Family Information
| Genus: | $12$ |
| Quotient genus: | $0$ |
| Group name: | $D_{18}$ |
| Group identifier: | $[36,4]$ |
| Signature: | $[ 0; 2, 2, 3, 18 ]$ |
| Conjugacy classes for this refined passport: | $3, 4, 5, 11$ |
| Jacobian variety group algebra decomposition: | $A_{3}^{2}\times A_{3}^{2}$ |
| Corresponding character(s): | $7, 8$ |
Other Data
| Hyperelliptic curve(s): | no |
| Cyclic trigonal curve(s): | yes |
| Trigonal automorphism: | (1,2,3) (4,5,6) (7,8,9) (10,11,12) (13,14,15) (16,17,18) (19,20,21) (22,23,24) (25,26,27) (28,29,30) (31,32,33) (34,35,36) |
Generating vector(s)
Displaying 2 of 2 generating vectors for this refined passport.
12.36-4.0.2-2-3-18.2.1
| (1,19) (2,21) (3,20) (4,26) (5,25) (6,27) (7,23) (8,22) (9,24) (10,28) (11,30) (12,29) (13,35) (14,34) (15,36) (16,32) (17,31) (18,33) | |
| (1,34) (2,36) (3,35) (4,31) (5,33) (6,32) (7,28) (8,30) (9,29) (10,25) (11,27) (12,26) (13,22) (14,24) (15,23) (16,19) (17,21) (18,20) | |
| (1,3,2) (4,6,5) (7,9,8) (10,12,11) (13,15,14) (16,18,17) (19,21,20) (22,24,23) (25,27,26) (28,30,29) (31,33,32) (34,36,35) | |
| (1,15,8,12,5,16,2,13,9,10,6,17,3,14,7,11,4,18) (19,33,26,30,23,34,20,31,27,28,24,35,21,32,25,29,22,36) |
12.36-4.0.2-2-3-18.2.2
| (1,19) (2,21) (3,20) (4,26) (5,25) (6,27) (7,23) (8,22) (9,24) (10,28) (11,30) (12,29) (13,35) (14,34) (15,36) (16,32) (17,31) (18,33) | |
| (1,35) (2,34) (3,36) (4,32) (5,31) (6,33) (7,29) (8,28) (9,30) (10,26) (11,25) (12,27) (13,23) (14,22) (15,24) (16,20) (17,19) (18,21) | |
| (1,2,3) (4,5,6) (7,8,9) (10,11,12) (13,14,15) (16,17,18) (19,20,21) (22,23,24) (25,26,27) (28,29,30) (31,32,33) (34,35,36) | |
| (1,15,8,12,5,16,2,13,9,10,6,17,3,14,7,11,4,18) (19,33,26,30,23,34,20,31,27,28,24,35,21,32,25,29,22,36) |