Family Information
| Genus: | $14$ |
| Quotient genus: | $0$ |
| Group name: | $C_2\times C_6$ |
| Group identifier: | $[12,5]$ |
| Signature: | $[ 0; 2, 2, 2, 2, 2, 6, 6 ]$ |
| Conjugacy classes for this refined passport: | $3, 3, 3, 3, 3, 7, 12$ |
| Jacobian variety group algebra decomposition: | $A_{2}\times A_{2}\times A_{5}\times A_{5}$ |
| Corresponding character(s): | $2, 4, 6, 8$ |
Other Data
| Hyperelliptic curve(s): | yes |
| Hyperelliptic involution: | (1,7) (2,8) (3,9) (4,10) (5,11) (6,12) |
| Cyclic trigonal curve(s): | no |
| Equation(s) of curve(s) in this refined passport: |
| $y^2=x^{30}+a_{1}x^{24}+a_{2}x^{18}+a_{3}x^{12}+a_{4}x^{6}+1$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
14.12-5.0.2-2-2-2-2-6-6.34.1
| (1,7) (2,8) (3,9) (4,10) (5,11) (6,12) | |
| (1,7) (2,8) (3,9) (4,10) (5,11) (6,12) | |
| (1,7) (2,8) (3,9) (4,10) (5,11) (6,12) | |
| (1,7) (2,8) (3,9) (4,10) (5,11) (6,12) | |
| (1,7) (2,8) (3,9) (4,10) (5,11) (6,12) | |
| (1,5,3,4,2,6) (7,11,9,10,8,12) | |
| (1,12,2,10,3,11) (4,9,5,7,6,8) |