Polynomial Invariants | #Aut | Splitting Field | Number of | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
j | Ramification Polygon | Slopes | Residual Polynomials | eT | fT | #Gal | Gal | Polynomials | Extensions | |||
1 | {(1,1), (3,0), (21,0)} | [ 1/2, 0 ] | (z+1, z18+1) | {1} | 6 | 14 | { 28·37 } | { 21T92 } | 1 | 7·3 | 14·3 | 14·3 |
(z+2, z18+1) | {1} | 6 | 14 | { 28·37 } | { 21T92 } | 1 | 7·3 | |||||
2 | {(1,2), (3,0), (21,0)} | [ 1, 0 ] | (z2+1, z18+1) | {1} | 6 | 7 | { 14·37 } | { 21T78 } | 1 | 7·3 | 14·3 | 14·3 |
(z2+2, z18+1) | {3} | 6 | 7 | 3 | 7·3 | |||||||
4 | {(1,4), (3,0), (21,0)} | [ 2, 0 ] | (z2+1, z18+1) | {1} | 6 | 7 | 3 | 7·32 | 14·32 | 14·32 | ||
(z2+2, z18+1) | {3} | 6 | 7 | 32 | 7·32 | |||||||
5 | {(1,5), (3,0), (21,0)} | [ 5/2, 0 ] | (z+1, z18+1) | {1} | 6 | 14 | 3 | 7·32 | 14·32 | 14·32 | ||
(z+2, z18+1) | {1} | 6 | 14 | 3 | 7·32 | |||||||
7 | {(1,7), (3,0), (21,0)} | [ 7/2, 0 ] | (z+1, z18+1) | {1} | 6 | 14 | 32 | 7·33 | 14·33 | 14·33 | ||
(z+2, z18+1) | {1} | 6 | 14 | 32 | 7·33 | |||||||
8 | {(1,8), (3,0), (21,0)} | [ 4, 0 ] | (z2+1, z18+1) | {1} | 6 | 7 | 32 | 7·33 | 14·33 | 14·33 | ||
(z2+2, z18+1) | {3} | 6 | 7 | 33 | 7·33 | |||||||
10 | {(1,10), (3,0), (21,0)} | [ 5, 0 ] | (z2+1, z18+1) | {1} | 6 | 7 | 33 | 7·34 | 14·34 | 14·34 | ||
(z2+2, z18+1) | {3} | 6 | 7 | 34 | 7·34 | |||||||
11 | {(1,11), (3,0), (21,0)} | [ 11/2, 0 ] | (z+1, z18+1) | {1} | 6 | 14 | 33 | 7·34 | 14·34 | 14·34 | ||
(z+2, z18+1) | {1} | 6 | 14 | 33 | 7·34 | |||||||
13 | {(1,13), (3,0), (21,0)} | [ 13/2, 0 ] | (z+1, z18+1) | {1} | 6 | 14 | 34 | 7·35 | 14·35 | 14·35 | ||
(z+2, z18+1) | {1} | 6 | 14 | 34 | 7·35 | |||||||
14 | {(1,14), (3,0), (21,0)} | [ 7, 0 ] | (z2+1, z18+1) | {1} | 6 | 7 | 34 | 7·35 | 14·35 | 14·35 | ||
(z2+2, z18+1) | {3} | 6 | 7 | 35 | 7·35 | |||||||
16 | {(1,16), (3,0), (21,0)} | [ 8, 0 ] | (z2+1, z18+1) | {1} | 6 | 7 | 35 | 7·36 | 14·36 | 14·36 | ||
(z2+2, z18+1) | {3} | 6 | 7 | 36 | 7·36 | |||||||
17 | {(1,17), (3,0), (21,0)} | [ 17/2, 0 ] | (z+1, z18+1) | {1} | 6 | 14 | 35 | 7·36 | 14·36 | 14·36 | ||
(z+2, z18+1) | {1} | 6 | 14 | 35 | 7·36 | |||||||
19 | {(1,19), (3,0), (21,0)} | [ 19/2, 0 ] | (z+1, z18+1) | {1} | 6 | 14 | 36 | 7·37 | 14·37 | 14·37 | ||
(z+2, z18+1) | {1} | 6 | 14 | 36 | 7·37 | |||||||
20 | {(1,20), (3,0), (21,0)} | [ 10, 0 ] | (z2+1, z18+1) | {1} | 6 | 7 | 36 | 7·37 | 14·37 | 14·37 | ||
(z2+2, z18+1) | {3} | 6 | 7 | 37 | 7·37 | |||||||
21 | {(1,21), (3,0), (21,0)} | [ 21/2, 0 ] | (z+2, z18+1) | {1} | 6 | 14 | 37 | 7·38 | 7·38 | 7·38 |