Family Information
| Genus: | $4$ |
| Quotient genus: | $0$ |
| Group name: | $C_6\times S_3$ |
| Group identifier: | $[36,12]$ |
| Signature: | $[ 0; 2, 6, 6 ]$ |
| Conjugacy classes for this refined passport: | $4, 13, 16$ |
| Jacobian variety group algebra decomposition: | $E\times E\times E^{2}$ |
| Corresponding character(s): | $6, 7, 16$ |
Other Data
| Hyperelliptic curve(s): | no |
| Cyclic trigonal curve(s): | yes |
| Trigonal automorphism: | (1,4,7) (2,5,8) (3,6,9) (10,13,16) (11,14,17) (12,15,18) (19,22,25) (20,23,26) (21,24,27) (28,31,34) (29,32,35) (30,33,36) |
| Equation(s) of curve(s) in this refined passport: |
| $y^3 = (x^3-1)(x^3 + 1)$ |
Generating vector(s)
Displaying the unique generating vector for this refined passport.
4.36-12.0.2-6-6.3.1
| (1,28) (2,30) (3,29) (4,31) (5,33) (6,32) (7,34) (8,36) (9,35) (10,19) (11,21) (12,20) (13,22) (14,24) (15,23) (16,25) (17,27) (18,26) | |
| (1,14,9,10,5,18) (2,15,7,11,6,16) (3,13,8,12,4,17) (19,32,27,28,23,36) (20,33,25,29,24,34) (21,31,26,30,22,35) | |
| (1,26,4,20,7,23) (2,25,5,19,8,22) (3,27,6,21,9,24) (10,35,13,29,16,32) (11,34,14,28,17,31) (12,36,15,30,18,33) |