Family Information
| Genus: | $10$ |
| Quotient genus: | $0$ |
| Group name: | $C_5:C_4$ |
| Group identifier: | $[20,1]$ |
| Signature: | $[ 0; 2, 4, 4, 10 ]$ |
| Conjugacy classes for this refined passport: | $2, 3, 4, 7$ |
| Jacobian variety group algebra decomposition: | $A_{2}\times A_{8}$ |
| Corresponding character(s): | $3, 5$ |
Other Data
| Hyperelliptic curve(s): | yes |
| Hyperelliptic involution: | (1,6) (2,7) (3,8) (4,9) (5,10) (11,16) (12,17) (13,18) (14,19) (15,20) |
| Cyclic trigonal curve(s): | no |
| Equation(s) of curve(s) in this refined passport: |
| $y^2=x(x^{10}-1)(x^{10}+a_{1}x^{5}+1)$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
10.20-1.0.2-4-4-10.1.1
| (1,6) (2,7) (3,8) (4,9) (5,10) (11,16) (12,17) (13,18) (14,19) (15,20) | |
| (1,11,6,16) (2,15,7,20) (3,14,8,19) (4,13,9,18) (5,12,10,17) | |
| (1,20,6,15) (2,19,7,14) (3,18,8,13) (4,17,9,12) (5,16,10,11) | |
| (1,7,3,9,5,6,2,8,4,10) (11,17,13,19,15,16,12,18,14,20) |