Family Information
| Genus: | $8$ |
| Quotient genus: | $0$ |
| Group name: | $C_2\times C_6$ |
| Group identifier: | $[12,5]$ |
| Signature: | $[ 0; 2, 2, 2, 6, 6 ]$ |
| Conjugacy classes for this refined passport: | $2, 2, 2, 10, 11$ |
| Jacobian variety group algebra decomposition: | $E\times E\times A_{3}\times A_{3}$ |
| Corresponding character(s): | $2, 4, 6, 8$ |
Other Data
| Hyperelliptic curve(s): | yes |
| Hyperelliptic involution: | (1,4) (2,5) (3,6) (7,10) (8,11) (9,12) |
| Cyclic trigonal curve(s): | no |
| Equation(s) of curve(s) in this refined passport: |
| $y^2=x^{18}+a_{1}x^{12}+a_{2}x^{6}+1$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
8.12-5.0.2-2-2-6-6.2.1
| (1,4) (2,5) (3,6) (7,10) (8,11) (9,12) | |
| (1,4) (2,5) (3,6) (7,10) (8,11) (9,12) | |
| (1,4) (2,5) (3,6) (7,10) (8,11) (9,12) | |
| (1,9,2,7,3,8) (4,12,5,10,6,11) | |
| (1,11,3,10,2,12) (4,8,6,7,5,9) |