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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
3.15.1.0a1.1 $x^{15} + 2 x^{8} + x^{5} + 2 x^{2} + x + 1$ $3$ $15$ $1$ $0$ $C_{15}$ (as 15T1) $15$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{15}$ $[\ ]^{15}$ $[\ ]$ $[\ ]$ $t^{15} + 2 t^{8} + t^{5} + 2 t^{2} + t + 1$ $x - 3$ $[0]$ $[\ ]$ undefined
3.5.3.15a1.1 $( x^{5} + 2 x + 1 )^{3} + 6 ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $S_3 \times C_5$ (as 15T4) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}]_{2}^{5}$ $[\frac{1}{2}]_{2}^{5}$ $[\ ]_{2}$ $[\ ]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + 6 x + 3$ $[1, 0]$ $[1]$ $z + (2 t^{4} + 2)$ undefined
3.5.3.15a2.1 $( x^{5} + 2 x + 1 )^{3} + 3 ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $S_3 \times C_5$ (as 15T4) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}]_{2}^{5}$ $[\frac{1}{2}]_{2}^{5}$ $[\ ]_{2}$ $[\ ]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + 3 x + 3$ $[1, 0]$ $[1]$ $z + (t^{4} + 1)$ undefined
3.5.3.15a3.1 $( x^{5} + 2 x + 1 )^{3} + 6 x ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_3^4:C_{10}$ (as 15T33) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 3 t^{3} + 6 t^{2} + 6 t + 3\right) x + 3$ $[1, 0]$ $[1]$ $z + (t + 1)$ undefined
3.5.3.15a4.1 $( x^{5} + 2 x + 1 )^{3} + \left(6 x + 3\right) ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_3^4:C_{10}$ (as 15T33) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 3 t^{3} + 6 t^{2} + 6 t + 6\right) x + 3$ $[1, 0]$ $[1]$ $z + (t^{4} + t + 2)$ undefined
3.5.3.15a5.1 $( x^{5} + 2 x + 1 )^{3} + 3 x ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_3^4:C_{10}$ (as 15T33) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 3 t + 6\right) x + 3$ $[1, 0]$ $[1]$ $z + (2 t + 2)$ undefined
3.5.3.15a6.1 $( x^{5} + 2 x + 1 )^{3} + 6 x^{2} ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_7^3:C_6$ (as 15T44) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 3 t^{3} + 6 t^{2} + 6 t + 6\right) x + 3$ $[1, 0]$ $[1]$ $z + (t^{2} + t)$ undefined
3.5.3.15a7.1 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{2} + 6 x\right) ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_7^3:C_6$ (as 15T44) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{3} + 6 t\right) x + 3$ $[1, 0]$ $[1]$ $z + (t^{2} + 2 t + 1)$ undefined
3.5.3.15a8.1 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{2} + 6 x + 6\right) ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_7^3:C_6$ (as 15T44) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 6 t^{3} + 3 t + 3\right) x + 3$ $[1, 0]$ $[1]$ $z + (2 t^{4} + t^{2} + 2 t)$ undefined
3.5.3.15a9.1 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{2} + 6 x + 3\right) ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_7^3:C_6$ (as 15T44) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 6 t^{3} + 3 t^{2} + 3 t + 6\right) x + 3$ $[1, 0]$ $[1]$ $z + (t^{4} + 2 t^{2} + 2)$ undefined
3.5.3.15a10.1 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{2} + 3 x + 3\right) ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_7^3:C_6$ (as 15T44) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{2} + 3 t + 3\right) x + 3$ $[1, 0]$ $[1]$ $z + (t^{4} + 2 t^{2} + t)$ undefined
3.5.3.15a11.1 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{3} + 6 x\right) ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_7^3:C_6$ (as 15T44) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 3 t^{3} + 6 t^{2} + 3 t + 3\right) x + 3$ $[1, 0]$ $[1]$ $z + (t^{3} + t^{2} + t + 1)$ undefined
3.5.3.15a12.1 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{3} + 6 x + 3\right) ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_7^3:C_6$ (as 15T44) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 3 t^{3} + 6 t\right) x + 3$ $[1, 0]$ $[1]$ $z + (t^{4} + t^{3} + t^{2} + t + 2)$ undefined
3.5.3.15a13.1 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{3} + 6 x^{2}\right) ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_3^4:C_{10}$ (as 15T33) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{3} + 3 t^{2} + 3 t\right) x + 3$ $[1, 0]$ $[1]$ $z + (t^{3} + 2 t^{2} + t)$ undefined
3.5.3.15a14.1 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{3} + 6 x^{2} + 6 x\right) ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_3^4:C_{10}$ (as 15T33) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 6 t^{3} + 6 t^{2} + 3\right) x + 3$ $[1, 0]$ $[1]$ $z + (t^{3} + 2 t^{2} + 2 t + 1)$ undefined
3.5.3.15a15.1 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{3} + 3 x^{2}\right) ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_7^3:C_6$ (as 15T44) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{3} + 3 t^{2}\right) x + 3$ $[1, 0]$ $[1]$ $z + (t^{3} + 2 t)$ undefined
3.5.3.15a16.1 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{3} + 3 x^{2} + 6 x + 6\right) ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_7^3:C_6$ (as 15T44) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{2} + 6 t + 6\right) x + 3$ $[1, 0]$ $[1]$ $z + (2 t^{4} + t^{3})$ undefined
3.5.3.15a17.1 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{3} + 3 x^{2} + 3 x + 6\right) ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_3^4:C_{10}$ (as 15T33) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{3} + 3 t^{2} + 3 t + 6\right) x + 3$ $[1, 0]$ $[1]$ $z + (2 t^{4} + t^{3} + t + 1)$ undefined
3.5.3.15a18.1 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{3} + 6 x + 3\right) ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_7^3:C_6$ (as 15T44) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 6 t^{3} + 3 t\right) x + 3$ $[1, 0]$ $[1]$ $z + (t^{4} + 2 t^{3} + 2 t^{2} + t + 2)$ undefined
3.5.3.15a19.1 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{3} + 3 x^{2} + 6 x + 6\right) ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_7^3:C_6$ (as 15T44) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 6 t^{3} + 3 t^{2} + 3\right) x + 3$ $[1, 0]$ $[1]$ $z + (2 t^{4} + 2 t^{3} + t^{2})$ undefined
3.5.3.15a20.1 $( x^{5} + 2 x + 1 )^{3} + 6 x^{4} ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_7^3:C_6$ (as 15T44) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + 6 t^{4} x + 3$ $[1, 0]$ $[1]$ $z + (t^{4} + t^{3})$ undefined
3.5.3.15a21.1 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{4} + 3 x\right) ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_7^3:C_6$ (as 15T44) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{3} + 3\right) x + 3$ $[1, 0]$ $[1]$ $z + (t^{4} + t^{3} + 2 t + 2)$ undefined
3.5.3.15a22.1 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{4} + 6 x^{2} + 3\right) ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_3^4:C_{10}$ (as 15T33) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t + 6\right) x + 3$ $[1, 0]$ $[1]$ $z + (2 t^{4} + t^{3} + t^{2} + t + 1)$ undefined
3.5.3.15a23.1 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{4} + 6 x^{2} + 3 x\right) ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_7^3:C_6$ (as 15T44) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 6 t^{2} + 3 t\right) x + 3$ $[1, 0]$ $[1]$ $z + (t^{4} + t^{3} + t^{2} + 2)$ undefined
3.5.3.15a24.1 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{4} + 6 x^{2} + 3 x + 3\right) ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_7^3:C_6$ (as 15T44) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 6 t + 3\right) x + 3$ $[1, 0]$ $[1]$ $z + (2 t^{4} + t^{3} + t^{2})$ undefined
3.5.3.15a25.1 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{4} + 3 x^{2}\right) ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_3^4:C_{10}$ (as 15T33) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{3} + 6 t^{2} + 6 t + 3\right) x + 3$ $[1, 0]$ $[1]$ $z + (t^{4} + t^{3} + 2 t^{2} + 2 t)$ undefined
3.5.3.15a26.1 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{4} + 6 x^{3} + 6 x + 6\right) ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_3^4:C_{10}$ (as 15T33) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{3} + 3 t^{2}\right) x + 3$ $[1, 0]$ $[1]$ $z + (2 t^{3} + t^{2} + t)$ undefined
3.5.3.15a27.1 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{4} + 6 x^{3} + 6 x + 3\right) ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_3^4:C_{10}$ (as 15T33) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 3 t^{2} + 3\right) x + 3$ $[1, 0]$ $[1]$ $z + (2 t^{4} + 2 t^{3} + t^{2} + t + 2)$ undefined
3.5.3.15a28.1 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{4} + 6 x^{3} + 6 x^{2} + 3 x + 6\right) ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_7^3:C_6$ (as 15T44) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{2} + 6 t\right) x + 3$ $[1, 0]$ $[1]$ $z + (2 t^{3} + 2 t^{2} + 1)$ undefined
3.5.3.15a29.1 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{4} + 6 x^{3} + 3 x^{2} + 6\right) ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_7^3:C_6$ (as 15T44) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{3} + 3 t\right) x + 3$ $[1, 0]$ $[1]$ $z + (2 t^{3} + 2 t + 2)$ undefined
3.5.3.15a30.1 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{4} + 6 x^{3} + 3 x^{2} + 6 x\right) ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_7^3:C_6$ (as 15T44) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 6 t^{3} + 3 t + 6\right) x + 3$ $[1, 0]$ $[1]$ $z + (t^{4} + 2 t^{3} + 1)$ undefined
3.5.3.15a31.1 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{4} + 3 x^{3}\right) ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_7^3:C_6$ (as 15T44) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 6 t^{3} + 6 t^{2} + 3 t + 6\right) x + 3$ $[1, 0]$ $[1]$ $z + (t^{4} + 2 t^{2})$ undefined
3.5.3.15a32.1 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{4} + 3 x^{3} + 3\right) ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_3^4:C_{10}$ (as 15T33) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 6 t^{3} + 3\right) x + 3$ $[1, 0]$ $[1]$ $z + (2 t^{4} + 2 t^{2} + 1)$ undefined
3.5.3.15a33.1 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{4} + 3 x^{3} + 3 x + 6\right) ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_7^3:C_6$ (as 15T44) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 3 t^{3} + 3 t + 6\right) x + 3$ $[1, 0]$ $[1]$ $z + (2 t^{2} + 2 t + 1)$ undefined
3.5.3.15a34.1 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{4} + 3 x^{3} + 3 x + 3\right) ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_7^3:C_6$ (as 15T44) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 3 t^{3} + 3 t + 3\right) x + 3$ $[1, 0]$ $[1]$ $z + (2 t^{4} + 2 t^{2} + 2 t)$ undefined
3.5.3.15a35.1 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{4} + 3 x^{3} + 6 x^{2} + 6 x\right) ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_7^3:C_6$ (as 15T44) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{2} + 3 t + 3\right) x + 3$ $[1, 0]$ $[1]$ $z + (t^{4} + 2 t + 1)$ undefined
3.5.3.15a36.1 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{4} + 3 x^{3} + 6 x^{2} + 6 x + 3\right) ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_7^3:C_6$ (as 15T44) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{2} + 3 t + 6\right) x + 3$ $[1, 0]$ $[1]$ $z + (2 t^{4} + 2 t + 2)$ undefined
3.5.3.15a37.1 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{4} + 3 x^{3} + 6 x^{2} + 3 x\right) ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_7^3:C_6$ (as 15T44) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 6 t^{2} + 6 t + 6\right) x + 3$ $[1, 0]$ $[1]$ $z + (t^{4} + 2)$ undefined
3.5.3.15a38.1 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{4} + 3 x^{3} + 3 x^{2} + 3\right) ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_7^3:C_6$ (as 15T44) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{3} + 3 t^{2} + 3 t + 6\right) x + 3$ $[1, 0]$ $[1]$ $z + (2 t^{4} + t^{2} + 2 t + 1)$ undefined
3.5.3.15a39.1 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{4} + 3 x^{3} + 3 x^{2} + 6 x\right) ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_3^4:C_{10}$ (as 15T33) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{3} + 3 t^{2} + 3 t + 3\right) x + 3$ $[1, 0]$ $[1]$ $z + (t^{4} + t^{2} + 1)$ undefined
3.5.3.15a40.1 $( x^{5} + 2 x + 1 )^{3} + \left(6 x^{4} + 3 x^{3} + 3 x^{2} + 3 x\right) ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_7^3:C_6$ (as 15T44) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{3} + 6 t^{2} + 3\right) x + 3$ $[1, 0]$ $[1]$ $z + (t^{4} + t^{2} + t + 2)$ undefined
3.5.3.15a41.1 $( x^{5} + 2 x + 1 )^{3} + 3 x^{4} ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_7^3:C_6$ (as 15T44) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 6 t^{2} + 6 t + 3\right) x + 3$ $[1, 0]$ $[1]$ $z + (2 t^{4} + 2 t^{3})$ undefined
3.5.3.15a42.1 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{4} + 3\right) ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_7^3:C_6$ (as 15T44) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 3\right) x + 3$ $[1, 0]$ $[1]$ $z + (2 t^{3} + 1)$ undefined
3.5.3.15a43.1 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{4} + 3 x^{2} + 6 x + 3\right) ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_3^4:C_{10}$ (as 15T33) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 6 t^{2} + 6 t + 3\right) x + 3$ $[1, 0]$ $[1]$ $z + (2 t^{3} + 2 t^{2} + 2)$ undefined
3.5.3.15a44.1 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{4} + 6 x^{3} + 6 x^{2} + 6 x\right) ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_7^3:C_6$ (as 15T44) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 6 t^{3} + 6 t^{2} + 6 t\right) x + 3$ $[1, 0]$ $[1]$ $z + (2 t^{4} + 2 t^{2} + 2 t + 1)$ undefined
3.5.3.15a45.1 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{4} + 6 x^{3} + 3 x^{2}\right) ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_7^3:C_6$ (as 15T44) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 3 t\right) x + 3$ $[1, 0]$ $[1]$ $z + (2 t^{4} + 2 t)$ undefined
3.5.3.15a46.1 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{4} + 6 x^{3} + 3 x^{2} + 6 x + 3\right) ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_3^4:C_{10}$ (as 15T33) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 3 t^{3} + 6 t^{2} + 6\right) x + 3$ $[1, 0]$ $[1]$ $z + 2$ undefined
3.5.3.15a47.1 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{4} + 3 x^{3} + 3\right) ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_3^4:C_{10}$ (as 15T33) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(6 t^{4} + 3 t^{3} + 3 t^{2} + 6 t + 6\right) x + 3$ $[1, 0]$ $[1]$ $z + (t^{3} + 2 t^{2} + 1)$ undefined
3.5.3.15a48.1 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{4} + 3 x^{3} + 3 x + 6\right) ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_3^4:C_{10}$ (as 15T33) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 3 t^{3} + 3 t^{2} + 3 t + 6\right) x + 3$ $[1, 0]$ $[1]$ $z + (t^{4} + t^{3} + 2 t^{2} + 2 t + 1)$ undefined
3.5.3.15a49.1 $( x^{5} + 2 x + 1 )^{3} + \left(3 x^{4} + 3 x^{3} + 6 x^{2} + 6 x\right) ( x^{5} + 2 x + 1 ) + 3$ $3$ $5$ $3$ $15$ $C_7^3:C_6$ (as 15T44) $5$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{5}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{5}$ $[\frac{3}{2},\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ $t^{5} + 2 t + 1$ $x^{3} + \left(3 t^{4} + 6 t\right) x + 3$ $[1, 0]$ $[1]$ $z + (2 t^{4} + t^{3} + 2 t + 1)$ undefined
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