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: | $2, 3, 4, 8$ |
| 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.
8.32-18.0.2-2-2-16.1.1
| (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) | |
| (1,18) (2,17) (3,19) (4,20) (5,24) (6,23) (7,22) (8,21) (9,30) (10,29) (11,31) (12,32) (13,26) (14,25) (15,27) (16,28) | |
| (1,25,7,31,3,27,6,30,2,26,8,32,4,28,5,29) (9,23,15,19,11,22,14,18,10,24,16,20,12,21,13,17) |