Family Information
| Genus: | $7$ |
| Quotient genus: | $0$ |
| Group name: | $C_2\times D_8$ |
| Group identifier: | $[32,39]$ |
| Signature: | $[ 0; 2, 2, 2, 8 ]$ |
| Conjugacy classes for this refined passport: | $3, 5, 7, 13$ |
| Jacobian variety group algebra decomposition: | $E\times E^{2}\times A_{2}^{2}$ |
| Corresponding character(s): | $2, 10, 13$ |
Other Data
| Hyperelliptic curve(s): | yes |
| Hyperelliptic involution: | (1,5) (2,6) (3,7) (4,8) (9,13) (10,14) (11,15) (12,16) (17,21) (18,22) (19,23) (20,24) (25,29) (26,30) (27,31) (28,32) |
| Cyclic trigonal curve(s): | no |
| Equation(s) of curve(s) in this refined passport: |
| $y^2=x^{16}+a_1x^{8}+1$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
7.32-39.0.2-2-2-8.1.1
| (1,5) (2,6) (3,7) (4,8) (9,13) (10,14) (11,15) (12,16) (17,21) (18,22) (19,23) (20,24) (25,29) (26,30) (27,31) (28,32) | |
| (1,9) (2,10) (3,12) (4,11) (5,13) (6,14) (7,16) (8,15) (17,25) (18,26) (19,28) (20,27) (21,29) (22,30) (23,32) (24,31) | |
| (1,17) (2,18) (3,20) (4,19) (5,21) (6,22) (7,24) (8,23) (9,27) (10,28) (11,25) (12,26) (13,31) (14,32) (15,29) (16,30) | |
| (1,29,4,32,2,30,3,31) (5,25,8,28,6,26,7,27) (9,24,12,22,10,23,11,21) (13,20,16,18,14,19,15,17) |