Family Information
| Genus: | $5$ |
| Quotient genus: | $0$ |
| Group name: | $C_2\times A_4$ |
| Group identifier: | $[24,13]$ |
| Signature: | $[ 0; 2, 2, 3, 3 ]$ |
| Conjugacy classes for this refined passport: | $2, 4, 5, 6$ |
| Jacobian variety group algebra decomposition: | $A_{2}\times E^{3}$ |
| Corresponding character(s): | $4, 8$ |
Other Data
| Hyperelliptic curve(s): | yes |
| Hyperelliptic involution: | (1,13) (2,14) (3,15) (4,16) (5,17) (6,18) (7,19) (8,20) (9,21) (10,22) (11,23) (12,24) |
| Cyclic trigonal curve(s): | no |
| Equation(s) of curve(s) in this refined passport: |
| $y^2=x^{12}-a_1x^{10}-33x^8+2a_1x^6-33x^4-a_1x^2+1$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
5.24-13.0.2-2-3-3.1.1
| (1,13) (2,14) (3,15) (4,16) (5,17) (6,18) (7,19) (8,20) (9,21) (10,22) (11,23) (12,24) | |
| (1,14) (2,13) (3,16) (4,15) (5,18) (6,17) (7,20) (8,19) (9,22) (10,21) (11,24) (12,23) | |
| (1,5,9) (2,8,11) (3,6,12) (4,7,10) (13,17,21) (14,20,23) (15,18,24) (16,19,22) | |
| (1,10,8) (2,12,5) (3,11,7) (4,9,6) (13,22,20) (14,24,17) (15,23,19) (16,21,18) |