Family Information
| Genus: | $5$ |
| Quotient genus: | $0$ |
| Group name: | $D_6$ |
| Group identifier: | $[12,4]$ |
| Signature: | $[ 0; 2, 2, 2, 2, 3 ]$ |
| Conjugacy classes for this refined passport: | $2, 2, 3, 3, 5$ |
| Jacobian variety group algebra decomposition: | $E\times A_{2}^{2}$ |
| 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: |
| $y^2=(x^{6}+a_{1}x^{3}+1)(x^{6}+a_{2}x^{3}+1)$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
5.12-4.0.2-2-2-2-3.1.1
| (1,4) (2,5) (3,6) (7,10) (8,11) (9,12) | |
| (1,4) (2,5) (3,6) (7,10) (8,11) (9,12) | |
| (1,7) (2,9) (3,8) (4,10) (5,12) (6,11) | |
| (1,9) (2,8) (3,7) (4,12) (5,11) (6,10) | |
| (1,2,3) (4,5,6) (7,8,9) (10,11,12) |