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The results below are complete, since the LMFDB contains all p-adic fields of degree at most 23 and residue characteristic at most 199

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Degree $n$ Residue characteristic $p$ Discriminant exponent $c$ Galois group
Ramification index $e$ Residue field degree $f$ Galois tame degree $t$ Galois unram. degree $u$
Num. automorphisms Inertia subgroup Indices Assoc. Inertia Jump Set
Top Artin slope Galois Artin Visible Artin Wild inertia subgroup
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Results (48 matches)

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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
2.1.4.4a1.1 $x^{4} + 2 x + 2$ $2$ $1$ $4$ $4$ $S_4$ (as 4T5) $2$ $3$ $[\frac{4}{3}, \frac{4}{3}]$ $[\frac{1}{3},\frac{1}{3}]$ $[\frac{4}{3}, \frac{4}{3}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3}]_{3}^{2}$ $[\ ]^{2}_{3}$ $[\ ]^{2}_{3}$ $t + 1$ $x^{4} + 2 x + 2$ $[1, 1, 0]$ $[1]$ $z + 1$ $[1, 2, 5]$
2.1.4.6a1.1 $x^{4} + 2 x^{3} + 2$ $2$ $1$ $4$ $6$ $D_{4}$ (as 4T3) $2$ $1$ $[2, 2]$ $[1,1]$ $[2, 2]^{2}$ $[1,1]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $t + 1$ $x^{4} + 2 x^{3} + 2$ $[3, 3, 0]$ $[2]$ $z^3 + 1$ $[1, 3, 6]$
2.1.4.6a1.2 $x^{4} + 2 x^{3} + 6$ $2$ $1$ $4$ $6$ $D_{4}$ (as 4T3) $2$ $1$ $[2, 2]$ $[1,1]$ $[2, 2]^{2}$ $[1,1]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $t + 1$ $x^{4} + 2 x^{3} + 6$ $[3, 3, 0]$ $[2]$ $z^3 + 1$ $[1, 3, 8]$
2.1.4.6a2.1 $x^{4} + 2 x^{3} + 2 x^{2} + 2$ $2$ $1$ $4$ $6$ $A_4$ (as 4T4) $3$ $1$ $[2, 2]$ $[1,1]$ $[2, 2]^{3}$ $[1,1]^{3}$ $[\ ]^{3}$ $[\ ]^{3}$ $t + 1$ $x^{4} + 2 x^{3} + 2 x^{2} + 2$ $[3, 2, 0]$ $[3]$ $z^3 + z + 1$ $[1, 2, 7]$
2.1.4.8a1.1 $x^{4} + 4 x + 2$ $2$ $1$ $4$ $8$ $S_4$ (as 4T5) $2$ $3$ $[\frac{8}{3}, \frac{8}{3}]$ $[\frac{5}{3},\frac{5}{3}]$ $[\frac{8}{3}, \frac{8}{3}]_{3}^{2}$ $[\frac{5}{3},\frac{5}{3}]_{3}^{2}$ $[\ ]^{2}_{3}$ $[\ ]^{2}_{3}$ $t + 1$ $x^{4} + 4 x + 2$ $[5, 4, 0]$ $[1]$ $z + 1$ $[1, 3, 7]$
2.1.4.8a1.2 $x^{4} + 4 x^{2} + 4 x + 2$ $2$ $1$ $4$ $8$ $S_4$ (as 4T5) $2$ $3$ $[\frac{8}{3}, \frac{8}{3}]$ $[\frac{5}{3},\frac{5}{3}]$ $[\frac{8}{3}, \frac{8}{3}]_{3}^{2}$ $[\frac{5}{3},\frac{5}{3}]_{3}^{2}$ $[\ ]^{2}_{3}$ $[\ ]^{2}_{3}$ $t + 1$ $x^{4} + 4 x^{2} + 4 x + 2$ $[5, 4, 0]$ $[1]$ $z + 1$ $[1, 3, 7]$
2.1.4.8b1.1 $x^{4} + 2 x^{2} + 4 x + 2$ $2$ $1$ $4$ $8$ $C_2^2$ (as 4T2) $1$ $1$ $[2, 3]$ $[1,2]$ $[2, 3]$ $[1,2]$ $[\ ]$ $[\ ]$ $t + 1$ $x^{4} + 2 x^{2} + 4 x + 2$ $[5, 2, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 2, 4]$
2.1.4.8b1.2 $x^{4} + 2 x^{2} + 4 x + 10$ $2$ $1$ $4$ $8$ $C_2^2$ (as 4T2) $1$ $1$ $[2, 3]$ $[1,2]$ $[2, 3]$ $[1,2]$ $[\ ]$ $[\ ]$ $t + 1$ $x^{4} + 2 x^{2} + 4 x + 10$ $[5, 2, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 8, 12]$
2.1.4.8b1.3 $x^{4} + 4 x^{3} + 2 x^{2} + 4 x + 2$ $2$ $1$ $4$ $8$ $D_{4}$ (as 4T3) $2$ $1$ $[2, 3]$ $[1,2]$ $[2, 3]^{2}$ $[1,2]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $t + 1$ $x^{4} + 4 x^{3} + 2 x^{2} + 4 x + 2$ $[5, 2, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 7, 11]$
2.1.4.8b1.4 $x^{4} + 2 x^{2} + 4 x + 6$ $2$ $1$ $4$ $8$ $D_{4}$ (as 4T3) $2$ $1$ $[2, 3]$ $[1,2]$ $[2, 3]^{2}$ $[1,2]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $t + 1$ $x^{4} + 2 x^{2} + 4 x + 6$ $[5, 2, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 2, 8]$
2.1.4.8b1.5 $x^{4} + 4 x^{3} + 2 x^{2} + 4 x + 6$ $2$ $1$ $4$ $8$ $C_2^2$ (as 4T2) $1$ $1$ $[2, 3]$ $[1,2]$ $[2, 3]$ $[1,2]$ $[\ ]$ $[\ ]$ $t + 1$ $x^{4} + 4 x^{3} + 2 x^{2} + 4 x + 6$ $[5, 2, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 2, 8]$
2.1.4.8b1.6 $x^{4} + 4 x^{3} + 2 x^{2} + 4 x + 14$ $2$ $1$ $4$ $8$ $C_2^2$ (as 4T2) $1$ $1$ $[2, 3]$ $[1,2]$ $[2, 3]$ $[1,2]$ $[\ ]$ $[\ ]$ $t + 1$ $x^{4} + 4 x^{3} + 2 x^{2} + 4 x + 14$ $[5, 2, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 2, 8]$
2.1.4.9a1.1 $x^{4} + 2 x^{2} + 2$ $2$ $1$ $4$ $9$ $D_{4}$ (as 4T3) $1$ $1$ $[2, \frac{7}{2}]$ $[1,\frac{5}{2}]$ $[2, 3, \frac{7}{2}]$ $[1,2,\frac{5}{2}]$ $[3]$ $[2]$ $t + 1$ $x^{4} + 2 x^{2} + 2$ $[6, 2, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 5, 9]$
2.1.4.9a1.2 $x^{4} + 10 x^{2} + 2$ $2$ $1$ $4$ $9$ $D_{4}$ (as 4T3) $1$ $1$ $[2, \frac{7}{2}]$ $[1,\frac{5}{2}]$ $[2, 3, \frac{7}{2}]$ $[1,2,\frac{5}{2}]$ $[3]$ $[2]$ $t + 1$ $x^{4} + 10 x^{2} + 2$ $[6, 2, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 5, 9]$
2.1.4.9a1.3 $x^{4} + 4 x^{3} + 2 x^{2} + 2$ $2$ $1$ $4$ $9$ $D_{4}$ (as 4T3) $1$ $1$ $[2, \frac{7}{2}]$ $[1,\frac{5}{2}]$ $[2, 3, \frac{7}{2}]$ $[1,2,\frac{5}{2}]$ $[3]$ $[2]$ $t + 1$ $x^{4} + 4 x^{3} + 2 x^{2} + 2$ $[6, 2, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 5, 9]$
2.1.4.9a1.4 $x^{4} + 4 x^{3} + 10 x^{2} + 2$ $2$ $1$ $4$ $9$ $D_{4}$ (as 4T3) $1$ $1$ $[2, \frac{7}{2}]$ $[1,\frac{5}{2}]$ $[2, 3, \frac{7}{2}]$ $[1,2,\frac{5}{2}]$ $[3]$ $[2]$ $t + 1$ $x^{4} + 4 x^{3} + 10 x^{2} + 2$ $[6, 2, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 5, 9]$
2.1.4.9a1.5 $x^{4} + 2 x^{2} + 6$ $2$ $1$ $4$ $9$ $D_{4}$ (as 4T3) $1$ $1$ $[2, \frac{7}{2}]$ $[1,\frac{5}{2}]$ $[2, 3, \frac{7}{2}]$ $[1,2,\frac{5}{2}]$ $[3]$ $[2]$ $t + 1$ $x^{4} + 2 x^{2} + 6$ $[6, 2, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 2, 8]$
2.1.4.9a1.6 $x^{4} + 10 x^{2} + 6$ $2$ $1$ $4$ $9$ $D_{4}$ (as 4T3) $1$ $1$ $[2, \frac{7}{2}]$ $[1,\frac{5}{2}]$ $[2, 3, \frac{7}{2}]$ $[1,2,\frac{5}{2}]$ $[3]$ $[2]$ $t + 1$ $x^{4} + 10 x^{2} + 6$ $[6, 2, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 2, 8]$
2.1.4.9a1.7 $x^{4} + 2 x^{2} + 8 x + 6$ $2$ $1$ $4$ $9$ $D_{4}$ (as 4T3) $1$ $1$ $[2, \frac{7}{2}]$ $[1,\frac{5}{2}]$ $[2, 3, \frac{7}{2}]$ $[1,2,\frac{5}{2}]$ $[3]$ $[2]$ $t + 1$ $x^{4} + 2 x^{2} + 8 x + 6$ $[6, 2, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 2, 8]$
2.1.4.9a1.8 $x^{4} + 4 x^{3} + 2 x^{2} + 8 x + 6$ $2$ $1$ $4$ $9$ $D_{4}$ (as 4T3) $1$ $1$ $[2, \frac{7}{2}]$ $[1,\frac{5}{2}]$ $[2, 3, \frac{7}{2}]$ $[1,2,\frac{5}{2}]$ $[3]$ $[2]$ $t + 1$ $x^{4} + 4 x^{3} + 2 x^{2} + 8 x + 6$ $[6, 2, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 2, 8]$
2.1.4.10a1.1 $x^{4} + 4 x^{3} + 2$ $2$ $1$ $4$ $10$ $D_{4}$ (as 4T3) $1$ $1$ $[3, \frac{7}{2}]$ $[2,\frac{5}{2}]$ $[2, 3, \frac{7}{2}]$ $[1,2,\frac{5}{2}]$ $[2]$ $[1]$ $t + 1$ $x^{4} + 4 x^{3} + 2$ $[7, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.1.4.10a1.2 $x^{4} + 4 x^{3} + 8 x^{2} + 2$ $2$ $1$ $4$ $10$ $D_{4}$ (as 4T3) $1$ $1$ $[3, \frac{7}{2}]$ $[2,\frac{5}{2}]$ $[2, 3, \frac{7}{2}]$ $[1,2,\frac{5}{2}]$ $[2]$ $[1]$ $t + 1$ $x^{4} + 4 x^{3} + 8 x^{2} + 2$ $[7, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.1.4.10a1.3 $x^{4} + 4 x^{3} + 10$ $2$ $1$ $4$ $10$ $D_{4}$ (as 4T3) $1$ $1$ $[3, \frac{7}{2}]$ $[2,\frac{5}{2}]$ $[2, 3, \frac{7}{2}]$ $[1,2,\frac{5}{2}]$ $[2]$ $[1]$ $t + 1$ $x^{4} + 4 x^{3} + 10$ $[7, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.1.4.10a1.4 $x^{4} + 4 x^{3} + 8 x^{2} + 10$ $2$ $1$ $4$ $10$ $D_{4}$ (as 4T3) $1$ $1$ $[3, \frac{7}{2}]$ $[2,\frac{5}{2}]$ $[2, 3, \frac{7}{2}]$ $[1,2,\frac{5}{2}]$ $[2]$ $[1]$ $t + 1$ $x^{4} + 4 x^{3} + 8 x^{2} + 10$ $[7, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.1.4.10a1.5 $x^{4} + 4 x^{3} + 4 x^{2} + 2$ $2$ $1$ $4$ $10$ $D_{4}$ (as 4T3) $1$ $1$ $[3, \frac{7}{2}]$ $[2,\frac{5}{2}]$ $[2, 3, \frac{7}{2}]$ $[1,2,\frac{5}{2}]$ $[2]$ $[1]$ $t + 1$ $x^{4} + 4 x^{3} + 4 x^{2} + 2$ $[7, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.1.4.10a1.6 $x^{4} + 4 x^{3} + 12 x^{2} + 2$ $2$ $1$ $4$ $10$ $D_{4}$ (as 4T3) $1$ $1$ $[3, \frac{7}{2}]$ $[2,\frac{5}{2}]$ $[2, 3, \frac{7}{2}]$ $[1,2,\frac{5}{2}]$ $[2]$ $[1]$ $t + 1$ $x^{4} + 4 x^{3} + 12 x^{2} + 2$ $[7, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.1.4.10a1.7 $x^{4} + 4 x^{3} + 4 x^{2} + 10$ $2$ $1$ $4$ $10$ $D_{4}$ (as 4T3) $1$ $1$ $[3, \frac{7}{2}]$ $[2,\frac{5}{2}]$ $[2, 3, \frac{7}{2}]$ $[1,2,\frac{5}{2}]$ $[2]$ $[1]$ $t + 1$ $x^{4} + 4 x^{3} + 4 x^{2} + 10$ $[7, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.1.4.10a1.8 $x^{4} + 4 x^{3} + 12 x^{2} + 10$ $2$ $1$ $4$ $10$ $D_{4}$ (as 4T3) $1$ $1$ $[3, \frac{7}{2}]$ $[2,\frac{5}{2}]$ $[2, 3, \frac{7}{2}]$ $[1,2,\frac{5}{2}]$ $[2]$ $[1]$ $t + 1$ $x^{4} + 4 x^{3} + 12 x^{2} + 10$ $[7, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.1.4.11a1.1 $x^{4} + 2$ $2$ $1$ $4$ $11$ $D_{4}$ (as 4T3) $1$ $1$ $[3, 4]$ $[2,3]$ $[2, 3, 4]$ $[1,2,3]$ $[2]$ $[1]$ $t + 1$ $x^{4} + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.1.4.11a1.2 $x^{4} + 18$ $2$ $1$ $4$ $11$ $D_{4}$ (as 4T3) $1$ $1$ $[3, 4]$ $[2,3]$ $[2, 3, 4]$ $[1,2,3]$ $[2]$ $[1]$ $t + 1$ $x^{4} + 18$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.1.4.11a1.3 $x^{4} + 8 x + 2$ $2$ $1$ $4$ $11$ $D_{4}$ (as 4T3) $2$ $1$ $[3, 4]$ $[2,3]$ $[3, 4]^{2}$ $[2,3]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $t + 1$ $x^{4} + 8 x + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.1.4.11a1.4 $x^{4} + 8 x^{3} + 8 x + 2$ $2$ $1$ $4$ $11$ $D_{4}$ (as 4T3) $2$ $1$ $[3, 4]$ $[2,3]$ $[3, 4]^{2}$ $[2,3]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $t + 1$ $x^{4} + 8 x^{3} + 8 x + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.1.4.11a1.5 $x^{4} + 10$ $2$ $1$ $4$ $11$ $D_{4}$ (as 4T3) $1$ $1$ $[3, 4]$ $[2,3]$ $[2, 3, 4]$ $[1,2,3]$ $[2]$ $[1]$ $t + 1$ $x^{4} + 10$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.1.4.11a1.6 $x^{4} + 26$ $2$ $1$ $4$ $11$ $D_{4}$ (as 4T3) $1$ $1$ $[3, 4]$ $[2,3]$ $[2, 3, 4]$ $[1,2,3]$ $[2]$ $[1]$ $t + 1$ $x^{4} + 26$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.1.4.11a1.7 $x^{4} + 8 x + 10$ $2$ $1$ $4$ $11$ $D_{4}$ (as 4T3) $2$ $1$ $[3, 4]$ $[2,3]$ $[3, 4]^{2}$ $[2,3]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $t + 1$ $x^{4} + 8 x + 10$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.1.4.11a1.8 $x^{4} + 8 x^{3} + 8 x + 10$ $2$ $1$ $4$ $11$ $D_{4}$ (as 4T3) $2$ $1$ $[3, 4]$ $[2,3]$ $[3, 4]^{2}$ $[2,3]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $t + 1$ $x^{4} + 8 x^{3} + 8 x + 10$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.1.4.11a1.9 $x^{4} + 4 x^{2} + 2$ $2$ $1$ $4$ $11$ $C_4$ (as 4T1) $1$ $1$ $[3, 4]$ $[2,3]$ $[3, 4]$ $[2,3]$ $[\ ]$ $[\ ]$ $t + 1$ $x^{4} + 4 x^{2} + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.1.4.11a1.10 $x^{4} + 4 x^{2} + 18$ $2$ $1$ $4$ $11$ $C_4$ (as 4T1) $1$ $1$ $[3, 4]$ $[2,3]$ $[3, 4]$ $[2,3]$ $[\ ]$ $[\ ]$ $t + 1$ $x^{4} + 4 x^{2} + 18$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.1.4.11a1.11 $x^{4} + 8 x^{3} + 4 x^{2} + 2$ $2$ $1$ $4$ $11$ $C_4$ (as 4T1) $1$ $1$ $[3, 4]$ $[2,3]$ $[3, 4]$ $[2,3]$ $[\ ]$ $[\ ]$ $t + 1$ $x^{4} + 8 x^{3} + 4 x^{2} + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.1.4.11a1.12 $x^{4} + 8 x^{3} + 4 x^{2} + 18$ $2$ $1$ $4$ $11$ $C_4$ (as 4T1) $1$ $1$ $[3, 4]$ $[2,3]$ $[3, 4]$ $[2,3]$ $[\ ]$ $[\ ]$ $t + 1$ $x^{4} + 8 x^{3} + 4 x^{2} + 18$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.1.4.11a1.13 $x^{4} + 4 x^{2} + 8 x + 2$ $2$ $1$ $4$ $11$ $D_{4}$ (as 4T3) $1$ $1$ $[3, 4]$ $[2,3]$ $[2, 3, 4]$ $[1,2,3]$ $[2]$ $[1]$ $t + 1$ $x^{4} + 4 x^{2} + 8 x + 2$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.1.4.11a1.14 $x^{4} + 4 x^{2} + 8 x + 18$ $2$ $1$ $4$ $11$ $D_{4}$ (as 4T3) $1$ $1$ $[3, 4]$ $[2,3]$ $[2, 3, 4]$ $[1,2,3]$ $[2]$ $[1]$ $t + 1$ $x^{4} + 4 x^{2} + 8 x + 18$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.1.4.11a1.15 $x^{4} + 4 x^{2} + 10$ $2$ $1$ $4$ $11$ $C_4$ (as 4T1) $1$ $1$ $[3, 4]$ $[2,3]$ $[3, 4]$ $[2,3]$ $[\ ]$ $[\ ]$ $t + 1$ $x^{4} + 4 x^{2} + 10$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.1.4.11a1.16 $x^{4} + 4 x^{2} + 26$ $2$ $1$ $4$ $11$ $C_4$ (as 4T1) $1$ $1$ $[3, 4]$ $[2,3]$ $[3, 4]$ $[2,3]$ $[\ ]$ $[\ ]$ $t + 1$ $x^{4} + 4 x^{2} + 26$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.1.4.11a1.17 $x^{4} + 8 x^{3} + 4 x^{2} + 10$ $2$ $1$ $4$ $11$ $C_4$ (as 4T1) $1$ $1$ $[3, 4]$ $[2,3]$ $[3, 4]$ $[2,3]$ $[\ ]$ $[\ ]$ $t + 1$ $x^{4} + 8 x^{3} + 4 x^{2} + 10$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.1.4.11a1.18 $x^{4} + 8 x^{3} + 4 x^{2} + 26$ $2$ $1$ $4$ $11$ $C_4$ (as 4T1) $1$ $1$ $[3, 4]$ $[2,3]$ $[3, 4]$ $[2,3]$ $[\ ]$ $[\ ]$ $t + 1$ $x^{4} + 8 x^{3} + 4 x^{2} + 26$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.1.4.11a1.19 $x^{4} + 4 x^{2} + 8 x + 10$ $2$ $1$ $4$ $11$ $D_{4}$ (as 4T3) $1$ $1$ $[3, 4]$ $[2,3]$ $[2, 3, 4]$ $[1,2,3]$ $[2]$ $[1]$ $t + 1$ $x^{4} + 4 x^{2} + 8 x + 10$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
2.1.4.11a1.20 $x^{4} + 4 x^{2} + 8 x + 26$ $2$ $1$ $4$ $11$ $D_{4}$ (as 4T3) $1$ $1$ $[3, 4]$ $[2,3]$ $[2, 3, 4]$ $[1,2,3]$ $[2]$ $[1]$ $t + 1$ $x^{4} + 4 x^{2} + 8 x + 26$ $[8, 4, 0]$ $[1, 1]$ $z^2 + 1,z + 1$ $[1, 3, 7]$
  displayed columns for results