| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.4.4.1 |
$4$ |
$x^{4} + 6 x^{3} + 17 x^{2} + 24 x + 13$ |
$2$ |
$2$ |
$2$ |
$4$ |
$C_2^2$ (as 4T2) |
$2$ |
$1$ |
$[2]$ |
$[2]^{2}$ |
$t^{2} + t + 1$ |
$x^{2} + 2 x + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.4.6.1 |
$4$ |
$x^{4} + 2 x^{3} + 31 x^{2} + 30 x + 183$ |
$2$ |
$2$ |
$2$ |
$6$ |
$C_2^2$ (as 4T2) |
$2$ |
$1$ |
$[3]$ |
$[3]^{2}$ |
$t^{2} + t + 1$ |
$x^{2} + 14$ |
$[2, 0]$ |
$[1]$ |
| 2.4.6.2 |
$4$ |
$x^{4} + 4 x^{3} + 16 x^{2} + 24 x + 12$ |
$2$ |
$2$ |
$2$ |
$6$ |
$C_2^2$ (as 4T2) |
$2$ |
$1$ |
$[3]$ |
$[3]^{2}$ |
$t^{2} + t + 1$ |
$x^{2} + \left(4 t + 4\right) x + 4 t + 2$ |
$[2, 0]$ |
$[1]$ |
| 2.4.8.1 |
$4$ |
$x^{4} + 2 x^{2} + 4 x + 10$ |
$2$ |
$4$ |
$1$ |
$8$ |
$C_2^2$ (as 4T2) |
$1$ |
$1$ |
$[2, 3]$ |
$[2, 3]$ |
$t + 1$ |
$x^{4} + 2 x^{2} + 4 x + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.4.8.2 |
$4$ |
$x^{4} + 2 x^{2} + 4 x + 2$ |
$2$ |
$4$ |
$1$ |
$8$ |
$C_2^2$ (as 4T2) |
$1$ |
$1$ |
$[2, 3]$ |
$[2, 3]$ |
$t + 1$ |
$x^{4} + 2 x^{2} + 4 x + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.4.8.3 |
$4$ |
$x^{4} + 6 x^{2} + 4 x + 14$ |
$2$ |
$4$ |
$1$ |
$8$ |
$C_2^2$ (as 4T2) |
$1$ |
$1$ |
$[2, 3]$ |
$[2, 3]$ |
$t + 1$ |
$x^{4} + 6 x^{2} + 4 x + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.4.8.4 |
$4$ |
$x^{4} + 6 x^{2} + 4 x + 6$ |
$2$ |
$4$ |
$1$ |
$8$ |
$C_2^2$ (as 4T2) |
$1$ |
$1$ |
$[2, 3]$ |
$[2, 3]$ |
$t + 1$ |
$x^{4} + 6 x^{2} + 4 x + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 3.4.2.1 |
$4$ |
$x^{4} + 4 x^{3} + 14 x^{2} + 20 x + 13$ |
$3$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{2} + 3$ |
$[0]$ |
$[1]$ |
| 5.4.2.1 |
$4$ |
$x^{4} + 48 x^{3} + 670 x^{2} + 2256 x + 1449$ |
$5$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$t^{2} + 4 t + 2$ |
$x^{2} + 20 x + 5$ |
$[0]$ |
$[1]$ |
| 7.4.2.1 |
$4$ |
$x^{4} + 12 x^{3} + 56 x^{2} + 120 x + 268$ |
$7$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$t^{2} + 6 t + 3$ |
$x^{2} + 7$ |
$[0]$ |
$[1]$ |
| 11.4.2.1 |
$4$ |
$x^{4} + 14 x^{3} + 75 x^{2} + 182 x + 620$ |
$11$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$t^{2} + 7 t + 2$ |
$x^{2} + 11$ |
$[0]$ |
$[1]$ |
| 13.4.2.1 |
$4$ |
$x^{4} + 284 x^{3} + 21754 x^{2} + 225780 x + 59193$ |
$13$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$t^{2} + 12 t + 2$ |
$x^{2} + 130 x + 13$ |
$[0]$ |
$[1]$ |
| 17.4.2.1 |
$4$ |
$x^{4} + 338 x^{3} + 31049 x^{2} + 420472 x + 123735$ |
$17$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$t^{2} + 16 t + 3$ |
$x^{2} + 153 x + 17$ |
$[0]$ |
$[1]$ |
| 19.4.2.1 |
$4$ |
$x^{4} + 36 x^{3} + 366 x^{2} + 756 x + 6445$ |
$19$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$t^{2} + 18 t + 2$ |
$x^{2} + 19$ |
$[0]$ |
$[1]$ |
| 23.4.2.1 |
$4$ |
$x^{4} + 42 x^{3} + 497 x^{2} + 1176 x + 10467$ |
$23$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$t^{2} + 21 t + 5$ |
$x^{2} + 23$ |
$[0]$ |
$[1]$ |
| 29.4.2.1 |
$4$ |
$x^{4} + 1440 x^{3} + 535166 x^{2} + 12071520 x + 1504089$ |
$29$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$t^{2} + 24 t + 2$ |
$x^{2} + 696 x + 29$ |
$[0]$ |
$[1]$ |
| 31.4.2.1 |
$4$ |
$x^{4} + 58 x^{3} + 909 x^{2} + 1972 x + 26855$ |
$31$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$t^{2} + 29 t + 3$ |
$x^{2} + 31$ |
$[0]$ |
$[1]$ |
| 37.4.2.1 |
$4$ |
$x^{4} + 1916 x^{3} + 948367 x^{2} + 29317674 x + 2943243$ |
$37$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$t^{2} + 33 t + 2$ |
$x^{2} + 925 x + 37$ |
$[0]$ |
$[1]$ |
| 41.4.2.1 |
$4$ |
$x^{4} + 1962 x^{3} + 998289 x^{2} + 35245368 x + 7080121$ |
$41$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$t^{2} + 38 t + 6$ |
$x^{2} + 943 x + 41$ |
$[0]$ |
$[1]$ |
| 43.4.2.1 |
$4$ |
$x^{4} + 84 x^{3} + 1856 x^{2} + 3864 x + 77452$ |
$43$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$t^{2} + 42 t + 3$ |
$x^{2} + 43$ |
$[0]$ |
$[1]$ |
| 47.4.2.1 |
$4$ |
$x^{4} + 90 x^{3} + 2129 x^{2} + 4680 x + 96939$ |
$47$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$t^{2} + 45 t + 5$ |
$x^{2} + 47$ |
$[0]$ |
$[1]$ |
| 53.4.2.1 |
$4$ |
$x^{4} + 4974 x^{3} + 6304741 x^{2} + 297375564 x + 18587952$ |
$53$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$t^{2} + 49 t + 2$ |
$x^{2} + 2438 x + 53$ |
$[0]$ |
$[1]$ |
| 59.4.2.1 |
$4$ |
$x^{4} + 116 x^{3} + 3486 x^{2} + 7076 x + 201725$ |
$59$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$t^{2} + 58 t + 2$ |
$x^{2} + 59$ |
$[0]$ |
$[1]$ |
| 61.4.2.1 |
$4$ |
$x^{4} + 4878 x^{3} + 6091587 x^{2} + 348450174 x + 20534983$ |
$61$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$t^{2} + 60 t + 2$ |
$x^{2} + 2379 x + 61$ |
$[0]$ |
$[1]$ |
| 67.4.2.1 |
$4$ |
$x^{4} + 126 x^{3} + 4107 x^{2} + 8694 x + 270148$ |
$67$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$t^{2} + 63 t + 2$ |
$x^{2} + 67$ |
$[0]$ |
$[1]$ |
| 71.4.2.1 |
$4$ |
$x^{4} + 138 x^{3} + 4917 x^{2} + 10764 x + 342127$ |
$71$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$t^{2} + 69 t + 7$ |
$x^{2} + 71$ |
$[0]$ |
$[1]$ |
| 73.4.2.1 |
$4$ |
$x^{4} + 8024 x^{3} + 16372240 x^{2} + 1107697152 x + 99582464$ |
$73$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$t^{2} + 70 t + 5$ |
$x^{2} + 3942 x + 73$ |
$[0]$ |
$[1]$ |
| 79.4.2.1 |
$4$ |
$x^{4} + 156 x^{3} + 6248 x^{2} + 12792 x + 486412$ |
$79$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$t^{2} + 78 t + 3$ |
$x^{2} + 79$ |
$[0]$ |
$[1]$ |
| 83.4.2.1 |
$4$ |
$x^{4} + 164 x^{3} + 6894 x^{2} + 13940 x + 564653$ |
$83$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$t^{2} + 82 t + 2$ |
$x^{2} + 83$ |
$[0]$ |
$[1]$ |
| 89.4.2.1 |
$4$ |
$x^{4} + 12268 x^{3} + 38122404 x^{2} + 3045212032 x + 156142232$ |
$89$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$t^{2} + 82 t + 3$ |
$x^{2} + 6052 x + 89$ |
$[0]$ |
$[1]$ |
| 97.4.2.1 |
$4$ |
$x^{4} + 10474 x^{3} + 27919909 x^{2} + 2585716380 x + 183392493$ |
$97$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$t^{2} + 96 t + 5$ |
$x^{2} + 5141 x + 97$ |
$[0]$ |
$[1]$ |
| 101.4.2.1 |
$4$ |
$x^{4} + 16556 x^{3} + 69319047 x^{2} + 6570770114 x + 216554003$ |
$101$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$t^{2} + 97 t + 2$ |
$x^{2} + 8181 x + 101$ |
$[0]$ |
$[1]$ |
| 103.4.2.1 |
$4$ |
$x^{4} + 204 x^{3} + 10620 x^{2} + 22032 x + 1081216$ |
$103$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$t^{2} + 102 t + 5$ |
$x^{2} + 103$ |
$[0]$ |
$[1]$ |
| 107.4.2.1 |
$4$ |
$x^{4} + 206 x^{3} + 10827 x^{2} + 22454 x + 1146188$ |
$107$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$t^{2} + 103 t + 2$ |
$x^{2} + 107$ |
$[0]$ |
$[1]$ |
| 109.4.2.1 |
$4$ |
$x^{4} + 14604 x^{3} + 54096386 x^{2} + 5674982964 x + 401153281$ |
$109$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$t^{2} + 108 t + 6$ |
$x^{2} + 7194 x + 109$ |
$[0]$ |
$[1]$ |
| 113.4.2.1 |
$4$ |
$x^{4} + 18960 x^{3} + 90817911 x^{2} + 8982404280 x + 374946100$ |
$113$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$t^{2} + 101 t + 3$ |
$x^{2} + 9379 x + 113$ |
$[0]$ |
$[1]$ |
| 127.4.2.1 |
$4$ |
$x^{4} + 252 x^{3} + 16136 x^{2} + 32760 x + 2031628$ |
$127$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$t^{2} + 126 t + 3$ |
$x^{2} + 127$ |
$[0]$ |
$[1]$ |
| 131.4.2.1 |
$4$ |
$x^{4} + 254 x^{3} + 16395 x^{2} + 33782 x + 2129540$ |
$131$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$t^{2} + 127 t + 2$ |
$x^{2} + 131$ |
$[0]$ |
$[1]$ |
| 137.4.2.1 |
$4$ |
$x^{4} + 20538 x^{3} + 106780719 x^{2} + 13640908302 x + 496637065$ |
$137$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$t^{2} + 131 t + 3$ |
$x^{2} + 10138 x + 137$ |
$[0]$ |
$[1]$ |
| 139.4.2.1 |
$4$ |
$x^{4} + 276 x^{3} + 19326 x^{2} + 38916 x + 2665885$ |
$139$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$t^{2} + 138 t + 2$ |
$x^{2} + 139$ |
$[0]$ |
$[1]$ |
| 149.4.2.1 |
$4$ |
$x^{4} + 26514 x^{3} + 177649591 x^{2} + 25208742294 x + 634090662$ |
$149$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$t^{2} + 145 t + 2$ |
$x^{2} + 13112 x + 149$ |
$[0]$ |
$[1]$ |
| 151.4.2.1 |
$4$ |
$x^{4} + 298 x^{3} + 22515 x^{2} + 46786 x + 3373376$ |
$151$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$t^{2} + 149 t + 6$ |
$x^{2} + 151$ |
$[0]$ |
$[1]$ |
| 157.4.2.1 |
$4$ |
$x^{4} + 32018 x^{3} + 258698669 x^{2} + 38591103292 x + 1651335445$ |
$157$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$t^{2} + 152 t + 5$ |
$x^{2} + 15857 x + 157$ |
$[0]$ |
$[1]$ |
| 163.4.2.1 |
$4$ |
$x^{4} + 318 x^{3} + 25611 x^{2} + 52470 x + 4146724$ |
$163$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$t^{2} + 159 t + 2$ |
$x^{2} + 163$ |
$[0]$ |
$[1]$ |
| 167.4.2.1 |
$4$ |
$x^{4} + 332 x^{3} + 27900 x^{2} + 57104 x + 4628096$ |
$167$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$t^{2} + 166 t + 5$ |
$x^{2} + 167$ |
$[0]$ |
$[1]$ |
| 173.4.2.1 |
$4$ |
$x^{4} + 55698 x^{3} + 780245071 x^{2} + 130285141230 x + 2355971094$ |
$173$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$t^{2} + 169 t + 2$ |
$x^{2} + 27680 x + 173$ |
$[0]$ |
$[1]$ |
| 179.4.2.1 |
$4$ |
$x^{4} + 344 x^{3} + 29946 x^{2} + 62264 x + 5326865$ |
$179$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$t^{2} + 172 t + 2$ |
$x^{2} + 179$ |
$[0]$ |
$[1]$ |
| 181.4.2.1 |
$4$ |
$x^{4} + 52120 x^{3} + 683705257 x^{2} + 119397981420 x + 2183938221$ |
$181$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$t^{2} + 177 t + 2$ |
$x^{2} + 25883 x + 181$ |
$[0]$ |
$[1]$ |
| 191.4.2.1 |
$4$ |
$x^{4} + 380 x^{3} + 36520 x^{2} + 79800 x + 6924684$ |
$191$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$t^{2} + 190 t + 19$ |
$x^{2} + 191$ |
$[0]$ |
$[1]$ |
| 193.4.2.1 |
$4$ |
$x^{4} + 62916 x^{3} + 995609232 x^{2} + 188857096344 x + 6083572132$ |
$193$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$t^{2} + 192 t + 5$ |
$x^{2} + 31266 x + 193$ |
$[0]$ |
$[1]$ |
