Family Information
| Genus: | $5$ |
| Quotient genus: | $0$ |
| Group name: | $D_{10}$ |
| Group identifier: | $[20,4]$ |
| Signature: | $[ 0; 2, 2, 2, 10 ]$ |
| Conjugacy classes for this refined passport: | $2, 3, 3, 8$ |
| Jacobian variety group algebra decomposition: | $E\times A_{2}^{2}$ |
| 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: |
| $y^2=x(x^{10}+a_{1}x^{5}+1)$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
5.20-4.0.2-2-2-10.2.1
| (1,6) (2,7) (3,8) (4,9) (5,10) (11,16) (12,17) (13,18) (14,19) (15,20) | |
| (1,11) (2,15) (3,14) (4,13) (5,12) (6,16) (7,20) (8,19) (9,18) (10,17) | |
| (1,13) (2,12) (3,11) (4,15) (5,14) (6,18) (7,17) (8,16) (9,20) (10,19) | |
| (1,9,2,10,3,6,4,7,5,8) (11,19,12,20,13,16,14,17,15,18) |