Family Information
| Genus: | $14$ |
| Quotient genus: | $0$ |
| Group name: | $C_7:C_4$ |
| Group identifier: | $[28,1]$ |
| Signature: | $[ 0; 2, 4, 4, 14 ]$ |
| Conjugacy classes for this refined passport: | $2, 3, 4, 8$ |
| Jacobian variety group algebra decomposition: | $A_{2}\times A_{12}$ |
| 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: |
| $y^2=x(x^{14}-1)(x^{14}+a_{1}x^{7}+1)$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
14.28-1.0.2-4-4-14.1.1
| (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) | |
| (1,15,8,22) (2,21,9,28) (3,20,10,27) (4,19,11,26) (5,18,12,25) (6,17,13,24) (7,16,14,23) | |
| (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) | |
| (1,9,3,11,5,13,7,8,2,10,4,12,6,14) (15,23,17,25,19,27,21,22,16,24,18,26,20,28) |