Family Information
| Genus: | $3$ |
| Quotient genus: | $0$ |
| Group name: | $C_4$ |
| Group identifier: | $[4,1]$ |
| Signature: | $[ 0; 2, 2, 2, 4, 4 ]$ |
| Conjugacy classes for this refined passport: | $2, 2, 2, 3, 3$ |
| Jacobian variety group algebra decomposition: | $A_{3}$ |
Other Data
| Hyperelliptic curve(s): | yes |
| Hyperelliptic involution: | (1,2) (3,4) |
| Cyclic trigonal curve(s): | no |
| Equation(s) of curve(s) in this refined passport: |
| $y^2=x(x^{6}+a_{1}x^{4}+a_{2}x^{2}+1)$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
3.4-1.0.2-2-2-4-4.1.1
| (1,2) (3,4) | |
| (1,2) (3,4) | |
| (1,2) (3,4) | |
| (1,3,2,4) | |
| (1,3,2,4) |