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: | $2, 8, 9$ |
| 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.
5.30-2.0.2-6-15.3.1
| (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) | |
| (1,30,6,20,11,25) (2,29,7,19,12,24) (3,28,8,18,13,23) (4,27,9,17,14,22) (5,26,10,16,15,21) | |
| (1,7,13,4,10,11,2,8,14,5,6,12,3,9,15) (16,22,28,19,25,26,17,23,29,20,21,27,18,24,30) |