Family Information
| Genus: | $5$ |
| Quotient genus: | $0$ |
| Group name: | $C_3\times D_5$ |
| Group identifier: | $[30,2]$ |
| Signature: | $[ 0; 2, 6, 15 ]$ |
| Conjugacy classes for this refined passport: | $2, 7, 12$ |
| Jacobian variety group algebra decomposition: | $E\times A_{2}^{2}$ |
| Corresponding character(s): | $3, 9$ |
Other Data
| Hyperelliptic curve(s): | no |
| Cyclic trigonal curve(s): | yes |
| Trigonal automorphism: | (1,6,11) (2,7,12) (3,8,13) (4,9,14) (5,10,15) (16,21,26) (17,22,27) (18,23,28) (19,24,29) (20,25,30) |
| Equation(s) of curve(s) in this refined passport: |
| $y^3=(x^5-1)x^2$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
5.30-2.0.2-6-15.2.1
| (1,16) (2,20) (3,19) (4,18) (5,17) (6,21) (7,25) (8,24) (9,23) (10,22) (11,26) (12,30) (13,29) (14,28) (15,27) | |
| (1,25,11,20,6,30) (2,24,12,19,7,29) (3,23,13,18,8,28) (4,22,14,17,9,27) (5,21,15,16,10,26) | |
| (1,12,8,4,15,6,2,13,9,5,11,7,3,14,10) (16,27,23,19,30,21,17,28,24,20,26,22,18,29,25) |