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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 (48 matches)

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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
2.6.4.2 $x^{6} - 2 x^{3} + 4$ $2$ $3$ $2$ $4$ $S_3\times C_3$ (as 6T5) $[\ ]$ $[\ ]_{3}^{6}$ $t^{2} + t + 1$ $x^{3} + 2 t$
3.6.7.3 $x^{6} + 3 x^{3} + 6 x^{2} + 6$ $3$ $6$ $1$ $7$ $S_3\times C_3$ (as 6T5) $[3/2]$ $[3/2]_{2}^{3}$ $t + 1$ $x^{6} + 3 x^{3} + 6 x^{2} + 6$
3.6.7.6 $x^{6} + 3 x^{3} + 3 x^{2} + 3$ $3$ $6$ $1$ $7$ $S_3\times C_3$ (as 6T5) $[3/2]$ $[3/2]_{2}^{3}$ $t + 1$ $x^{6} + 3 x^{3} + 3 x^{2} + 3$
3.6.8.10 $x^{6} + 9 x^{4} + 42 x^{3} + 441$ $3$ $3$ $2$ $8$ $S_3\times C_3$ (as 6T5) $[2]$ $[2, 2]^{2}$ $t^{2} + 2 t + 2$ $x^{3} + \left(3 t + 3\right) x^{2} + 21$
3.6.8.7 $x^{6} + 6 x^{5} + 9 x^{4} + 6 x^{3} + 18 x^{2} + 90$ $3$ $3$ $2$ $8$ $S_3\times C_3$ (as 6T5) $[2]$ $[2]^{6}$ $t^{2} + 2 t + 2$ $x^{3} + 3 x^{2} + 9 t + 12$
3.6.8.8 $x^{6} + 9 x^{4} + 24 x^{3} + 144$ $3$ $3$ $2$ $8$ $S_3\times C_3$ (as 6T5) $[2]$ $[2, 2]^{2}$ $t^{2} + 2 t + 2$ $x^{3} + \left(3 t + 3\right) x^{2} + 12$
3.6.8.9 $x^{6} + 36 x^{4} + 6 x^{3} + 9$ $3$ $3$ $2$ $8$ $S_3\times C_3$ (as 6T5) $[2]$ $[2, 2]^{2}$ $t^{2} + 2 t + 2$ $x^{3} + \left(6 t + 6\right) x^{2} + 3$
3.6.9.13 $x^{6} + 3 x^{5} + 6 x^{4} + 21$ $3$ $6$ $1$ $9$ $S_3\times C_3$ (as 6T5) $[2]$ $[3/2, 2]_{2}$ $t + 1$ $x^{6} + 3 x^{5} + 6 x^{4} + 21$
3.6.9.14 $x^{6} + 3 x^{5} + 6 x^{4} + 12$ $3$ $6$ $1$ $9$ $S_3\times C_3$ (as 6T5) $[2]$ $[3/2, 2]_{2}$ $t + 1$ $x^{6} + 3 x^{5} + 6 x^{4} + 12$
3.6.9.15 $x^{6} + 6 x^{5} + 6 x^{4} + 3$ $3$ $6$ $1$ $9$ $S_3\times C_3$ (as 6T5) $[2]$ $[3/2, 2]_{2}$ $t + 1$ $x^{6} + 6 x^{5} + 6 x^{4} + 3$
3.6.9.5 $x^{6} + 3 x^{5} + 3 x^{4} + 6$ $3$ $6$ $1$ $9$ $S_3\times C_3$ (as 6T5) $[2]$ $[3/2, 2]_{2}$ $t + 1$ $x^{6} + 3 x^{5} + 3 x^{4} + 6$
3.6.9.6 $x^{6} + 6 x^{5} + 3 x^{4} + 24$ $3$ $6$ $1$ $9$ $S_3\times C_3$ (as 6T5) $[2]$ $[3/2, 2]_{2}$ $t + 1$ $x^{6} + 6 x^{5} + 3 x^{4} + 24$
3.6.9.7 $x^{6} + 3 x^{5} + 3 x^{4} + 15$ $3$ $6$ $1$ $9$ $S_3\times C_3$ (as 6T5) $[2]$ $[3/2, 2]_{2}$ $t + 1$ $x^{6} + 3 x^{5} + 3 x^{4} + 15$
3.6.11.10 $x^{6} + 9 x^{3} + 18 x^{2} + 21$ $3$ $6$ $1$ $11$ $S_3\times C_3$ (as 6T5) $[5/2]$ $[5/2]_{2}^{3}$ $t + 1$ $x^{6} + 9 x^{3} + 18 x^{2} + 21$
3.6.11.11 $x^{6} + 9 x^{3} + 9 x^{2} + 12$ $3$ $6$ $1$ $11$ $S_3\times C_3$ (as 6T5) $[5/2]$ $[5/2]_{2}^{3}$ $t + 1$ $x^{6} + 9 x^{3} + 9 x^{2} + 12$
3.6.11.12 $x^{6} + 9 x^{3} + 3$ $3$ $6$ $1$ $11$ $S_3\times C_3$ (as 6T5) $[5/2]$ $[5/2]_{2}^{3}$ $t + 1$ $x^{6} + 9 x^{3} + 3$
3.6.11.13 $x^{6} + 24 x^{3} + 9 x + 21$ $3$ $6$ $1$ $11$ $S_3\times C_3$ (as 6T5) $[5/2]$ $[2, 5/2]_{2}$ $t + 1$ $x^{6} + 24 x^{3} + 9 x + 21$
3.6.11.14 $x^{6} + 18 x^{2} + 18 x + 3$ $3$ $6$ $1$ $11$ $S_3\times C_3$ (as 6T5) $[5/2]$ $[2, 5/2]_{2}$ $t + 1$ $x^{6} + 18 x^{2} + 18 x + 3$
3.6.11.15 $x^{6} + 18 x + 3$ $3$ $6$ $1$ $11$ $S_3\times C_3$ (as 6T5) $[5/2]$ $[2, 5/2]_{2}$ $t + 1$ $x^{6} + 18 x + 3$
3.6.11.16 $x^{6} + 18 x^{2} + 18 x + 21$ $3$ $6$ $1$ $11$ $S_3\times C_3$ (as 6T5) $[5/2]$ $[2, 5/2]_{2}$ $t + 1$ $x^{6} + 18 x^{2} + 18 x + 21$
3.6.11.17 $x^{6} + 9 x^{3} + 18 x^{2} + 18 x + 21$ $3$ $6$ $1$ $11$ $S_3\times C_3$ (as 6T5) $[5/2]$ $[2, 5/2]_{2}$ $t + 1$ $x^{6} + 9 x^{3} + 18 x^{2} + 18 x + 21$
3.6.11.18 $x^{6} + 3 x^{3} + 18 x^{2} + 18 x + 12$ $3$ $6$ $1$ $11$ $S_3\times C_3$ (as 6T5) $[5/2]$ $[2, 5/2]_{2}$ $t + 1$ $x^{6} + 3 x^{3} + 18 x^{2} + 18 x + 12$
3.6.11.19 $x^{6} + 15 x^{3} + 9 x + 21$ $3$ $6$ $1$ $11$ $S_3\times C_3$ (as 6T5) $[5/2]$ $[2, 5/2]_{2}$ $t + 1$ $x^{6} + 15 x^{3} + 9 x + 21$
3.6.11.20 $x^{6} + 9 x^{2} + 9 x + 12$ $3$ $6$ $1$ $11$ $S_3\times C_3$ (as 6T5) $[5/2]$ $[2, 5/2]_{2}$ $t + 1$ $x^{6} + 9 x^{2} + 9 x + 12$
3.6.11.21 $x^{6} + 9 x^{3} + 9 x^{2} + 9 x + 12$ $3$ $6$ $1$ $11$ $S_3\times C_3$ (as 6T5) $[5/2]$ $[2, 5/2]_{2}$ $t + 1$ $x^{6} + 9 x^{3} + 9 x^{2} + 9 x + 12$
5.6.4.2 $x^{6} + 10 x^{3} - 25$ $5$ $3$ $2$ $4$ $S_3\times C_3$ (as 6T5) $[\ ]$ $[\ ]_{3}^{6}$ $t^{2} + 4 t + 2$ $x^{3} + 5 t + 15$
11.6.4.2 $x^{6} - 110 x^{3} - 16819$ $11$ $3$ $2$ $4$ $S_3\times C_3$ (as 6T5) $[\ ]$ $[\ ]_{3}^{6}$ $t^{2} + 7 t + 2$ $x^{3} + 44 t + 99$
17.6.4.2 $x^{6} + 204 x^{3} - 7225$ $17$ $3$ $2$ $4$ $S_3\times C_3$ (as 6T5) $[\ ]$ $[\ ]_{3}^{6}$ $t^{2} + 16 t + 3$ $x^{3} + 17 t + 238$
23.6.4.2 $x^{6} - 483 x^{3} + 2645$ $23$ $3$ $2$ $4$ $S_3\times C_3$ (as 6T5) $[\ ]$ $[\ ]_{3}^{6}$ $t^{2} + 21 t + 5$ $x^{3} + 23 t$
29.6.4.2 $x^{6} - 1914 x^{3} - 2069701$ $29$ $3$ $2$ $4$ $S_3\times C_3$ (as 6T5) $[\ ]$ $[\ ]_{3}^{6}$ $t^{2} + 24 t + 2$ $x^{3} + 145 t + 783$
41.6.4.2 $x^{6} - 1804 x^{3} - 4557191$ $41$ $3$ $2$ $4$ $S_3\times C_3$ (as 6T5) $[\ ]$ $[\ ]_{3}^{6}$ $t^{2} + 38 t + 6$ $x^{3} + 123 t + 1435$
47.6.4.2 $x^{6} - 2115 x^{3} + 11045$ $47$ $3$ $2$ $4$ $S_3\times C_3$ (as 6T5) $[\ ]$ $[\ ]_{3}^{6}$ $t^{2} + 45 t + 5$ $x^{3} + 47 t$
53.6.4.2 $x^{6} - 2597 x^{3} + 5618$ $53$ $3$ $2$ $4$ $S_3\times C_3$ (as 6T5) $[\ ]$ $[\ ]_{3}^{6}$ $t^{2} + 49 t + 2$ $x^{3} + 53 t$
59.6.4.2 $x^{6} + 3304 x^{3} - 191455$ $59$ $3$ $2$ $4$ $S_3\times C_3$ (as 6T5) $[\ ]$ $[\ ]_{3}^{6}$ $t^{2} + 58 t + 2$ $x^{3} + 59 t + 3363$
71.6.4.2 $x^{6} - 710 x^{3} - 23733028$ $71$ $3$ $2$ $4$ $S_3\times C_3$ (as 6T5) $[\ ]$ $[\ ]_{3}^{6}$ $t^{2} + 69 t + 7$ $x^{3} + 142 t + 4544$
83.6.4.2 $x^{6} + 6640 x^{3} - 544231$ $83$ $3$ $2$ $4$ $S_3\times C_3$ (as 6T5) $[\ ]$ $[\ ]_{3}^{6}$ $t^{2} + 82 t + 2$ $x^{3} + 83 t + 6723$
89.6.4.2 $x^{6} - 35778 x^{3} - 331264141$ $89$ $3$ $2$ $4$ $S_3\times C_3$ (as 6T5) $[\ ]$ $[\ ]_{3}^{6}$ $t^{2} + 82 t + 3$ $x^{3} + 623 t + 7654$
101.6.4.2 $x^{6} - 19190 x^{3} - 291534379$ $101$ $3$ $2$ $4$ $S_3\times C_3$ (as 6T5) $[\ ]$ $[\ ]_{3}^{6}$ $t^{2} + 97 t + 2$ $x^{3} + 404 t + 9999$
107.6.4.2 $x^{6} - 11021 x^{3} + 22898$ $107$ $3$ $2$ $4$ $S_3\times C_3$ (as 6T5) $[\ ]$ $[\ ]_{3}^{6}$ $t^{2} + 103 t + 2$ $x^{3} + 107 t$
113.6.4.2 $x^{6} - 11413 x^{3} + 38307$ $113$ $3$ $2$ $4$ $S_3\times C_3$ (as 6T5) $[\ ]$ $[\ ]_{3}^{6}$ $t^{2} + 101 t + 3$ $x^{3} + 113 t$
131.6.4.2 $x^{6} - 16637 x^{3} + 34322$ $131$ $3$ $2$ $4$ $S_3\times C_3$ (as 6T5) $[\ ]$ $[\ ]_{3}^{6}$ $t^{2} + 127 t + 2$ $x^{3} + 131 t$
137.6.4.2 $x^{6} - 70966 x^{3} - 1637782940$ $137$ $3$ $2$ $4$ $S_3\times C_3$ (as 6T5) $[\ ]$ $[\ ]_{3}^{6}$ $t^{2} + 131 t + 3$ $x^{3} + 822 t + 18358$
149.6.4.2 $x^{6} - 21605 x^{3} + 44402$ $149$ $3$ $2$ $4$ $S_3\times C_3$ (as 6T5) $[\ ]$ $[\ ]_{3}^{6}$ $t^{2} + 145 t + 2$ $x^{3} + 149 t$
167.6.4.2 $x^{6} + 26386 x^{3} - 17932627$ $167$ $3$ $2$ $4$ $S_3\times C_3$ (as 6T5) $[\ ]$ $[\ ]_{3}^{6}$ $t^{2} + 166 t + 5$ $x^{3} + 167 t + 27054$
173.6.4.2 $x^{6} - 57782 x^{3} - 2583561067$ $173$ $3$ $2$ $4$ $S_3\times C_3$ (as 6T5) $[\ ]$ $[\ ]_{3}^{6}$ $t^{2} + 169 t + 2$ $x^{3} + 692 t + 29583$
179.6.4.2 $x^{6} - 152150 x^{3} - 5821240921$ $179$ $3$ $2$ $4$ $S_3\times C_3$ (as 6T5) $[\ ]$ $[\ ]_{3}^{6}$ $t^{2} + 172 t + 2$ $x^{3} + 1253 t + 31683$
191.6.4.2 $x^{6} + 29414 x^{3} - 112252037$ $191$ $3$ $2$ $4$ $S_3\times C_3$ (as 6T5) $[\ ]$ $[\ ]_{3}^{6}$ $t^{2} + 190 t + 19$ $x^{3} + 191 t + 32852$
197.6.4.2 $x^{6} - 112290 x^{3} - 5787392125$ $197$ $3$ $2$ $4$ $S_3\times C_3$ (as 6T5) $[\ ]$ $[\ ]_{3}^{6}$ $t^{2} + 192 t + 2$ $x^{3} + 985 t + 38415$
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