Family Information
| Genus: | $12$ |
| Quotient genus: | $0$ |
| Group name: | $D_{21}$ |
| Group identifier: | $[42,5]$ |
| Signature: | $[ 0; 2, 2, 3, 7 ]$ |
| Conjugacy classes for this refined passport: | $2, 2, 3, 6$ |
| Jacobian variety group algebra decomposition: | $A_{6}^{2}$ |
| Corresponding character(s): | $7$ |
Other Data
| Hyperelliptic curve(s): | no |
| Cyclic trigonal curve(s): | yes |
| Trigonal automorphism: | (1,8,15) (2,9,16) (3,10,17) (4,11,18) (5,12,19) (6,13,20) (7,14,21) (22,29,36) (23,30,37) (24,31,38) (25,32,39) (26,33,40) (27,34,41) (28,35,42) |
Generating vector(s)
Displaying 2 of 2 generating vectors for this refined passport.
12.42-5.0.2-2-3-7.3.1
| (1,22) (2,28) (3,27) (4,26) (5,25) (6,24) (7,23) (8,36) (9,42) (10,41) (11,40) (12,39) (13,38) (14,37) (15,29) (16,35) (17,34) (18,33) (19,32) (20,31) (21,30) | |
| (1,40) (2,39) (3,38) (4,37) (5,36) (6,42) (7,41) (8,33) (9,32) (10,31) (11,30) (12,29) (13,35) (14,34) (15,26) (16,25) (17,24) (18,23) (19,22) (20,28) (21,27) | |
| (1,8,15) (2,9,16) (3,10,17) (4,11,18) (5,12,19) (6,13,20) (7,14,21) (22,29,36) (23,30,37) (24,31,38) (25,32,39) (26,33,40) (27,34,41) (28,35,42) | |
| (1,4,7,3,6,2,5) (8,11,14,10,13,9,12) (15,18,21,17,20,16,19) (22,25,28,24,27,23,26) (29,32,35,31,34,30,33) (36,39,42,38,41,37,40) |
12.42-5.0.2-2-3-7.3.2
| (1,22) (2,28) (3,27) (4,26) (5,25) (6,24) (7,23) (8,36) (9,42) (10,41) (11,40) (12,39) (13,38) (14,37) (15,29) (16,35) (17,34) (18,33) (19,32) (20,31) (21,30) | |
| (1,39) (2,38) (3,37) (4,36) (5,42) (6,41) (7,40) (8,32) (9,31) (10,30) (11,29) (12,35) (13,34) (14,33) (15,25) (16,24) (17,23) (18,22) (19,28) (20,27) (21,26) | |
| (1,8,15) (2,9,16) (3,10,17) (4,11,18) (5,12,19) (6,13,20) (7,14,21) (22,29,36) (23,30,37) (24,31,38) (25,32,39) (26,33,40) (27,34,41) (28,35,42) | |
| (1,5,2,6,3,7,4) (8,12,9,13,10,14,11) (15,19,16,20,17,21,18) (22,26,23,27,24,28,25) (29,33,30,34,31,35,32) (36,40,37,41,38,42,39) |