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Properties

Label 5.3.5.27a
Base 5.1.1.0a1.1
Degree \(15\)
e \(5\)
f \(3\)
c \(27\)

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Defining polynomial over unramified subextension

$x^{5} + 25b_{6} x + 5$

Invariants

Residue field characteristic: $5$
Degree: $15$
Base field: $\Q_{5}$
Ramification index $e$: $5$
Residue field degree $f$: $3$
Discriminant exponent $c$: $27$
Artin slopes: $[\frac{9}{4}]$
Swan slopes: $[\frac{5}{4}]$
Means: $\langle1\rangle$
Rams: $(\frac{5}{4})$
Field count: $45$ (complete)
Ambiguity: $3$
Mass: $125$
Absolute Mass: $125/3$

Diagrams

Varying

Indices of inseparability: $[5,0]$
Associated inertia: $[1]$
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 45

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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
5.3.5.27a1.1 5 $( x^{3} + 3 x + 3 )^{5} + 5$ $F_5\times C_3$ (as 15T8) $60$ $3$ $[\frac{9}{4}]_{4}^{3}$ $[\frac{5}{4}]_{4}^{3}$ $[\ ]_{4}$ $[\ ]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
5.3.5.27a1.2 40 $( x^{3} + 3 x + 3 )^{5} + 25 x ( x^{3} + 3 x + 3 ) + 5$ $C_5^3:C_{12}$ (as 15T38) $1500$ $1$ $[\frac{5}{4}, \frac{5}{4}, \frac{9}{4}]_{4}^{3}$ $[\frac{1}{4},\frac{1}{4},\frac{5}{4}]_{4}^{3}$ $[\frac{5}{4},\frac{5}{4}]_{4}$ $[\frac{1}{4},\frac{1}{4}]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
5.3.5.27a1.3 40 $( x^{3} + 3 x + 3 )^{5} + \left(25 x^{2} + 25 x\right) ( x^{3} + 3 x + 3 ) + 5$ $C_5^3:C_{12}$ (as 15T38) $1500$ $1$ $[\frac{5}{4}, \frac{5}{4}, \frac{9}{4}]_{4}^{3}$ $[\frac{1}{4},\frac{1}{4},\frac{5}{4}]_{4}^{3}$ $[\frac{5}{4},\frac{5}{4}]_{4}$ $[\frac{1}{4},\frac{1}{4}]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
5.3.5.27a1.4 40 $( x^{3} + 3 x + 3 )^{5} + 50 x ( x^{3} + 3 x + 3 ) + 5$ $C_5^3:C_{12}$ (as 15T38) $1500$ $1$ $[\frac{5}{4}, \frac{5}{4}, \frac{9}{4}]_{4}^{3}$ $[\frac{1}{4},\frac{1}{4},\frac{5}{4}]_{4}^{3}$ $[\frac{5}{4},\frac{5}{4}]_{4}$ $[\frac{1}{4},\frac{1}{4}]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
5.3.5.27a1.5 40 $( x^{3} + 3 x + 3 )^{5} + \left(50 x^{2} + 50 x\right) ( x^{3} + 3 x + 3 ) + 5$ $C_5^3:C_{12}$ (as 15T38) $1500$ $1$ $[\frac{5}{4}, \frac{5}{4}, \frac{9}{4}]_{4}^{3}$ $[\frac{1}{4},\frac{1}{4},\frac{5}{4}]_{4}^{3}$ $[\frac{5}{4},\frac{5}{4}]_{4}$ $[\frac{1}{4},\frac{1}{4}]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
5.3.5.27a1.6 40 $( x^{3} + 3 x + 3 )^{5} + \left(75 x^{2} + 50 x\right) ( x^{3} + 3 x + 3 ) + 5$ $C_5^3:C_{12}$ (as 15T38) $1500$ $1$ $[\frac{5}{4}, \frac{5}{4}, \frac{9}{4}]_{4}^{3}$ $[\frac{1}{4},\frac{1}{4},\frac{5}{4}]_{4}^{3}$ $[\frac{5}{4},\frac{5}{4}]_{4}$ $[\frac{1}{4},\frac{1}{4}]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
5.3.5.27a1.7 40 $( x^{3} + 3 x + 3 )^{5} + 75 x ( x^{3} + 3 x + 3 ) + 5$ $C_5^3:C_{12}$ (as 15T38) $1500$ $1$ $[\frac{5}{4}, \frac{5}{4}, \frac{9}{4}]_{4}^{3}$ $[\frac{1}{4},\frac{1}{4},\frac{5}{4}]_{4}^{3}$ $[\frac{5}{4},\frac{5}{4}]_{4}$ $[\frac{1}{4},\frac{1}{4}]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
5.3.5.27a1.8 40 $( x^{3} + 3 x + 3 )^{5} + \left(25 x^{2} + 75 x\right) ( x^{3} + 3 x + 3 ) + 5$ $C_5^3:C_{12}$ (as 15T38) $1500$ $1$ $[\frac{5}{4}, \frac{5}{4}, \frac{9}{4}]_{4}^{3}$ $[\frac{1}{4},\frac{1}{4},\frac{5}{4}]_{4}^{3}$ $[\frac{5}{4},\frac{5}{4}]_{4}$ $[\frac{1}{4},\frac{1}{4}]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
5.3.5.27a1.9 40 $( x^{3} + 3 x + 3 )^{5} + 100 x ( x^{3} + 3 x + 3 ) + 5$ $C_5^3:C_{12}$ (as 15T38) $1500$ $1$ $[\frac{5}{4}, \frac{5}{4}, \frac{9}{4}]_{4}^{3}$ $[\frac{1}{4},\frac{1}{4},\frac{5}{4}]_{4}^{3}$ $[\frac{5}{4},\frac{5}{4}]_{4}$ $[\frac{1}{4},\frac{1}{4}]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
5.3.5.27a1.10 5 $( x^{3} + 3 x + 3 )^{5} + 25 ( x^{3} + 3 x + 3 ) + 5$ $F_5\times C_3$ (as 15T8) $60$ $3$ $[\frac{9}{4}]_{4}^{3}$ $[\frac{5}{4}]_{4}^{3}$ $[\ ]_{4}$ $[\ ]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
5.3.5.27a1.11 40 $( x^{3} + 3 x + 3 )^{5} + \left(25 x + 25\right) ( x^{3} + 3 x + 3 ) + 5$ $C_5^3:C_{12}$ (as 15T38) $1500$ $1$ $[\frac{5}{4}, \frac{5}{4}, \frac{9}{4}]_{4}^{3}$ $[\frac{1}{4},\frac{1}{4},\frac{5}{4}]_{4}^{3}$ $[\frac{5}{4},\frac{5}{4}]_{4}$ $[\frac{1}{4},\frac{1}{4}]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
5.3.5.27a1.12 40 $( x^{3} + 3 x + 3 )^{5} + \left(25 x^{2} + 25 x + 25\right) ( x^{3} + 3 x + 3 ) + 5$ $C_5^3:C_{12}$ (as 15T38) $1500$ $1$ $[\frac{5}{4}, \frac{5}{4}, \frac{9}{4}]_{4}^{3}$ $[\frac{1}{4},\frac{1}{4},\frac{5}{4}]_{4}^{3}$ $[\frac{5}{4},\frac{5}{4}]_{4}$ $[\frac{1}{4},\frac{1}{4}]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
5.3.5.27a1.13 40 $( x^{3} + 3 x + 3 )^{5} + \left(50 x + 25\right) ( x^{3} + 3 x + 3 ) + 5$ $C_5^3:C_{12}$ (as 15T38) $1500$ $1$ $[\frac{5}{4}, \frac{5}{4}, \frac{9}{4}]_{4}^{3}$ $[\frac{1}{4},\frac{1}{4},\frac{5}{4}]_{4}^{3}$ $[\frac{5}{4},\frac{5}{4}]_{4}$ $[\frac{1}{4},\frac{1}{4}]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
5.3.5.27a1.14 40 $( x^{3} + 3 x + 3 )^{5} + \left(50 x^{2} + 50 x + 25\right) ( x^{3} + 3 x + 3 ) + 5$ $C_5^3:C_{12}$ (as 15T38) $1500$ $1$ $[\frac{5}{4}, \frac{5}{4}, \frac{9}{4}]_{4}^{3}$ $[\frac{1}{4},\frac{1}{4},\frac{5}{4}]_{4}^{3}$ $[\frac{5}{4},\frac{5}{4}]_{4}$ $[\frac{1}{4},\frac{1}{4}]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
5.3.5.27a1.15 40 $( x^{3} + 3 x + 3 )^{5} + \left(75 x^{2} + 50 x + 25\right) ( x^{3} + 3 x + 3 ) + 5$ $C_5^3:C_{12}$ (as 15T38) $1500$ $1$ $[\frac{5}{4}, \frac{5}{4}, \frac{9}{4}]_{4}^{3}$ $[\frac{1}{4},\frac{1}{4},\frac{5}{4}]_{4}^{3}$ $[\frac{5}{4},\frac{5}{4}]_{4}$ $[\frac{1}{4},\frac{1}{4}]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
5.3.5.27a1.16 40 $( x^{3} + 3 x + 3 )^{5} + \left(75 x + 25\right) ( x^{3} + 3 x + 3 ) + 5$ $C_5^3:C_{12}$ (as 15T38) $1500$ $1$ $[\frac{5}{4}, \frac{5}{4}, \frac{9}{4}]_{4}^{3}$ $[\frac{1}{4},\frac{1}{4},\frac{5}{4}]_{4}^{3}$ $[\frac{5}{4},\frac{5}{4}]_{4}$ $[\frac{1}{4},\frac{1}{4}]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
5.3.5.27a1.17 40 $( x^{3} + 3 x + 3 )^{5} + \left(25 x^{2} + 75 x + 25\right) ( x^{3} + 3 x + 3 ) + 5$ $C_5^3:C_{12}$ (as 15T38) $1500$ $1$ $[\frac{5}{4}, \frac{5}{4}, \frac{9}{4}]_{4}^{3}$ $[\frac{1}{4},\frac{1}{4},\frac{5}{4}]_{4}^{3}$ $[\frac{5}{4},\frac{5}{4}]_{4}$ $[\frac{1}{4},\frac{1}{4}]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
5.3.5.27a1.18 40 $( x^{3} + 3 x + 3 )^{5} + \left(100 x + 25\right) ( x^{3} + 3 x + 3 ) + 5$ $C_5^3:C_{12}$ (as 15T38) $1500$ $1$ $[\frac{5}{4}, \frac{5}{4}, \frac{9}{4}]_{4}^{3}$ $[\frac{1}{4},\frac{1}{4},\frac{5}{4}]_{4}^{3}$ $[\frac{5}{4},\frac{5}{4}]_{4}$ $[\frac{1}{4},\frac{1}{4}]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
5.3.5.27a1.19 5 $( x^{3} + 3 x + 3 )^{5} + 50 ( x^{3} + 3 x + 3 ) + 5$ $F_5\times C_3$ (as 15T8) $60$ $3$ $[\frac{9}{4}]_{4}^{3}$ $[\frac{5}{4}]_{4}^{3}$ $[\ ]_{4}$ $[\ ]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
5.3.5.27a1.20 40 $( x^{3} + 3 x + 3 )^{5} + \left(25 x + 50\right) ( x^{3} + 3 x + 3 ) + 5$ $C_5^3:C_{12}$ (as 15T38) $1500$ $1$ $[\frac{5}{4}, \frac{5}{4}, \frac{9}{4}]_{4}^{3}$ $[\frac{1}{4},\frac{1}{4},\frac{5}{4}]_{4}^{3}$ $[\frac{5}{4},\frac{5}{4}]_{4}$ $[\frac{1}{4},\frac{1}{4}]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
5.3.5.27a1.21 40 $( x^{3} + 3 x + 3 )^{5} + \left(25 x^{2} + 25 x + 50\right) ( x^{3} + 3 x + 3 ) + 5$ $C_5^3:C_{12}$ (as 15T38) $1500$ $1$ $[\frac{5}{4}, \frac{5}{4}, \frac{9}{4}]_{4}^{3}$ $[\frac{1}{4},\frac{1}{4},\frac{5}{4}]_{4}^{3}$ $[\frac{5}{4},\frac{5}{4}]_{4}$ $[\frac{1}{4},\frac{1}{4}]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
5.3.5.27a1.22 40 $( x^{3} + 3 x + 3 )^{5} + \left(50 x + 50\right) ( x^{3} + 3 x + 3 ) + 5$ $C_5^3:C_{12}$ (as 15T38) $1500$ $1$ $[\frac{5}{4}, \frac{5}{4}, \frac{9}{4}]_{4}^{3}$ $[\frac{1}{4},\frac{1}{4},\frac{5}{4}]_{4}^{3}$ $[\frac{5}{4},\frac{5}{4}]_{4}$ $[\frac{1}{4},\frac{1}{4}]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
5.3.5.27a1.23 40 $( x^{3} + 3 x + 3 )^{5} + \left(50 x^{2} + 50 x + 50\right) ( x^{3} + 3 x + 3 ) + 5$ $C_5^3:C_{12}$ (as 15T38) $1500$ $1$ $[\frac{5}{4}, \frac{5}{4}, \frac{9}{4}]_{4}^{3}$ $[\frac{1}{4},\frac{1}{4},\frac{5}{4}]_{4}^{3}$ $[\frac{5}{4},\frac{5}{4}]_{4}$ $[\frac{1}{4},\frac{1}{4}]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
5.3.5.27a1.24 40 $( x^{3} + 3 x + 3 )^{5} + \left(75 x^{2} + 50 x + 50\right) ( x^{3} + 3 x + 3 ) + 5$ $C_5^3:C_{12}$ (as 15T38) $1500$ $1$ $[\frac{5}{4}, \frac{5}{4}, \frac{9}{4}]_{4}^{3}$ $[\frac{1}{4},\frac{1}{4},\frac{5}{4}]_{4}^{3}$ $[\frac{5}{4},\frac{5}{4}]_{4}$ $[\frac{1}{4},\frac{1}{4}]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
5.3.5.27a1.25 40 $( x^{3} + 3 x + 3 )^{5} + \left(75 x + 50\right) ( x^{3} + 3 x + 3 ) + 5$ $C_5^3:C_{12}$ (as 15T38) $1500$ $1$ $[\frac{5}{4}, \frac{5}{4}, \frac{9}{4}]_{4}^{3}$ $[\frac{1}{4},\frac{1}{4},\frac{5}{4}]_{4}^{3}$ $[\frac{5}{4},\frac{5}{4}]_{4}$ $[\frac{1}{4},\frac{1}{4}]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
5.3.5.27a1.26 40 $( x^{3} + 3 x + 3 )^{5} + \left(25 x^{2} + 75 x + 50\right) ( x^{3} + 3 x + 3 ) + 5$ $C_5^3:C_{12}$ (as 15T38) $1500$ $1$ $[\frac{5}{4}, \frac{5}{4}, \frac{9}{4}]_{4}^{3}$ $[\frac{1}{4},\frac{1}{4},\frac{5}{4}]_{4}^{3}$ $[\frac{5}{4},\frac{5}{4}]_{4}$ $[\frac{1}{4},\frac{1}{4}]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
5.3.5.27a1.27 40 $( x^{3} + 3 x + 3 )^{5} + \left(100 x + 50\right) ( x^{3} + 3 x + 3 ) + 5$ $C_5^3:C_{12}$ (as 15T38) $1500$ $1$ $[\frac{5}{4}, \frac{5}{4}, \frac{9}{4}]_{4}^{3}$ $[\frac{1}{4},\frac{1}{4},\frac{5}{4}]_{4}^{3}$ $[\frac{5}{4},\frac{5}{4}]_{4}$ $[\frac{1}{4},\frac{1}{4}]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
5.3.5.27a1.28 5 $( x^{3} + 3 x + 3 )^{5} + 75 ( x^{3} + 3 x + 3 ) + 5$ $F_5\times C_3$ (as 15T8) $60$ $3$ $[\frac{9}{4}]_{4}^{3}$ $[\frac{5}{4}]_{4}^{3}$ $[\ ]_{4}$ $[\ ]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
5.3.5.27a1.29 40 $( x^{3} + 3 x + 3 )^{5} + \left(25 x + 75\right) ( x^{3} + 3 x + 3 ) + 5$ $C_5^3:C_{12}$ (as 15T38) $1500$ $1$ $[\frac{5}{4}, \frac{5}{4}, \frac{9}{4}]_{4}^{3}$ $[\frac{1}{4},\frac{1}{4},\frac{5}{4}]_{4}^{3}$ $[\frac{5}{4},\frac{5}{4}]_{4}$ $[\frac{1}{4},\frac{1}{4}]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
5.3.5.27a1.30 40 $( x^{3} + 3 x + 3 )^{5} + \left(25 x^{2} + 25 x + 75\right) ( x^{3} + 3 x + 3 ) + 5$ $C_5^3:C_{12}$ (as 15T38) $1500$ $1$ $[\frac{5}{4}, \frac{5}{4}, \frac{9}{4}]_{4}^{3}$ $[\frac{1}{4},\frac{1}{4},\frac{5}{4}]_{4}^{3}$ $[\frac{5}{4},\frac{5}{4}]_{4}$ $[\frac{1}{4},\frac{1}{4}]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
5.3.5.27a1.31 40 $( x^{3} + 3 x + 3 )^{5} + \left(50 x + 75\right) ( x^{3} + 3 x + 3 ) + 5$ $C_5^3:C_{12}$ (as 15T38) $1500$ $1$ $[\frac{5}{4}, \frac{5}{4}, \frac{9}{4}]_{4}^{3}$ $[\frac{1}{4},\frac{1}{4},\frac{5}{4}]_{4}^{3}$ $[\frac{5}{4},\frac{5}{4}]_{4}$ $[\frac{1}{4},\frac{1}{4}]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
5.3.5.27a1.32 40 $( x^{3} + 3 x + 3 )^{5} + \left(50 x^{2} + 50 x + 75\right) ( x^{3} + 3 x + 3 ) + 5$ $C_5^3:C_{12}$ (as 15T38) $1500$ $1$ $[\frac{5}{4}, \frac{5}{4}, \frac{9}{4}]_{4}^{3}$ $[\frac{1}{4},\frac{1}{4},\frac{5}{4}]_{4}^{3}$ $[\frac{5}{4},\frac{5}{4}]_{4}$ $[\frac{1}{4},\frac{1}{4}]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
5.3.5.27a1.33 40 $( x^{3} + 3 x + 3 )^{5} + \left(75 x^{2} + 50 x + 75\right) ( x^{3} + 3 x + 3 ) + 5$ $C_5^3:C_{12}$ (as 15T38) $1500$ $1$ $[\frac{5}{4}, \frac{5}{4}, \frac{9}{4}]_{4}^{3}$ $[\frac{1}{4},\frac{1}{4},\frac{5}{4}]_{4}^{3}$ $[\frac{5}{4},\frac{5}{4}]_{4}$ $[\frac{1}{4},\frac{1}{4}]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
5.3.5.27a1.34 40 $( x^{3} + 3 x + 3 )^{5} + \left(75 x + 75\right) ( x^{3} + 3 x + 3 ) + 5$ $C_5^3:C_{12}$ (as 15T38) $1500$ $1$ $[\frac{5}{4}, \frac{5}{4}, \frac{9}{4}]_{4}^{3}$ $[\frac{1}{4},\frac{1}{4},\frac{5}{4}]_{4}^{3}$ $[\frac{5}{4},\frac{5}{4}]_{4}$ $[\frac{1}{4},\frac{1}{4}]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
5.3.5.27a1.35 40 $( x^{3} + 3 x + 3 )^{5} + \left(25 x^{2} + 75 x + 75\right) ( x^{3} + 3 x + 3 ) + 5$ $C_5^3:C_{12}$ (as 15T38) $1500$ $1$ $[\frac{5}{4}, \frac{5}{4}, \frac{9}{4}]_{4}^{3}$ $[\frac{1}{4},\frac{1}{4},\frac{5}{4}]_{4}^{3}$ $[\frac{5}{4},\frac{5}{4}]_{4}$ $[\frac{1}{4},\frac{1}{4}]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
5.3.5.27a1.36 40 $( x^{3} + 3 x + 3 )^{5} + \left(100 x + 75\right) ( x^{3} + 3 x + 3 ) + 5$ $C_5^3:C_{12}$ (as 15T38) $1500$ $1$ $[\frac{5}{4}, \frac{5}{4}, \frac{9}{4}]_{4}^{3}$ $[\frac{1}{4},\frac{1}{4},\frac{5}{4}]_{4}^{3}$ $[\frac{5}{4},\frac{5}{4}]_{4}$ $[\frac{1}{4},\frac{1}{4}]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
5.3.5.27a1.37 5 $( x^{3} + 3 x + 3 )^{5} + 100 ( x^{3} + 3 x + 3 ) + 5$ $F_5\times C_3$ (as 15T8) $60$ $3$ $[\frac{9}{4}]_{4}^{3}$ $[\frac{5}{4}]_{4}^{3}$ $[\ ]_{4}$ $[\ ]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
5.3.5.27a1.38 40 $( x^{3} + 3 x + 3 )^{5} + \left(25 x + 100\right) ( x^{3} + 3 x + 3 ) + 5$ $C_5^3:C_{12}$ (as 15T38) $1500$ $1$ $[\frac{5}{4}, \frac{5}{4}, \frac{9}{4}]_{4}^{3}$ $[\frac{1}{4},\frac{1}{4},\frac{5}{4}]_{4}^{3}$ $[\frac{5}{4},\frac{5}{4}]_{4}$ $[\frac{1}{4},\frac{1}{4}]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
5.3.5.27a1.39 40 $( x^{3} + 3 x + 3 )^{5} + \left(25 x^{2} + 25 x + 100\right) ( x^{3} + 3 x + 3 ) + 5$ $C_5^3:C_{12}$ (as 15T38) $1500$ $1$ $[\frac{5}{4}, \frac{5}{4}, \frac{9}{4}]_{4}^{3}$ $[\frac{1}{4},\frac{1}{4},\frac{5}{4}]_{4}^{3}$ $[\frac{5}{4},\frac{5}{4}]_{4}$ $[\frac{1}{4},\frac{1}{4}]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
5.3.5.27a1.40 40 $( x^{3} + 3 x + 3 )^{5} + \left(50 x + 100\right) ( x^{3} + 3 x + 3 ) + 5$ $C_5^3:C_{12}$ (as 15T38) $1500$ $1$ $[\frac{5}{4}, \frac{5}{4}, \frac{9}{4}]_{4}^{3}$ $[\frac{1}{4},\frac{1}{4},\frac{5}{4}]_{4}^{3}$ $[\frac{5}{4},\frac{5}{4}]_{4}$ $[\frac{1}{4},\frac{1}{4}]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
5.3.5.27a1.41 40 $( x^{3} + 3 x + 3 )^{5} + \left(50 x^{2} + 50 x + 100\right) ( x^{3} + 3 x + 3 ) + 5$ $C_5^3:C_{12}$ (as 15T38) $1500$ $1$ $[\frac{5}{4}, \frac{5}{4}, \frac{9}{4}]_{4}^{3}$ $[\frac{1}{4},\frac{1}{4},\frac{5}{4}]_{4}^{3}$ $[\frac{5}{4},\frac{5}{4}]_{4}$ $[\frac{1}{4},\frac{1}{4}]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
5.3.5.27a1.42 40 $( x^{3} + 3 x + 3 )^{5} + \left(75 x^{2} + 50 x + 100\right) ( x^{3} + 3 x + 3 ) + 5$ $C_5^3:C_{12}$ (as 15T38) $1500$ $1$ $[\frac{5}{4}, \frac{5}{4}, \frac{9}{4}]_{4}^{3}$ $[\frac{1}{4},\frac{1}{4},\frac{5}{4}]_{4}^{3}$ $[\frac{5}{4},\frac{5}{4}]_{4}$ $[\frac{1}{4},\frac{1}{4}]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
5.3.5.27a1.43 40 $( x^{3} + 3 x + 3 )^{5} + \left(75 x + 100\right) ( x^{3} + 3 x + 3 ) + 5$ $C_5^3:C_{12}$ (as 15T38) $1500$ $1$ $[\frac{5}{4}, \frac{5}{4}, \frac{9}{4}]_{4}^{3}$ $[\frac{1}{4},\frac{1}{4},\frac{5}{4}]_{4}^{3}$ $[\frac{5}{4},\frac{5}{4}]_{4}$ $[\frac{1}{4},\frac{1}{4}]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
5.3.5.27a1.44 40 $( x^{3} + 3 x + 3 )^{5} + \left(25 x^{2} + 75 x + 100\right) ( x^{3} + 3 x + 3 ) + 5$ $C_5^3:C_{12}$ (as 15T38) $1500$ $1$ $[\frac{5}{4}, \frac{5}{4}, \frac{9}{4}]_{4}^{3}$ $[\frac{1}{4},\frac{1}{4},\frac{5}{4}]_{4}^{3}$ $[\frac{5}{4},\frac{5}{4}]_{4}$ $[\frac{1}{4},\frac{1}{4}]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
5.3.5.27a1.45 40 $( x^{3} + 3 x + 3 )^{5} + \left(100 x + 100\right) ( x^{3} + 3 x + 3 ) + 5$ $C_5^3:C_{12}$ (as 15T38) $1500$ $1$ $[\frac{5}{4}, \frac{5}{4}, \frac{9}{4}]_{4}^{3}$ $[\frac{1}{4},\frac{1}{4},\frac{5}{4}]_{4}^{3}$ $[\frac{5}{4},\frac{5}{4}]_{4}$ $[\frac{1}{4},\frac{1}{4}]_{4}$ $[5, 0]$ $[1]$ $z + (4 t + 3)$ undefined
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