| Label |
$n$ |
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 |
$\#\Aut(K/\Q_p)$ |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
Resid. Poly |
Jump Set |
| 5.15.1.0a1.1 |
$15$ |
$x^{15} + 2 x^{5} + 3 x^{3} + 3 x^{2} + 4 x + 3$ |
$5$ |
$15$ |
$1$ |
$0$ |
$C_{15}$ (as 15T1) |
$15$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{15}$ |
$[\ ]^{15}$ |
$[\ ]$ |
$[\ ]$ |
$15$ |
$t^{15} + 2 t^{5} + 3 t^{3} + 3 t^{2} + 4 t + 3$ |
$x - 5$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 5.5.3.10a1.1 |
$15$ |
$( x^{5} + 4 x + 3 )^{3} + 5$ |
$5$ |
$5$ |
$3$ |
$10$ |
$S_3 \times C_5$ (as 15T4) |
$10$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{10}$ |
$[\ ]_{3}^{10}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$5$ |
$t^{5} + 4 t + 3$ |
$x^{3} + 5$ |
$[0]$ |
$[2]$ |
$z^2 + 3 z + 3$ |
undefined |
| 5.3.5.15a1.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + 20 ( x^{3} + 3 x + 3 ) + 5$ |
$5$ |
$3$ |
$5$ |
$15$ |
$F_5\times C_3$ (as 15T8) |
$3$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}]_{4}^{3}$ |
$[\frac{1}{4}]_{4}^{3}$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$3$ |
$t^{3} + 3 t + 3$ |
$x^{5} + 20 x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (3 t^2 + 3)$ |
undefined |
| 5.3.5.15a2.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + 15 ( x^{3} + 3 x + 3 ) + 5$ |
$5$ |
$3$ |
$5$ |
$15$ |
$F_5\times C_3$ (as 15T8) |
$3$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}]_{4}^{3}$ |
$[\frac{1}{4}]_{4}^{3}$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$3$ |
$t^{3} + 3 t + 3$ |
$x^{5} + 15 x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (t^2 + 1)$ |
undefined |
| 5.3.5.15a3.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + 10 ( x^{3} + 3 x + 3 ) + 5$ |
$5$ |
$3$ |
$5$ |
$15$ |
$F_5\times C_3$ (as 15T8) |
$3$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}]_{4}^{3}$ |
$[\frac{1}{4}]_{4}^{3}$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$3$ |
$t^{3} + 3 t + 3$ |
$x^{5} + 10 x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (4 t^2 + 4)$ |
undefined |
| 5.3.5.15a4.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + 5 ( x^{3} + 3 x + 3 ) + 5$ |
$5$ |
$3$ |
$5$ |
$15$ |
$F_5\times C_3$ (as 15T8) |
$3$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}]_{4}^{3}$ |
$[\frac{1}{4}]_{4}^{3}$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$3$ |
$t^{3} + 3 t + 3$ |
$x^{5} + 5 x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (2 t^2 + 2)$ |
undefined |
| 5.3.5.15a5.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + 20 x ( x^{3} + 3 x + 3 ) + 5$ |
$5$ |
$3$ |
$5$ |
$15$ |
$(C_5^2 : C_4):C_3$ (as 15T19) |
$3$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}]_{4}^{3}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}^{3}$ |
$[\frac{5}{4}]_{4}$ |
$[\frac{1}{4}]_{4}$ |
$1$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(15 t^{2} + 5 t + 5\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (4 t + 1)$ |
undefined |
| 5.3.5.15a6.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + 15 x ( x^{3} + 3 x + 3 ) + 5$ |
$5$ |
$3$ |
$5$ |
$15$ |
$(C_5^2 : C_4):C_3$ (as 15T19) |
$3$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}]_{4}^{3}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}^{3}$ |
$[\frac{5}{4}]_{4}$ |
$[\frac{1}{4}]_{4}$ |
$1$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(20 t^{2} + 15\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (3 t + 2)$ |
undefined |
| 5.3.5.15a7.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + \left(15 x + 15\right) ( x^{3} + 3 x + 3 ) + 5$ |
$5$ |
$3$ |
$5$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}, \frac{5}{4}]_{4}^{3}$ |
$[\frac{1}{4},\frac{1}{4},\frac{1}{4}]_{4}^{3}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}$ |
$1$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(5 t^{2} + 10 t\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (t^2 + 3 t + 3)$ |
undefined |
| 5.3.5.15a8.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + 10 x ( x^{3} + 3 x + 3 ) + 5$ |
$5$ |
$3$ |
$5$ |
$15$ |
$(C_5^2 : C_4):C_3$ (as 15T19) |
$3$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}]_{4}^{3}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}^{3}$ |
$[\frac{5}{4}]_{4}$ |
$[\frac{1}{4}]_{4}$ |
$1$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(5 t^{2} + 10\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (2 t + 3)$ |
undefined |
| 5.3.5.15a9.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + 5 x ( x^{3} + 3 x + 3 ) + 5$ |
$5$ |
$3$ |
$5$ |
$15$ |
$(C_5^2 : C_4):C_3$ (as 15T19) |
$3$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}]_{4}^{3}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}^{3}$ |
$[\frac{5}{4}]_{4}$ |
$[\frac{1}{4}]_{4}$ |
$1$ |
$t^{3} + 3 t + 3$ |
$x^{5} + 5 t x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (t + 4)$ |
undefined |
| 5.3.5.15a10.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + \left(5 x + 10\right) ( x^{3} + 3 x + 3 ) + 5$ |
$5$ |
$3$ |
$5$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}, \frac{5}{4}]_{4}^{3}$ |
$[\frac{1}{4},\frac{1}{4},\frac{1}{4}]_{4}^{3}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}$ |
$1$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(15 t^{2} + 15\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (4 t^2 + t + 3)$ |
undefined |
| 5.3.5.15a11.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + \left(5 x + 5\right) ( x^{3} + 3 x + 3 ) + 5$ |
$5$ |
$3$ |
$5$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}, \frac{5}{4}]_{4}^{3}$ |
$[\frac{1}{4},\frac{1}{4},\frac{1}{4}]_{4}^{3}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}$ |
$1$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(5 t + 5\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (2 t^2 + t + 1)$ |
undefined |
| 5.3.5.15a12.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + 20 x^{2} ( x^{3} + 3 x + 3 ) + 5$ |
$5$ |
$3$ |
$5$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}, \frac{5}{4}]_{4}^{3}$ |
$[\frac{1}{4},\frac{1}{4},\frac{1}{4}]_{4}^{3}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}$ |
$1$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(15 t + 10\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (4 t^2 + t)$ |
undefined |
| 5.3.5.15a13.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + \left(20 x^{2} + 20 x + 20\right) ( x^{3} + 3 x + 3 ) + 5$ |
$5$ |
$3$ |
$5$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}, \frac{5}{4}]_{4}^{3}$ |
$[\frac{1}{4},\frac{1}{4},\frac{1}{4}]_{4}^{3}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}$ |
$1$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(20 t^{2} + 20 t + 20\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (2 t^2 + 4)$ |
undefined |
| 5.3.5.15a14.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + \left(20 x^{2} + 15 x + 20\right) ( x^{3} + 3 x + 3 ) + 5$ |
$5$ |
$3$ |
$5$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}, \frac{5}{4}]_{4}^{3}$ |
$[\frac{1}{4},\frac{1}{4},\frac{1}{4}]_{4}^{3}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}$ |
$1$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(20 t^{2} + 15 t + 20\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (2 t^2 + 4 t)$ |
undefined |
| 5.3.5.15a15.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + \left(20 x^{2} + 10 x + 15\right) ( x^{3} + 3 x + 3 ) + 5$ |
$5$ |
$3$ |
$5$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}, \frac{5}{4}]_{4}^{3}$ |
$[\frac{1}{4},\frac{1}{4},\frac{1}{4}]_{4}^{3}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}$ |
$1$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(10 t^{2} + 10 t + 20\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (3 t + 4)$ |
undefined |
| 5.3.5.15a16.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + \left(20 x^{2} + 10 x + 10\right) ( x^{3} + 3 x + 3 ) + 5$ |
$5$ |
$3$ |
$5$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}, \frac{5}{4}]_{4}^{3}$ |
$[\frac{1}{4},\frac{1}{4},\frac{1}{4}]_{4}^{3}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}$ |
$1$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(20 t^{2} + 10 t + 10\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (3 t^2 + 3 t + 2)$ |
undefined |
| 5.3.5.15a17.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + \left(20 x^{2} + 5 x + 20\right) ( x^{3} + 3 x + 3 ) + 5$ |
$5$ |
$3$ |
$5$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}, \frac{5}{4}]_{4}^{3}$ |
$[\frac{1}{4},\frac{1}{4},\frac{1}{4}]_{4}^{3}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}$ |
$1$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(20 t^{2} + 5 t + 20\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (2 t^2 + 2 t + 2)$ |
undefined |
| 5.3.5.15a18.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + 15 x^{2} ( x^{3} + 3 x + 3 ) + 5$ |
$5$ |
$3$ |
$5$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}, \frac{5}{4}]_{4}^{3}$ |
$[\frac{1}{4},\frac{1}{4},\frac{1}{4}]_{4}^{3}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}$ |
$1$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(5 t + 20\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (3 t^2 + 2 t)$ |
undefined |
| 5.3.5.15a19.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + \left(15 x^{2} + 20 x + 20\right) ( x^{3} + 3 x + 3 ) + 5$ |
$5$ |
$3$ |
$5$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}, \frac{5}{4}]_{4}^{3}$ |
$[\frac{1}{4},\frac{1}{4},\frac{1}{4}]_{4}^{3}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}$ |
$1$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(15 t^{2} + 10 t + 20\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (t^2 + t + 4)$ |
undefined |
| 5.3.5.15a20.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + \left(15 x^{2} + 15 x\right) ( x^{3} + 3 x + 3 ) + 5$ |
$5$ |
$3$ |
$5$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}, \frac{5}{4}]_{4}^{3}$ |
$[\frac{1}{4},\frac{1}{4},\frac{1}{4}]_{4}^{3}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}$ |
$1$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(5 t^{2} + 15 t + 5\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (3 t^2 + 2)$ |
undefined |
| 5.3.5.15a21.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + \left(15 x^{2} + 15 x + 10\right) ( x^{3} + 3 x + 3 ) + 5$ |
$5$ |
$3$ |
$5$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}, \frac{5}{4}]_{4}^{3}$ |
$[\frac{1}{4},\frac{1}{4},\frac{1}{4}]_{4}^{3}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}$ |
$1$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(15 t^{2} + 15 t + 10\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (2 t^2 + 1)$ |
undefined |
| 5.3.5.15a22.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + \left(15 x^{2} + 15 x + 5\right) ( x^{3} + 3 x + 3 ) + 5$ |
$5$ |
$3$ |
$5$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}, \frac{5}{4}]_{4}^{3}$ |
$[\frac{1}{4},\frac{1}{4},\frac{1}{4}]_{4}^{3}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}$ |
$1$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(5 t^{2} + 15 t + 10\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + 4$ |
undefined |
| 5.3.5.15a23.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + \left(15 x^{2} + 10 x\right) ( x^{3} + 3 x + 3 ) + 5$ |
$5$ |
$3$ |
$5$ |
$15$ |
$(C_5^2 : C_4):C_3$ (as 15T19) |
$3$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}]_{4}^{3}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}^{3}$ |
$[\frac{5}{4}]_{4}$ |
$[\frac{1}{4}]_{4}$ |
$1$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(15 t^{2} + 10 t\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (3 t^2 + 4 t + 3)$ |
undefined |
| 5.3.5.15a24.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + \left(15 x^{2} + 10 x + 15\right) ( x^{3} + 3 x + 3 ) + 5$ |
$5$ |
$3$ |
$5$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}, \frac{5}{4}]_{4}^{3}$ |
$[\frac{1}{4},\frac{1}{4},\frac{1}{4}]_{4}^{3}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}$ |
$1$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(20 t^{2} + 20 t\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (4 t^2 + 4 t + 4)$ |
undefined |
| 5.3.5.15a25.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + \left(15 x^{2} + 10 x + 5\right) ( x^{3} + 3 x + 3 ) + 5$ |
$5$ |
$3$ |
$5$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}, \frac{5}{4}]_{4}^{3}$ |
$[\frac{1}{4},\frac{1}{4},\frac{1}{4}]_{4}^{3}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}$ |
$1$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(20 t^{2} + 20 t + 15\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + 4 t$ |
undefined |
| 5.3.5.15a26.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + \left(15 x^{2} + 5 x + 20\right) ( x^{3} + 3 x + 3 ) + 5$ |
$5$ |
$3$ |
$5$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}, \frac{5}{4}]_{4}^{3}$ |
$[\frac{1}{4},\frac{1}{4},\frac{1}{4}]_{4}^{3}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}$ |
$1$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(20 t + 15\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (t^2 + 3 t + 2)$ |
undefined |
| 5.3.5.15a27.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + \left(15 x^{2} + 5 x + 15\right) ( x^{3} + 3 x + 3 ) + 5$ |
$5$ |
$3$ |
$5$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}, \frac{5}{4}]_{4}^{3}$ |
$[\frac{1}{4},\frac{1}{4},\frac{1}{4}]_{4}^{3}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}$ |
$1$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(20 t + 10\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (4 t^2 + 3 t)$ |
undefined |
| 5.3.5.15a28.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + \left(15 x^{2} + 5 x + 10\right) ( x^{3} + 3 x + 3 ) + 5$ |
$5$ |
$3$ |
$5$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}, \frac{5}{4}]_{4}^{3}$ |
$[\frac{1}{4},\frac{1}{4},\frac{1}{4}]_{4}^{3}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}$ |
$1$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(20 t + 5\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (2 t^2 + 3 t + 3)$ |
undefined |
| 5.3.5.15a29.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + \left(10 x^{2} + 15\right) ( x^{3} + 3 x + 3 ) + 5$ |
$5$ |
$3$ |
$5$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}, \frac{5}{4}]_{4}^{3}$ |
$[\frac{1}{4},\frac{1}{4},\frac{1}{4}]_{4}^{3}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}$ |
$1$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(15 t^{2} + 5 t\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (3 t^2 + 3 t + 1)$ |
undefined |
| 5.3.5.15a30.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + \left(10 x^{2} + 20 x + 10\right) ( x^{3} + 3 x + 3 ) + 5$ |
$5$ |
$3$ |
$5$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}, \frac{5}{4}]_{4}^{3}$ |
$[\frac{1}{4},\frac{1}{4},\frac{1}{4}]_{4}^{3}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}$ |
$1$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(5 t + 15\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (t^2 + 2 t)$ |
undefined |
| 5.3.5.15a31.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + \left(10 x^{2} + 15 x\right) ( x^{3} + 3 x + 3 ) + 5$ |
$5$ |
$3$ |
$5$ |
$15$ |
$(C_5^2 : C_4):C_3$ (as 15T19) |
$3$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}]_{4}^{3}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}^{3}$ |
$[\frac{5}{4}]_{4}$ |
$[\frac{1}{4}]_{4}$ |
$1$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(10 t^{2} + 5 t\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (2 t^2 + t + 2)$ |
undefined |
| 5.3.5.15a32.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + \left(10 x^{2} + 15 x + 10\right) ( x^{3} + 3 x + 3 ) + 5$ |
$5$ |
$3$ |
$5$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}, \frac{5}{4}]_{4}^{3}$ |
$[\frac{1}{4},\frac{1}{4},\frac{1}{4}]_{4}^{3}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}$ |
$1$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(5 t^{2} + 5 t\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (t^2 + t + 1)$ |
undefined |
| 5.3.5.15a33.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + \left(10 x^{2} + 10 x + 10\right) ( x^{3} + 3 x + 3 ) + 5$ |
$5$ |
$3$ |
$5$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}, \frac{5}{4}]_{4}^{3}$ |
$[\frac{1}{4},\frac{1}{4},\frac{1}{4}]_{4}^{3}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}$ |
$1$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(10 t^{2} + 10 t + 10\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (t^2 + 2)$ |
undefined |
| 5.3.5.15a34.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + \left(10 x^{2} + 10 x + 5\right) ( x^{3} + 3 x + 3 ) + 5$ |
$5$ |
$3$ |
$5$ |
$15$ |
$(C_5^2 : C_4):C_3$ (as 15T19) |
$3$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}]_{4}^{3}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}^{3}$ |
$[\frac{5}{4}]_{4}$ |
$[\frac{1}{4}]_{4}$ |
$1$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(10 t^{2} + 10 t + 5\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + 4 t^2$ |
undefined |
| 5.3.5.15a35.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + \left(10 x^{2} + 5 x + 20\right) ( x^{3} + 3 x + 3 ) + 5$ |
$5$ |
$3$ |
$5$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}, \frac{5}{4}]_{4}^{3}$ |
$[\frac{1}{4},\frac{1}{4},\frac{1}{4}]_{4}^{3}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}$ |
$1$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(10 t^{2} + 5 t + 20\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (4 t + 2)$ |
undefined |
| 5.3.5.15a36.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + \left(10 x^{2} + 5 x + 15\right) ( x^{3} + 3 x + 3 ) + 5$ |
$5$ |
$3$ |
$5$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}, \frac{5}{4}]_{4}^{3}$ |
$[\frac{1}{4},\frac{1}{4},\frac{1}{4}]_{4}^{3}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}$ |
$1$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(10 t^{2} + 15 t + 15\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (3 t^2 + 4 t)$ |
undefined |
| 5.3.5.15a37.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + \left(10 x^{2} + 5 x + 5\right) ( x^{3} + 3 x + 3 ) + 5$ |
$5$ |
$3$ |
$5$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}, \frac{5}{4}]_{4}^{3}$ |
$[\frac{1}{4},\frac{1}{4},\frac{1}{4}]_{4}^{3}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}$ |
$1$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(10 t^{2} + 5 t + 5\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (4 t^2 + 4 t + 1)$ |
undefined |
| 5.3.5.15a38.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + 5 x^{2} ( x^{3} + 3 x + 3 ) + 5$ |
$5$ |
$3$ |
$5$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}, \frac{5}{4}]_{4}^{3}$ |
$[\frac{1}{4},\frac{1}{4},\frac{1}{4}]_{4}^{3}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}$ |
$1$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(10 t + 15\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (t^2 + 4 t)$ |
undefined |
| 5.3.5.15a39.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + \left(5 x^{2} + 20\right) ( x^{3} + 3 x + 3 ) + 5$ |
$5$ |
$3$ |
$5$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}, \frac{5}{4}]_{4}^{3}$ |
$[\frac{1}{4},\frac{1}{4},\frac{1}{4}]_{4}^{3}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}$ |
$1$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(5 t^{2} + 20\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (4 t^2 + 4 t + 3)$ |
undefined |
| 5.3.5.15a40.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + \left(5 x^{2} + 5\right) ( x^{3} + 3 x + 3 ) + 5$ |
$5$ |
$3$ |
$5$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}, \frac{5}{4}]_{4}^{3}$ |
$[\frac{1}{4},\frac{1}{4},\frac{1}{4}]_{4}^{3}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}$ |
$1$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(20 t^{2} + 15 t + 10\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (3 t^2 + 4 t + 2)$ |
undefined |
| 5.3.5.15a41.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + \left(5 x^{2} + 20 x\right) ( x^{3} + 3 x + 3 ) + 5$ |
$5$ |
$3$ |
$5$ |
$15$ |
$(C_5^2 : C_4):C_3$ (as 15T19) |
$3$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}]_{4}^{3}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}^{3}$ |
$[\frac{5}{4}]_{4}$ |
$[\frac{1}{4}]_{4}$ |
$1$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(5 t^{2} + 15 t\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (t^2 + 3 t + 1)$ |
undefined |
| 5.3.5.15a42.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + \left(5 x^{2} + 15 x + 20\right) ( x^{3} + 3 x + 3 ) + 5$ |
$5$ |
$3$ |
$5$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}, \frac{5}{4}]_{4}^{3}$ |
$[\frac{1}{4},\frac{1}{4},\frac{1}{4}]_{4}^{3}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}$ |
$1$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(5 t^{2} + 15 t + 20\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (4 t^2 + 2 t)$ |
undefined |
| 5.3.5.15a43.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + \left(5 x^{2} + 10 x + 15\right) ( x^{3} + 3 x + 3 ) + 5$ |
$5$ |
$3$ |
$5$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}, \frac{5}{4}]_{4}^{3}$ |
$[\frac{1}{4},\frac{1}{4},\frac{1}{4}]_{4}^{3}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}$ |
$1$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(5 t^{2} + 10 t + 15\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (2 t^2 + t + 4)$ |
undefined |
| 5.3.5.15a44.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + \left(5 x^{2} + 10 x + 5\right) ( x^{3} + 3 x + 3 ) + 5$ |
$5$ |
$3$ |
$5$ |
$15$ |
$C_5^3:C_{12}$ (as 15T38) |
$3$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}, \frac{5}{4}]_{4}^{3}$ |
$[\frac{1}{4},\frac{1}{4},\frac{1}{4}]_{4}^{3}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}$ |
$1$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(20 t^{2} + 10\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (3 t^2 + t)$ |
undefined |
| 5.3.5.18a1.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + 10 ( x^{3} + 3 x + 3 )^{2} + 5$ |
$5$ |
$3$ |
$5$ |
$18$ |
$D_5\times C_3$ (as 15T3) |
$3$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{2}^{3}$ |
$[\frac{1}{2}]_{2}^{3}$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$3$ |
$t^{3} + 3 t + 3$ |
$x^{5} + 10 x^{2} + 5$ |
$[2, 0]$ |
$[1]$ |
$z^2 + (t^2 + 3 t + 4)$ |
undefined |
| 5.3.5.18a2.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + 20 ( x^{3} + 3 x + 3 )^{2} + 5$ |
$5$ |
$3$ |
$5$ |
$18$ |
$F_5\times C_3$ (as 15T8) |
$6$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{2}^{6}$ |
$[\frac{1}{2}]_{2}^{6}$ |
$[\ ]^{2}_{2}$ |
$[\ ]^{2}_{2}$ |
$3$ |
$t^{3} + 3 t + 3$ |
$x^{5} + 20 x^{2} + 5$ |
$[2, 0]$ |
$[2]$ |
$z^2 + (2 t^2 + t + 3)$ |
undefined |
| 5.3.5.18a3.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + 5 ( x^{3} + 3 x + 3 )^{2} + 5$ |
$5$ |
$3$ |
$5$ |
$18$ |
$F_5\times C_3$ (as 15T8) |
$6$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{2}^{6}$ |
$[\frac{1}{2}]_{2}^{6}$ |
$[\ ]^{2}_{2}$ |
$[\ ]^{2}_{2}$ |
$3$ |
$t^{3} + 3 t + 3$ |
$x^{5} + 5 x^{2} + 5$ |
$[2, 0]$ |
$[2]$ |
$z^2 + (3 t^2 + 4 t + 2)$ |
undefined |
| 5.3.5.18a4.1 |
$15$ |
$( x^{3} + 3 x + 3 )^{5} + 15 ( x^{3} + 3 x + 3 )^{2} + 5$ |
$5$ |
$3$ |
$5$ |
$18$ |
$D_5\times C_3$ (as 15T3) |
$3$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{2}^{3}$ |
$[\frac{1}{2}]_{2}^{3}$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$3$ |
$t^{3} + 3 t + 3$ |
$x^{5} + 15 x^{2} + 5$ |
$[2, 0]$ |
$[1]$ |
$z^2 + (4 t^2 + 2 t + 1)$ |
undefined |
