Polynomial Invariants | #Aut | Splitting Field | Number of | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
j | Ramification Polygon | Slopes | Residual Polynomials | fT | eT | #Gal | Gal | Polynomials | Extensions | |||
1 | {(1,1), (2,0), (18,0)} | [ 1, 0 ] | (z+1, z16+1) | {2} | 6 | 9 | { 3456 } | { 18T433 } | 2 | 9·2 | 9·2 | 9·2 |
3 | {(1,3), (2,0), (18,0)} | [ 3, 0 ] | (z+1, z16+1) | {2} | 6 | 9 | { 216, 13824 } | { 18T101, 18T98, 18T588 } | 22 | 9·22 | 9·22 | 9·22 |
5 | {(1,5), (2,0), (18,0)} | [ 5, 0 ] | (z+1, z16+1) | {2} | 6 | 9 | { 3456, 13824, ...} | { ..., 18T588, 18T433 } | 23 | 9·23 | 9·23 | 9·23 |
7 | {(1,7), (2,0), (18,0)} | [ 7, 0 ] | (z+1, z16+1) | {2} | 6 | 9 | { 3456, 13824 } | { 18T588, 18T433 } | 24 | 9·24 | 9·24 | 9·24 |
9 | {(1,9), (2,0), (18,0)} | [ 9, 0 ] | (z+1, z16+1) | {2} | 6 | 9 | { 108, 432, 6912, 27648 } | { 18T45, 18T147, 18T656, 18T512 } | 25 | 9·25 | 9·25 | 9·25 |
11 | {(1,11), (2,0), (18,0)} | [ 11, 0 ] | (z+1, z16+1) | {2} | 6 | 9 | { 3456, 13824, ...} | { ..., 18T588, 18T434, 18T433 } | 26 | 9·26 | 9·26 | 9·26 |
13 | {(1,13), (2,0), (18,0)} | [ 13, 0 ] | (z+1, z16+1) | {2} | 6 | 9 | { 3456, 6912, 13824, 27648, ...} | { 18T588, 18T512, 18T656, 18T434, 18T592, 18T433 } | 27 | 9·27 | 9·27 | 9·27 |
15 | {(1,15), (2,0), (18,0)} | [ 15, 0 ] | (z+1, z16+1) | {2} | 6 | 9 | { 13824, 27648, ...} | { 18T656, 18T588 } | 28 | 9·28 | 9·28 | 9·28 |
17 | {(1,17), (2,0), (18,0)} | [ 17, 0 ] | (z+1, z16+1) | {2} | 6 | 9 | { 3456, 6912, 13824, 27648, ...} | { 18T588, 18T656, 18T512, 18T434, 18T592, 18T433 } | 29 | 9·29 | 9·29 | 9·29 |
18 | {(1,18), (2,0), (18,0)} | [ 18, 0 ] | (z+1, z16+1) | {2} | 6 | 9 | { 6912, 27648, ...} | { 18T656, 18T512 } | 210 [.] | 9·210 | 9·210 | 9·210 |