Family Information
| Genus: | $14$ |
| Quotient genus: | $0$ |
| Group name: | $C_2\times C_{10}$ |
| Group identifier: | $[20,5]$ |
| Signature: | $[ 0; 2, 2, 2, 10, 10 ]$ |
| Conjugacy classes for this refined passport: | $2, 2, 2, 15, 18$ |
| Jacobian variety group algebra decomposition: | $E\times E\times A_{6}\times A_{6}$ |
| Corresponding character(s): | $3, 4, 7, 8$ |
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: |
| $y^2=x^{30}+a_{1}x^{20}+a_{2}x^{10}+1$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
14.20-5.0.2-2-2-10-10.3.1
| (1,6) (2,7) (3,8) (4,9) (5,10) (11,16) (12,17) (13,18) (14,19) (15,20) | |
| (1,6) (2,7) (3,8) (4,9) (5,10) (11,16) (12,17) (13,18) (14,19) (15,20) | |
| (1,6) (2,7) (3,8) (4,9) (5,10) (11,16) (12,17) (13,18) (14,19) (15,20) | |
| (1,13,5,12,4,11,3,15,2,14) (6,18,10,17,9,16,8,20,7,19) | |
| (1,19,2,20,3,16,4,17,5,18) (6,14,7,15,8,11,9,12,10,13) |