Family Information
| Genus: | $5$ |
| Quotient genus: | $0$ |
| Group name: | $C_6$ |
| Group identifier: | $[6,2]$ |
| Signature: | $[ 0; 2, 2, 2, 2, 3, 3 ]$ |
| Conjugacy classes for this refined passport: | $2, 2, 2, 2, 3, 4$ |
| Jacobian variety group algebra decomposition: | $E\times A_{4}$ |
Other Data
| Hyperelliptic curve(s): | yes |
| Hyperelliptic involution: | (1,4) (2,5) (3,6) |
| Cyclic trigonal curve(s): | no |
| Equation(s) of curve(s) in this refined passport: |
| $y^2=x^{12}+a_{1}x^{9}+a_{2}x^{6}+a_{3}x^{3}+1$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
5.6-2.0.2-2-2-2-3-3.1.1
| (1,4) (2,5) (3,6) | |
| (1,4) (2,5) (3,6) | |
| (1,4) (2,5) (3,6) | |
| (1,4) (2,5) (3,6) | |
| (1,2,3) (4,5,6) | |
| (1,3,2) (4,6,5) |