Family Information
| Genus: | $12$ |
| Quotient genus: | $0$ |
| Group name: | $C_3:C_4$ |
| Group identifier: | $[12,1]$ |
| Signature: | $[ 0; 2, 2, 2, 4, 4, 6 ]$ |
| Conjugacy classes for this refined passport: | $2, 2, 2, 4, 5, 6$ |
| Jacobian variety group algebra decomposition: | $A_{4}\times A_{8}$ |
| Corresponding character(s): | $3, 5$ |
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: |
| $y^2=x(x^{6}-1)(x^{6}+a_{1}x^{3}+1)(x^{6}+a_{2}x^{3}+1)(x^{6}+a_{3}x^{3}+1)$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
12.12-1.0.2-2-2-4-4-6.1.1
| (1,4) (2,5) (3,6) (7,10) (8,11) (9,12) | |
| (1,4) (2,5) (3,6) (7,10) (8,11) (9,12) | |
| (1,4) (2,5) (3,6) (7,10) (8,11) (9,12) | |
| (1,7,4,10) (2,9,5,12) (3,8,6,11) | |
| (1,12,4,9) (2,11,5,8) (3,10,6,7) | |
| (1,5,3,4,2,6) (7,11,9,10,8,12) |