Family Information
| Genus: | $8$ |
| Quotient genus: | $0$ |
| Group name: | $D_{16}$ |
| Group identifier: | $[32,18]$ |
| Signature: | $[ 0; 2, 2, 2, 16 ]$ |
| Conjugacy classes for this refined passport: | $2, 3, 4, 9$ |
| Jacobian variety group algebra decomposition: | $A_{4}^{2}$ |
| Corresponding character(s): | $8$ |
Other Data
| Hyperelliptic curve(s): | yes |
| Hyperelliptic involution: | (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16) (17,18) (19,20) (21,22) (23,24) (25,26) (27,28) (29,30) (31,32) |
| Cyclic trigonal curve(s): | no |
| Equation(s) of curve(s) in this refined passport: |
| $y^2=x(x^{16}+a_{1}x^{8}+1)$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
8.32-18.0.2-2-2-16.2.1
| (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16) (17,18) (19,20) (21,22) (23,24) (25,26) (27,28) (29,30) (31,32) | |
| (1,9) (2,10) (3,12) (4,11) (5,15) (6,16) (7,13) (8,14) (17,25) (18,26) (19,28) (20,27) (21,31) (22,32) (23,29) (24,30) | |
| (1,20) (2,19) (3,18) (4,17) (5,21) (6,22) (7,24) (8,23) (9,32) (10,31) (11,30) (12,29) (13,28) (14,27) (15,26) (16,25) | |
| (1,28,8,30,3,25,5,32,2,27,7,29,4,26,6,31) (9,21,16,18,11,23,13,20,10,22,15,17,12,24,14,19) |