Family Information
| Genus: | $3$ |
| Quotient genus: | $0$ |
| Group name: | $D_6$ |
| Group identifier: | $[12,4]$ |
| Signature: | $[ 0; 2, 2, 2, 6 ]$ |
| Conjugacy classes for this refined passport: | $2, 4, 4, 6$ |
| Jacobian variety group algebra decomposition: | $E\times E^{2}$ |
| Corresponding character(s): | $3, 6$ |
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: |
| $y^2=x(x^{6}+a_{1}x^{3}+1)$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
3.12-4.0.2-2-2-6.2.1
| (1,4) (2,5) (3,6) (7,10) (8,11) (9,12) | |
| (1,10) (2,12) (3,11) (4,7) (5,9) (6,8) | |
| (1,12) (2,11) (3,10) (4,9) (5,8) (6,7) | |
| (1,5,3,4,2,6) (7,11,9,10,8,12) |