Family Information
| Genus: | $13$ |
| Quotient genus: | $0$ |
| Group name: | $C_7:C_4$ |
| Group identifier: | $[28,1]$ |
| Signature: | $[ 0; 2, 4, 4, 7 ]$ |
| Conjugacy classes for this refined passport: | $2, 4, 4, 5$ |
| Jacobian variety group algebra decomposition: | $E\times A_{12}$ |
| Corresponding character(s): | $3, 7$ |
Other Data
| Hyperelliptic curve(s): | yes |
| Hyperelliptic involution: | (1,8) (2,9) (3,10) (4,11) (5,12) (6,13) (7,14) (15,22) (16,23) (17,24) (18,25) (19,26) (20,27) (21,28) |
| Cyclic trigonal curve(s): | no |
| Equation(s) of curve(s) in this refined passport: |
| $y^2=(x^{14}-1)(x^{14}+a_{1}x^{7}+1)$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
13.28-1.0.2-4-4-7.4.1
| (1,8) (2,9) (3,10) (4,11) (5,12) (6,13) (7,14) (15,22) (16,23) (17,24) (18,25) (19,26) (20,27) (21,28) | |
| (1,22,8,15) (2,28,9,21) (3,27,10,20) (4,26,11,19) (5,25,12,18) (6,24,13,17) (7,23,14,16) | |
| (1,28,8,21) (2,27,9,20) (3,26,10,19) (4,25,11,18) (5,24,12,17) (6,23,13,16) (7,22,14,15) | |
| (1,2,3,4,5,6,7) (8,9,10,11,12,13,14) (15,16,17,18,19,20,21) (22,23,24,25,26,27,28) |