Polynomial Invariants | #Aut | Splitting Field | Number of | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
j | Ramification Polygon | Slopes | Residual Polynomials | fT | eT | #Gal | Gal | Polynomials | Extensions | |||
1 | {(1,1), (2,0), (14,0)} | [ 1, 0 ] | (z+1, z12+1) | {2} | 3 | 7 | { 168, 336 } | { 14T18, 14T11 } | 2 | 7·2 | 7·2 | 7·2 |
3 | {(1,3), (2,0), (14,0)} | [ 3, 0 ] | (z+1, z12+1) | {2} | 3 | 7 | { 168, 336, 1344, 2688 } | { 14T35, 14T18, 14T11, 14T44 } | 22 | 7·22 | 7·22 | 7·22 |
5 | {(1,5), (2,0), (14,0)} | [ 5, 0 ] | (z+1, z12+1) | {2} | 3 | 7 | { 168, 336, 1344, 2688 } | { 14T35, 14T18, 14T11, 14T44 } | 23 | 7·23 | 7·23 | 7·23 |
7 | {(1,7), (2,0), (14,0)} | [ 7, 0 ] | (z+1, z12+1) | {2} | 3 | 7 | { 42, 336, 2688 } | { 14T5, 14T18, 14T44 } | 24 | 7·24 | 7·24 | 7·24 |
9 | {(1,9), (2,0), (14,0)} | [ 9, 0 ] | (z+1, z12+1) | {2} | 3 | 7 | { 168, 336, 1344, 2688 } | { 14T35, 14T18, 14T11, 14T44 } | 25 | 7·25 | 7·25 | 7·25 |
11 | {(1,11), (2,0), (14,0)} | [ 11, 0 ] | (z+1, z12+1) | {2} | 3 | 7 | { 168, 336, 1344, 2688 } | { 14T35, 14T18, 14T11, 14T44 } | 26 | 7·26 | 7·26 | 7·26 |
13 | {(1,13), (2,0), (14,0)} | [ 13, 0 ] | (z+1, z12+1) | {2} | 3 | 7 | { 168, 336, 1344, 2688 } | { 14T35, 14T18, 14T11, 14T44 } | 27 | 7·27 | 7·27 | 7·27 |
14 | {(1,14), (2,0), (14,0)} | [ 14, 0 ] | (z+1, z12+1) | {2} | 3 | 7 | { 42, 336, 2688 } | { 14T5, 14T18, 14T44 } | 28 [.] | 7·28 | 7·28 | 7·28 |