↑

Properties

Label 5.1.15.26a
Base 5.1.1.0a1.1
Degree \(15\)
e \(15\)
f \(1\)
c \(26\)

Related objects

Downloads

Learn more

Defining polynomial

$x^{15} + 5 b_{14} x^{14} + 5 b_{13} x^{13} + 5 a_{12} x^{12} + 25 c_{15} + 5$

Invariants

Residue field characteristic: $5$
Degree: $15$
Base field: $\Q_{5}$
Ramification index $e$: $15$
Residue field degree $f$: $1$
Discriminant exponent $c$: $26$
Artin slopes: $[2]$
Swan slopes: $[1]$
Means: $\langle\frac{4}{5}\rangle$
Rams: $(3)$
Field count: $200$ (complete)
Ambiguity: $5$
Mass: $100$
Absolute Mass: $100$

Diagrams

Varying

Indices of inseparability: $[12,0]$
Associated inertia: $[2,1]$ (show 125), $[2,2]$ (show 25), $[2,4]$ (show 50)
Jump Set: undefined

Galois groups and Hidden Artin slopes

Select desired size of Galois group.

Fields

Galois group Galois Artin Indices
Assoc. Inertia Jump Set Fields per packet
Sort order Select

Showing 1-50 of 200

Next   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
5.1.15.26a1.1 1 $x^{15} + 10 x^{12} + 5$ $C_{15} : C_4$ (as 15T6) $60$ $1$ $[2]_{3}^{4}$ $[1]_{3}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $[12, 0]$ $[2, 4]$ $z^{10} + 3 z^5 + 3,3 z^4 + 1$ undefined
5.1.15.26a1.2 4 $x^{15} + 5 x^{14} + 10 x^{12} + 5$ $C_5\wr C_3:C_4$ (as 15T37) $1500$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{4}$ $[\frac{1}{3},\frac{1}{3},1]_{3}^{4}$ $[\frac{4}{3},\frac{4}{3}]^{4}$ $[\frac{1}{3},\frac{1}{3}]^{4}$ $[12, 0]$ $[2, 4]$ $z^{10} + 3 z^5 + 3,3 z^4 + 1$ undefined
5.1.15.26a1.3 4 $x^{15} + 10 x^{14} + 10 x^{12} + 5$ $C_5\wr C_3:C_4$ (as 15T37) $1500$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{4}$ $[\frac{1}{3},\frac{1}{3},1]_{3}^{4}$ $[\frac{4}{3},\frac{4}{3}]^{4}$ $[\frac{1}{3},\frac{1}{3}]^{4}$ $[12, 0]$ $[2, 4]$ $z^{10} + 3 z^5 + 3,3 z^4 + 1$ undefined
5.1.15.26a1.4 4 $x^{15} + 15 x^{14} + 10 x^{12} + 5$ $C_5\wr C_3:C_4$ (as 15T37) $1500$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{4}$ $[\frac{1}{3},\frac{1}{3},1]_{3}^{4}$ $[\frac{4}{3},\frac{4}{3}]^{4}$ $[\frac{1}{3},\frac{1}{3}]^{4}$ $[12, 0]$ $[2, 4]$ $z^{10} + 3 z^5 + 3,3 z^4 + 1$ undefined
5.1.15.26a1.5 4 $x^{15} + 20 x^{14} + 10 x^{12} + 5$ $C_5\wr C_3:C_4$ (as 15T37) $1500$ $1$ $[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{4}$ $[\frac{1}{3},\frac{1}{3},1]_{3}^{4}$ $[\frac{4}{3},\frac{4}{3}]^{4}$ $[\frac{1}{3},\frac{1}{3}]^{4}$ $[12, 0]$ $[2, 4]$ $z^{10} + 3 z^5 + 3,3 z^4 + 1$ undefined
5.1.15.26a1.6 20 $x^{15} + 5 x^{13} + 10 x^{12} + 5$ $C_5\wr C_3:C_4$ (as 15T37) $1500$ $1$ $[\frac{5}{3}, \frac{5}{3}, 2]_{3}^{4}$ $[\frac{2}{3},\frac{2}{3},1]_{3}^{4}$ $[\frac{5}{3},\frac{5}{3}]^{4}$ $[\frac{2}{3},\frac{2}{3}]^{4}$ $[12, 0]$ $[2, 4]$ $z^{10} + 3 z^5 + 3,3 z^4 + 1$ undefined
5.1.15.26a1.7 20 $x^{15} + 5 x^{14} + 5 x^{13} + 10 x^{12} + 5$ $C_5\wr C_3:C_4$ (as 15T37) $1500$ $1$ $[\frac{5}{3}, \frac{5}{3}, 2]_{3}^{4}$ $[\frac{2}{3},\frac{2}{3},1]_{3}^{4}$ $[\frac{5}{3},\frac{5}{3}]^{4}$ $[\frac{2}{3},\frac{2}{3}]^{4}$ $[12, 0]$ $[2, 4]$ $z^{10} + 3 z^5 + 3,3 z^4 + 1$ undefined
5.1.15.26a1.8 20 $x^{15} + 10 x^{14} + 5 x^{13} + 10 x^{12} + 5$ $C_5\wr C_3:C_4$ (as 15T37) $1500$ $1$ $[\frac{5}{3}, \frac{5}{3}, 2]_{3}^{4}$ $[\frac{2}{3},\frac{2}{3},1]_{3}^{4}$ $[\frac{5}{3},\frac{5}{3}]^{4}$ $[\frac{2}{3},\frac{2}{3}]^{4}$ $[12, 0]$ $[2, 4]$ $z^{10} + 3 z^5 + 3,3 z^4 + 1$ undefined
5.1.15.26a1.9 20 $x^{15} + 15 x^{14} + 5 x^{13} + 10 x^{12} + 5$ $C_5\wr C_3:C_4$ (as 15T37) $1500$ $1$ $[\frac{5}{3}, \frac{5}{3}, 2]_{3}^{4}$ $[\frac{2}{3},\frac{2}{3},1]_{3}^{4}$ $[\frac{5}{3},\frac{5}{3}]^{4}$ $[\frac{2}{3},\frac{2}{3}]^{4}$ $[12, 0]$ $[2, 4]$ $z^{10} + 3 z^5 + 3,3 z^4 + 1$ undefined
5.1.15.26a1.10 20 $x^{15} + 20 x^{14} + 5 x^{13} + 10 x^{12} + 5$ $C_5\wr C_3:C_4$ (as 15T37) $1500$ $1$ $[\frac{5}{3}, \frac{5}{3}, 2]_{3}^{4}$ $[\frac{2}{3},\frac{2}{3},1]_{3}^{4}$ $[\frac{5}{3},\frac{5}{3}]^{4}$ $[\frac{2}{3},\frac{2}{3}]^{4}$ $[12, 0]$ $[2, 4]$ $z^{10} + 3 z^5 + 3,3 z^4 + 1$ undefined
5.1.15.26a1.11 20 $x^{15} + 10 x^{13} + 10 x^{12} + 5$ $C_5\wr C_3:C_4$ (as 15T37) $1500$ $1$ $[\frac{5}{3}, \frac{5}{3}, 2]_{3}^{4}$ $[\frac{2}{3},\frac{2}{3},1]_{3}^{4}$ $[\frac{5}{3},\frac{5}{3}]^{4}$ $[\frac{2}{3},\frac{2}{3}]^{4}$ $[12, 0]$ $[2, 4]$ $z^{10} + 3 z^5 + 3,3 z^4 + 1$ undefined
5.1.15.26a1.12 20 $x^{15} + 5 x^{14} + 10 x^{13} + 10 x^{12} + 5$ $C_5\wr C_3:C_4$ (as 15T37) $1500$ $1$ $[\frac{5}{3}, \frac{5}{3}, 2]_{3}^{4}$ $[\frac{2}{3},\frac{2}{3},1]_{3}^{4}$ $[\frac{5}{3},\frac{5}{3}]^{4}$ $[\frac{2}{3},\frac{2}{3}]^{4}$ $[12, 0]$ $[2, 4]$ $z^{10} + 3 z^5 + 3,3 z^4 + 1$ undefined
5.1.15.26a1.13 20 $x^{15} + 10 x^{14} + 10 x^{13} + 10 x^{12} + 5$ $C_5\wr C_3:C_4$ (as 15T37) $1500$ $1$ $[\frac{5}{3}, \frac{5}{3}, 2]_{3}^{4}$ $[\frac{2}{3},\frac{2}{3},1]_{3}^{4}$ $[\frac{5}{3},\frac{5}{3}]^{4}$ $[\frac{2}{3},\frac{2}{3}]^{4}$ $[12, 0]$ $[2, 4]$ $z^{10} + 3 z^5 + 3,3 z^4 + 1$ undefined
5.1.15.26a1.14 20 $x^{15} + 15 x^{14} + 10 x^{13} + 10 x^{12} + 5$ $C_5\wr C_3:C_4$ (as 15T37) $1500$ $1$ $[\frac{5}{3}, \frac{5}{3}, 2]_{3}^{4}$ $[\frac{2}{3},\frac{2}{3},1]_{3}^{4}$ $[\frac{5}{3},\frac{5}{3}]^{4}$ $[\frac{2}{3},\frac{2}{3}]^{4}$ $[12, 0]$ $[2, 4]$ $z^{10} + 3 z^5 + 3,3 z^4 + 1$ undefined
5.1.15.26a1.15 20 $x^{15} + 20 x^{14} + 10 x^{13} + 10 x^{12} + 5$ $C_5\wr C_3:C_4$ (as 15T37) $1500$ $1$ $[\frac{5}{3}, \frac{5}{3}, 2]_{3}^{4}$ $[\frac{2}{3},\frac{2}{3},1]_{3}^{4}$ $[\frac{5}{3},\frac{5}{3}]^{4}$ $[\frac{2}{3},\frac{2}{3}]^{4}$ $[12, 0]$ $[2, 4]$ $z^{10} + 3 z^5 + 3,3 z^4 + 1$ undefined
5.1.15.26a1.16 20 $x^{15} + 15 x^{13} + 10 x^{12} + 5$ $C_5\wr C_3:C_4$ (as 15T37) $1500$ $1$ $[\frac{5}{3}, \frac{5}{3}, 2]_{3}^{4}$ $[\frac{2}{3},\frac{2}{3},1]_{3}^{4}$ $[\frac{5}{3},\frac{5}{3}]^{4}$ $[\frac{2}{3},\frac{2}{3}]^{4}$ $[12, 0]$ $[2, 4]$ $z^{10} + 3 z^5 + 3,3 z^4 + 1$ undefined
5.1.15.26a1.17 20 $x^{15} + 5 x^{14} + 15 x^{13} + 10 x^{12} + 5$ $C_5\wr C_3:C_4$ (as 15T37) $1500$ $1$ $[\frac{5}{3}, \frac{5}{3}, 2]_{3}^{4}$ $[\frac{2}{3},\frac{2}{3},1]_{3}^{4}$ $[\frac{5}{3},\frac{5}{3}]^{4}$ $[\frac{2}{3},\frac{2}{3}]^{4}$ $[12, 0]$ $[2, 4]$ $z^{10} + 3 z^5 + 3,3 z^4 + 1$ undefined
5.1.15.26a1.18 20 $x^{15} + 10 x^{14} + 15 x^{13} + 10 x^{12} + 5$ $C_5\wr C_3:C_4$ (as 15T37) $1500$ $1$ $[\frac{5}{3}, \frac{5}{3}, 2]_{3}^{4}$ $[\frac{2}{3},\frac{2}{3},1]_{3}^{4}$ $[\frac{5}{3},\frac{5}{3}]^{4}$ $[\frac{2}{3},\frac{2}{3}]^{4}$ $[12, 0]$ $[2, 4]$ $z^{10} + 3 z^5 + 3,3 z^4 + 1$ undefined
5.1.15.26a1.19 20 $x^{15} + 15 x^{14} + 15 x^{13} + 10 x^{12} + 5$ $C_5\wr C_3:C_4$ (as 15T37) $1500$ $1$ $[\frac{5}{3}, \frac{5}{3}, 2]_{3}^{4}$ $[\frac{2}{3},\frac{2}{3},1]_{3}^{4}$ $[\frac{5}{3},\frac{5}{3}]^{4}$ $[\frac{2}{3},\frac{2}{3}]^{4}$ $[12, 0]$ $[2, 4]$ $z^{10} + 3 z^5 + 3,3 z^4 + 1$ undefined
5.1.15.26a1.20 20 $x^{15} + 20 x^{14} + 15 x^{13} + 10 x^{12} + 5$ $C_5\wr C_3:C_4$ (as 15T37) $1500$ $1$ $[\frac{5}{3}, \frac{5}{3}, 2]_{3}^{4}$ $[\frac{2}{3},\frac{2}{3},1]_{3}^{4}$ $[\frac{5}{3},\frac{5}{3}]^{4}$ $[\frac{2}{3},\frac{2}{3}]^{4}$ $[12, 0]$ $[2, 4]$ $z^{10} + 3 z^5 + 3,3 z^4 + 1$ undefined
5.1.15.26a1.21 20 $x^{15} + 20 x^{13} + 10 x^{12} + 5$ $C_5\wr C_3:C_4$ (as 15T37) $1500$ $1$ $[\frac{5}{3}, \frac{5}{3}, 2]_{3}^{4}$ $[\frac{2}{3},\frac{2}{3},1]_{3}^{4}$ $[\frac{5}{3},\frac{5}{3}]^{4}$ $[\frac{2}{3},\frac{2}{3}]^{4}$ $[12, 0]$ $[2, 4]$ $z^{10} + 3 z^5 + 3,3 z^4 + 1$ undefined
5.1.15.26a1.22 20 $x^{15} + 5 x^{14} + 20 x^{13} + 10 x^{12} + 5$ $C_5\wr C_3:C_4$ (as 15T37) $1500$ $1$ $[\frac{5}{3}, \frac{5}{3}, 2]_{3}^{4}$ $[\frac{2}{3},\frac{2}{3},1]_{3}^{4}$ $[\frac{5}{3},\frac{5}{3}]^{4}$ $[\frac{2}{3},\frac{2}{3}]^{4}$ $[12, 0]$ $[2, 4]$ $z^{10} + 3 z^5 + 3,3 z^4 + 1$ undefined
5.1.15.26a1.23 20 $x^{15} + 10 x^{14} + 20 x^{13} + 10 x^{12} + 5$ $C_5\wr C_3:C_4$ (as 15T37) $1500$ $1$ $[\frac{5}{3}, \frac{5}{3}, 2]_{3}^{4}$ $[\frac{2}{3},\frac{2}{3},1]_{3}^{4}$ $[\frac{5}{3},\frac{5}{3}]^{4}$ $[\frac{2}{3},\frac{2}{3}]^{4}$ $[12, 0]$ $[2, 4]$ $z^{10} + 3 z^5 + 3,3 z^4 + 1$ undefined
5.1.15.26a1.24 20 $x^{15} + 15 x^{14} + 20 x^{13} + 10 x^{12} + 5$ $C_5\wr C_3:C_4$ (as 15T37) $1500$ $1$ $[\frac{5}{3}, \frac{5}{3}, 2]_{3}^{4}$ $[\frac{2}{3},\frac{2}{3},1]_{3}^{4}$ $[\frac{5}{3},\frac{5}{3}]^{4}$ $[\frac{2}{3},\frac{2}{3}]^{4}$ $[12, 0]$ $[2, 4]$ $z^{10} + 3 z^5 + 3,3 z^4 + 1$ undefined
5.1.15.26a1.25 20 $x^{15} + 20 x^{14} + 20 x^{13} + 10 x^{12} + 5$ $C_5\wr C_3:C_4$ (as 15T37) $1500$ $1$ $[\frac{5}{3}, \frac{5}{3}, 2]_{3}^{4}$ $[\frac{2}{3},\frac{2}{3},1]_{3}^{4}$ $[\frac{5}{3},\frac{5}{3}]^{4}$ $[\frac{2}{3},\frac{2}{3}]^{4}$ $[12, 0]$ $[2, 4]$ $z^{10} + 3 z^5 + 3,3 z^4 + 1$ undefined
5.1.15.26a2.1 5 $x^{15} + 20 x^{12} + 5$ $S_3 \times C_5$ (as 15T4) $30$ $5$ $[2]_{3}^{2}$ $[1]_{3}^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[12, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z^4 + 2$ undefined
5.1.15.26a2.2 5 $x^{15} + 20 x^{12} + 30$ $S_3 \times C_5$ (as 15T4) $30$ $5$ $[2]_{3}^{2}$ $[1]_{3}^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[12, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z^4 + 2$ undefined
5.1.15.26a2.3 5 $x^{15} + 20 x^{12} + 55$ $S_3 \times C_5$ (as 15T4) $30$ $5$ $[2]_{3}^{2}$ $[1]_{3}^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[12, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z^4 + 2$ undefined
5.1.15.26a2.4 5 $x^{15} + 20 x^{12} + 80$ $S_3 \times C_5$ (as 15T4) $30$ $5$ $[2]_{3}^{2}$ $[1]_{3}^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[12, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z^4 + 2$ undefined
5.1.15.26a2.5 5 $x^{15} + 20 x^{12} + 105$ $S_3 \times C_5$ (as 15T4) $30$ $5$ $[2]_{3}^{2}$ $[1]_{3}^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[12, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z^4 + 2$ undefined
5.1.15.26a2.6 20 $x^{15} + 5 x^{14} + 20 x^{12} + 5$ $C_5\wr S_3$ (as 15T32) $750$ $5$ $[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3}]^{2}$ $[\frac{1}{3},\frac{1}{3}]^{2}$ $[12, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z^4 + 2$ undefined
5.1.15.26a2.7 20 $x^{15} + 5 x^{14} + 20 x^{12} + 30$ $C_5\wr S_3$ (as 15T32) $750$ $5$ $[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3}]^{2}$ $[\frac{1}{3},\frac{1}{3}]^{2}$ $[12, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z^4 + 2$ undefined
5.1.15.26a2.8 20 $x^{15} + 5 x^{14} + 20 x^{12} + 55$ $C_5\wr S_3$ (as 15T32) $750$ $5$ $[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3}]^{2}$ $[\frac{1}{3},\frac{1}{3}]^{2}$ $[12, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z^4 + 2$ undefined
5.1.15.26a2.9 20 $x^{15} + 5 x^{14} + 20 x^{12} + 80$ $C_5\wr S_3$ (as 15T32) $750$ $5$ $[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3}]^{2}$ $[\frac{1}{3},\frac{1}{3}]^{2}$ $[12, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z^4 + 2$ undefined
5.1.15.26a2.10 20 $x^{15} + 5 x^{14} + 20 x^{12} + 105$ $C_5\wr S_3$ (as 15T32) $750$ $5$ $[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3}]^{2}$ $[\frac{1}{3},\frac{1}{3}]^{2}$ $[12, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z^4 + 2$ undefined
5.1.15.26a2.11 20 $x^{15} + 10 x^{14} + 20 x^{12} + 5$ $C_5\wr S_3$ (as 15T32) $750$ $5$ $[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3}]^{2}$ $[\frac{1}{3},\frac{1}{3}]^{2}$ $[12, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z^4 + 2$ undefined
5.1.15.26a2.12 20 $x^{15} + 10 x^{14} + 20 x^{12} + 30$ $C_5\wr S_3$ (as 15T32) $750$ $5$ $[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3}]^{2}$ $[\frac{1}{3},\frac{1}{3}]^{2}$ $[12, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z^4 + 2$ undefined
5.1.15.26a2.13 20 $x^{15} + 10 x^{14} + 20 x^{12} + 55$ $C_5\wr S_3$ (as 15T32) $750$ $5$ $[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3}]^{2}$ $[\frac{1}{3},\frac{1}{3}]^{2}$ $[12, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z^4 + 2$ undefined
5.1.15.26a2.14 20 $x^{15} + 10 x^{14} + 20 x^{12} + 80$ $C_5\wr S_3$ (as 15T32) $750$ $5$ $[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3}]^{2}$ $[\frac{1}{3},\frac{1}{3}]^{2}$ $[12, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z^4 + 2$ undefined
5.1.15.26a2.15 20 $x^{15} + 10 x^{14} + 20 x^{12} + 105$ $C_5\wr S_3$ (as 15T32) $750$ $5$ $[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3}]^{2}$ $[\frac{1}{3},\frac{1}{3}]^{2}$ $[12, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z^4 + 2$ undefined
5.1.15.26a2.16 20 $x^{15} + 15 x^{14} + 20 x^{12} + 5$ $C_5\wr S_3$ (as 15T32) $750$ $5$ $[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3}]^{2}$ $[\frac{1}{3},\frac{1}{3}]^{2}$ $[12, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z^4 + 2$ undefined
5.1.15.26a2.17 20 $x^{15} + 15 x^{14} + 20 x^{12} + 30$ $C_5\wr S_3$ (as 15T32) $750$ $5$ $[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3}]^{2}$ $[\frac{1}{3},\frac{1}{3}]^{2}$ $[12, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z^4 + 2$ undefined
5.1.15.26a2.18 20 $x^{15} + 15 x^{14} + 20 x^{12} + 55$ $C_5\wr S_3$ (as 15T32) $750$ $5$ $[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3}]^{2}$ $[\frac{1}{3},\frac{1}{3}]^{2}$ $[12, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z^4 + 2$ undefined
5.1.15.26a2.19 20 $x^{15} + 15 x^{14} + 20 x^{12} + 80$ $C_5\wr S_3$ (as 15T32) $750$ $5$ $[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3}]^{2}$ $[\frac{1}{3},\frac{1}{3}]^{2}$ $[12, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z^4 + 2$ undefined
5.1.15.26a2.20 20 $x^{15} + 15 x^{14} + 20 x^{12} + 105$ $C_5\wr S_3$ (as 15T32) $750$ $5$ $[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3}]^{2}$ $[\frac{1}{3},\frac{1}{3}]^{2}$ $[12, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z^4 + 2$ undefined
5.1.15.26a2.21 20 $x^{15} + 20 x^{14} + 20 x^{12} + 5$ $C_5\wr S_3$ (as 15T32) $750$ $5$ $[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3}]^{2}$ $[\frac{1}{3},\frac{1}{3}]^{2}$ $[12, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z^4 + 2$ undefined
5.1.15.26a2.22 20 $x^{15} + 20 x^{14} + 20 x^{12} + 30$ $C_5\wr S_3$ (as 15T32) $750$ $5$ $[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3}]^{2}$ $[\frac{1}{3},\frac{1}{3}]^{2}$ $[12, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z^4 + 2$ undefined
5.1.15.26a2.23 20 $x^{15} + 20 x^{14} + 20 x^{12} + 55$ $C_5\wr S_3$ (as 15T32) $750$ $5$ $[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3}]^{2}$ $[\frac{1}{3},\frac{1}{3}]^{2}$ $[12, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z^4 + 2$ undefined
5.1.15.26a2.24 20 $x^{15} + 20 x^{14} + 20 x^{12} + 80$ $C_5\wr S_3$ (as 15T32) $750$ $5$ $[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3}]^{2}$ $[\frac{1}{3},\frac{1}{3}]^{2}$ $[12, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z^4 + 2$ undefined
5.1.15.26a2.25 20 $x^{15} + 20 x^{14} + 20 x^{12} + 105$ $C_5\wr S_3$ (as 15T32) $750$ $5$ $[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3}]^{2}$ $[\frac{1}{3},\frac{1}{3}]^{2}$ $[12, 0]$ $[2, 1]$ $z^{10} + 3 z^5 + 3,3 z^4 + 2$ undefined
Next   displayed columns for results