Family Information
| Genus: | $15$ |
| Quotient genus: | $0$ |
| Group name: | $C_{20}$ |
| Group identifier: | $[20,2]$ |
| Signature: | $[ 0; 2, 2, 2, 20, 20 ]$ |
| Conjugacy classes for this refined passport: | $2, 2, 2, 14, 15$ |
| Jacobian variety group algebra decomposition: | $A_{3}\times A_{12}$ |
Other Data
| Hyperelliptic curve(s): | yes |
| Hyperelliptic involution: | (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16) (17,18) (19,20) |
| Cyclic trigonal curve(s): | no |
| Equation(s) of curve(s) in this refined passport: |
| $y^2=x(x^{30}+a_{1}x^{20}+a_{2}x^{10}+1)$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
15.20-2.0.2-2-2-20-20.2.1
| (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16) (17,18) (19,20) | |
| (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16) (17,18) (19,20) | |
| (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16) (17,18) (19,20) | |
| (1,18,4,19,5,12,8,13,9,16,2,17,3,20,6,11,7,14,10,15) | |
| (1,16,10,13,7,12,6,19,3,18,2,15,9,14,8,11,5,20,4,17) |