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Properties

Label 3.1.15.22a
Base 3.1.1.0a1.1
Degree \(15\)
e \(15\)
f \(1\)
c \(22\)

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Defining polynomial

$x^{15} + 3 c_{12} x^{12} + 3 b_{11} x^{11} + 3 b_{10} x^{10} + 3 a_{8} x^{8} + 3$

Invariants

Residue field characteristic: $3$
Degree: $15$
Base field: $\Q_{3}$
Ramification index $e$: $15$
Residue field degree $f$: $1$
Discriminant exponent $c$: $22$
Artin slopes: $[\frac{9}{5}]$
Swan slopes: $[\frac{4}{5}]$
Means: $\langle\frac{8}{15}\rangle$
Rams: $(4)$
Field count: $36$ (complete)
Ambiguity: $3$
Mass: $18$
Absolute Mass: $18$

Diagrams

Varying

Indices of inseparability: $[8,0]$
Associated inertia: $[4,1]$ (show 27), $[4,2]$ (show 9)
Jump Set: undefined

Galois groups and Hidden Artin slopes

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Fields

Galois group Galois Artin Indices
Assoc. Inertia Jump Set Fields per packet
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Showing all 36

  displayed columns for results
Label Packet size Polynomial Galois group Galois degree $\#\Aut(K/\Q_p)$ Artin slope content Swan slope content Hidden Artin slopes Hidden Swan slopes Ind. of Insep. Assoc. Inertia Resid. Poly Jump Set
3.1.15.22a1.1 9 $x^{15} + 3 x^{8} + 3$ $C_3^4:F_5$ (as 15T41) $1620$ $3$ $[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{4}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{4}$ $[8, 0]$ $[4, 1]$ $z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 1$ undefined
3.1.15.22a1.2 18 $x^{15} + 3 x^{12} + 3 x^{8} + 3$ $C_3\wr F_5$ (as 15T56) $4860$ $3$ $[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{12}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{12}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{12}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{12}$ $[8, 0]$ $[4, 1]$ $z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 1$ undefined
3.1.15.22a1.3 18 $x^{15} + 6 x^{12} + 3 x^{8} + 3$ $C_3\wr F_5$ (as 15T56) $4860$ $3$ $[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{12}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{12}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{12}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{12}$ $[8, 0]$ $[4, 1]$ $z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 1$ undefined
3.1.15.22a1.4 9 $x^{15} + 3 x^{11} + 3 x^{8} + 3$ $C_3^4:F_5$ (as 15T41) $1620$ $3$ $[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{4}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{4}$ $[8, 0]$ $[4, 1]$ $z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 1$ undefined
3.1.15.22a1.5 18 $x^{15} + 3 x^{12} + 3 x^{11} + 3 x^{8} + 3$ $C_3\wr F_5$ (as 15T56) $4860$ $3$ $[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{12}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{12}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{12}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{12}$ $[8, 0]$ $[4, 1]$ $z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 1$ undefined
3.1.15.22a1.6 18 $x^{15} + 6 x^{12} + 3 x^{11} + 3 x^{8} + 3$ $C_3\wr F_5$ (as 15T56) $4860$ $3$ $[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{12}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{12}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{12}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{12}$ $[8, 0]$ $[4, 1]$ $z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 1$ undefined
3.1.15.22a1.7 9 $x^{15} + 6 x^{11} + 3 x^{8} + 3$ $C_3^4:F_5$ (as 15T41) $1620$ $3$ $[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{4}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{4}$ $[8, 0]$ $[4, 1]$ $z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 1$ undefined
3.1.15.22a1.8 18 $x^{15} + 3 x^{12} + 6 x^{11} + 3 x^{8} + 3$ $C_3\wr F_5$ (as 15T56) $4860$ $3$ $[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{12}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{12}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{12}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{12}$ $[8, 0]$ $[4, 1]$ $z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 1$ undefined
3.1.15.22a1.9 18 $x^{15} + 6 x^{12} + 6 x^{11} + 3 x^{8} + 3$ $C_3\wr F_5$ (as 15T56) $4860$ $3$ $[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{12}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{12}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{12}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{12}$ $[8, 0]$ $[4, 1]$ $z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 1$ undefined
3.1.15.22a1.10 9 $x^{15} + 3 x^{10} + 3 x^{8} + 3$ $C_3^4:F_5$ (as 15T41) $1620$ $3$ $[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{4}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{4}$ $[8, 0]$ $[4, 1]$ $z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 1$ undefined
3.1.15.22a1.11 18 $x^{15} + 3 x^{12} + 3 x^{10} + 3 x^{8} + 3$ $C_3\wr F_5$ (as 15T56) $4860$ $3$ $[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{12}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{12}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{12}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{12}$ $[8, 0]$ $[4, 1]$ $z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 1$ undefined
3.1.15.22a1.12 18 $x^{15} + 6 x^{12} + 3 x^{10} + 3 x^{8} + 3$ $C_3\wr F_5$ (as 15T56) $4860$ $3$ $[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{12}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{12}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{12}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{12}$ $[8, 0]$ $[4, 1]$ $z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 1$ undefined
3.1.15.22a1.13 9 $x^{15} + 3 x^{11} + 3 x^{10} + 3 x^{8} + 3$ $C_3^4:F_5$ (as 15T41) $1620$ $3$ $[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{4}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{4}$ $[8, 0]$ $[4, 1]$ $z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 1$ undefined
3.1.15.22a1.14 18 $x^{15} + 3 x^{12} + 3 x^{11} + 3 x^{10} + 3 x^{8} + 3$ $C_3\wr F_5$ (as 15T56) $4860$ $3$ $[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{12}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{12}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{12}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{12}$ $[8, 0]$ $[4, 1]$ $z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 1$ undefined
3.1.15.22a1.15 18 $x^{15} + 6 x^{12} + 3 x^{11} + 3 x^{10} + 3 x^{8} + 3$ $C_3\wr F_5$ (as 15T56) $4860$ $3$ $[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{12}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{12}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{12}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{12}$ $[8, 0]$ $[4, 1]$ $z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 1$ undefined
3.1.15.22a1.16 9 $x^{15} + 6 x^{11} + 3 x^{10} + 3 x^{8} + 3$ $C_3^4:F_5$ (as 15T41) $1620$ $3$ $[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{4}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{4}$ $[8, 0]$ $[4, 1]$ $z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 1$ undefined
3.1.15.22a1.17 18 $x^{15} + 3 x^{12} + 6 x^{11} + 3 x^{10} + 3 x^{8} + 3$ $C_3\wr F_5$ (as 15T56) $4860$ $3$ $[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{12}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{12}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{12}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{12}$ $[8, 0]$ $[4, 1]$ $z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 1$ undefined
3.1.15.22a1.18 18 $x^{15} + 6 x^{12} + 6 x^{11} + 3 x^{10} + 3 x^{8} + 3$ $C_3\wr F_5$ (as 15T56) $4860$ $3$ $[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{12}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{12}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{12}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{12}$ $[8, 0]$ $[4, 1]$ $z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 1$ undefined
3.1.15.22a1.19 9 $x^{15} + 6 x^{10} + 3 x^{8} + 3$ $C_3^4:F_5$ (as 15T41) $1620$ $3$ $[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{4}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{4}$ $[8, 0]$ $[4, 1]$ $z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 1$ undefined
3.1.15.22a1.20 18 $x^{15} + 3 x^{12} + 6 x^{10} + 3 x^{8} + 3$ $C_3\wr F_5$ (as 15T56) $4860$ $3$ $[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{12}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{12}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{12}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{12}$ $[8, 0]$ $[4, 1]$ $z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 1$ undefined
3.1.15.22a1.21 18 $x^{15} + 6 x^{12} + 6 x^{10} + 3 x^{8} + 3$ $C_3\wr F_5$ (as 15T56) $4860$ $3$ $[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{12}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{12}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{12}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{12}$ $[8, 0]$ $[4, 1]$ $z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 1$ undefined
3.1.15.22a1.22 9 $x^{15} + 3 x^{11} + 6 x^{10} + 3 x^{8} + 3$ $C_3^4:F_5$ (as 15T41) $1620$ $3$ $[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{4}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{4}$ $[8, 0]$ $[4, 1]$ $z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 1$ undefined
3.1.15.22a1.23 18 $x^{15} + 3 x^{12} + 3 x^{11} + 6 x^{10} + 3 x^{8} + 3$ $C_3\wr F_5$ (as 15T56) $4860$ $3$ $[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{12}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{12}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{12}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{12}$ $[8, 0]$ $[4, 1]$ $z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 1$ undefined
3.1.15.22a1.24 18 $x^{15} + 6 x^{12} + 3 x^{11} + 6 x^{10} + 3 x^{8} + 3$ $C_3\wr F_5$ (as 15T56) $4860$ $3$ $[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{12}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{12}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{12}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{12}$ $[8, 0]$ $[4, 1]$ $z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 1$ undefined
3.1.15.22a1.25 9 $x^{15} + 6 x^{11} + 6 x^{10} + 3 x^{8} + 3$ $C_3^4:F_5$ (as 15T41) $1620$ $3$ $[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{4}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{4}$ $[8, 0]$ $[4, 1]$ $z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 1$ undefined
3.1.15.22a1.26 18 $x^{15} + 3 x^{12} + 6 x^{11} + 6 x^{10} + 3 x^{8} + 3$ $C_3\wr F_5$ (as 15T56) $4860$ $3$ $[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{12}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{12}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{12}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{12}$ $[8, 0]$ $[4, 1]$ $z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 1$ undefined
3.1.15.22a1.27 18 $x^{15} + 6 x^{12} + 6 x^{11} + 6 x^{10} + 3 x^{8} + 3$ $C_3\wr F_5$ (as 15T56) $4860$ $3$ $[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{12}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{12}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{12}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{12}$ $[8, 0]$ $[4, 1]$ $z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 1$ undefined
3.1.15.22a2.1 9 $x^{15} + 6 x^{8} + 3$ $C_3^4:F_5$ (as 15T42) $1620$ $1$ $[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{4}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{4}$ $[8, 0]$ $[4, 2]$ $z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 2$ undefined
3.1.15.22a2.2 9 $x^{15} + 3 x^{11} + 6 x^{8} + 3$ $C_3^4:F_5$ (as 15T42) $1620$ $1$ $[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{4}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{4}$ $[8, 0]$ $[4, 2]$ $z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 2$ undefined
3.1.15.22a2.3 9 $x^{15} + 6 x^{11} + 6 x^{8} + 3$ $C_3^4:F_5$ (as 15T42) $1620$ $1$ $[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{4}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{4}$ $[8, 0]$ $[4, 2]$ $z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 2$ undefined
3.1.15.22a2.4 9 $x^{15} + 3 x^{10} + 6 x^{8} + 3$ $C_3^4:F_5$ (as 15T42) $1620$ $1$ $[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{4}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{4}$ $[8, 0]$ $[4, 2]$ $z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 2$ undefined
3.1.15.22a2.5 9 $x^{15} + 3 x^{11} + 3 x^{10} + 6 x^{8} + 3$ $C_3^4:F_5$ (as 15T42) $1620$ $1$ $[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{4}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{4}$ $[8, 0]$ $[4, 2]$ $z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 2$ undefined
3.1.15.22a2.6 9 $x^{15} + 6 x^{11} + 3 x^{10} + 6 x^{8} + 3$ $C_3^4:F_5$ (as 15T42) $1620$ $1$ $[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{4}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{4}$ $[8, 0]$ $[4, 2]$ $z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 2$ undefined
3.1.15.22a2.7 9 $x^{15} + 6 x^{10} + 6 x^{8} + 3$ $C_3^4:F_5$ (as 15T42) $1620$ $1$ $[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{4}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{4}$ $[8, 0]$ $[4, 2]$ $z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 2$ undefined
3.1.15.22a2.8 9 $x^{15} + 3 x^{11} + 6 x^{10} + 6 x^{8} + 3$ $C_3^4:F_5$ (as 15T42) $1620$ $1$ $[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{4}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{4}$ $[8, 0]$ $[4, 2]$ $z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 2$ undefined
3.1.15.22a2.9 9 $x^{15} + 6 x^{11} + 6 x^{10} + 6 x^{8} + 3$ $C_3^4:F_5$ (as 15T42) $1620$ $1$ $[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{4}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{4}$ $[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$ $[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{4}$ $[8, 0]$ $[4, 2]$ $z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 2$ undefined
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