Family Information
| Genus: | $4$ |
| Quotient genus: | $0$ |
| Group name: | $\SD_{32}$ |
| Group identifier: | $[32,19]$ |
| Signature: | $[ 0; 2, 4, 16 ]$ |
| Conjugacy classes for this refined passport: | $3, 5, 9$ |
| Jacobian variety group algebra decomposition: | $A_{2}^{2}$ |
| 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: |
| $y^2=x(x^{8}-1)$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
4.32-19.0.2-4-16.2.1
| (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) | |
| (1,19,2,20) (3,17,4,18) (5,22,6,21) (7,23,8,24) (9,31,10,32) (11,29,12,30) (13,27,14,28) (15,25,16,26) | |
| (1,27,7,30,3,26,6,32,2,28,8,29,4,25,5,31) (9,22,15,18,11,24,14,20,10,21,16,17,12,23,13,19) |