2) $2$ $6$ $[\ ]$ $[\ ]_{6}^{2}$ $t^{2} + 12 t + 2$ $x^{6} + 130 t + 26$ $[0]$ $[1]$
13.12.10.4 $x^{12} - 156 x^{6} + 338$ $13$ $6$ $2$ $10$ $C_{12}$ (as 12T1) $2$ $6$ $[\ ]$ $[\ ]_{6}^{2}$ $t^{2} + 12 t + 2$ $x^{6} + 13 t$ $[0]$ $[1]$
13.12.10.5 $x^{12} - 1586 x^{6} - 198575$ $13$ $6$ $2$ $10$ $C_{12}$ (as 12T1) $2$ $6$ $[\ ]$ $[\ ]_{6}^{2}$ $t^{2} + 12 t + 2$ $x^{6} + 156 t + 143$ $[0]$ $[1]$
13.12.10.6 $x^{12} - 1716 x^{6} - 91260$ $13$ $6$ $2$ $10$ $C_{12}$ (as 12T1) $2$ $6$ $[\ ]$ $[\ ]_{6}^{2}$ $t^{2} + 12 t + 2$ $x^{6} + 156 t + 78$ $[0]$ $[1]$
13.12.11.1 $x^{12} + 156$ $13$ $12$ $1$ $11$ $C_{12}$ (as 12T1) $1$ $12$ $[\ ]$ $[\ ]_{12}$ $t + 11$ $x^{12} + 156$ $[0]$ $[1]$
13.12.11.2 $x^{12} + 117$ $13$ $12$ $1$ $11$ $C_{12}$ (as 12T1) $1$ $12$ $[\ ]$ $[\ ]_{12}$ $t + 11$ $x^{12} + 117$ $[0]$ $[1]$
13.12.11.3 $x^{12} + 130$ $13$ $12$ $1$ $11$ $C_{12}$ (as 12T1) $1$ $12$ $[\ ]$ $[\ ]_{12}$ $t + 11$ $x^{12} + 130$ $[0]$ $[1]$
13.12.11.4 $x^{12} + 13$ $13$ $12$ $1$ $11$ $C_{12}$ (as 12T1) $1$ $12$ $[\ ]$ $[\ ]_{12}$ $t + 11$ $x^{12} + 13$ $[0]$ $[1]$
13.12.11.5 $x^{12} + 52$ $13$ $12$ $1$ $11$ $C_{12}$ (as 12T1) $1$ $12$ $[\ ]$ $[\ ]_{12}$ $t + 11$ $x^{12} + 52$ $[0]$ $[1]$
13.12.11.6 $x^{12} + 39$ $13$ $12$ $1$ $11$ $C_{12}$ (as 12T1) $1$ $12$ $[\ ]$ $[\ ]_{12}$ $t + 11$ $x^{12} + 39$ $[0]$ $[1]$
13.12.11.7 $x^{12} + 26$ $13$ $12$ $1$ $11$ $C_{12}$ (as 12T1) $1$ $12$ $[\ ]$ $[\ ]_{12}$ $t + 11$ $x^{12} + 26$ $[0]$ $[1]$
13.12.11.8 $x^{12} + 104$ $13$ $12$ $1$ $11$ $C_{12}$ (as 12T1) $1$ $12$ $[\ ]$ $[\ ]_{12}$ $t + 11$ $x^{12} + 104$ $[0]$ $[1]$
13.12.11.9 $x^{12} + 78$ $13$ $12$ $1$ $11$ $C_{12}$ (as 12T1) $1$ $12$ $[\ ]$ $[\ ]_{12}$ $t + 11$ $x^{12} + 78$ $[0]$ $[1]$
13.12.11.10 $x^{12} + 143$ $13$ $12$ $1$ $11$ $C_{12}$ (as 12T1) $1$ $12$ $[\ ]$ $[\ ]_{12}$ $t + 11$ $x^{12} + 143$ $[0]$ $[1]$
13.12.11.11 $x^{12} + 65$ $13$ $12$ $1$ $11$ $C_{12}$ (as 12T1) $1$ $12$ $[\ ]$ $[\ ]_{12}$ $t + 11$ $x^{12} + 65$ $[0]$ $[1]$
13.12.11.12 $x^{12} + 91$ $13$ $12$ $1$ $11$ $C_{12}$ (as 12T1) $1$ $12$ $[\ ]$ $[\ ]_{12}$ $t + 11$ $x^{12} + 91$ $[0]$ $[1]$
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