Family Information
| Genus: | $14$ |
| Quotient genus: | $0$ |
| Group name: | $D_{21}$ |
| Group identifier: | $[42,5]$ |
| Signature: | $[ 0; 2, 2, 3, 21 ]$ |
| Conjugacy classes for this refined passport: | $2, 2, 3, 10$ |
| Jacobian variety group algebra decomposition: | $E^{2}\times A_{6}^{2}$ |
| Corresponding character(s): | $3, 7$ |
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.
14.42-5.0.2-2-3-21.4.1
| (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) | |
| (1,24) (2,23) (3,22) (4,28) (5,27) (6,26) (7,25) (8,38) (9,37) (10,36) (11,42) (12,41) (13,40) (14,39) (15,31) (16,30) (17,29) (18,35) (19,34) (20,33) (21,32) | |
| (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) | |
| (1,20,11,2,21,12,3,15,13,4,16,14,5,17,8,6,18,9,7,19,10) (22,41,32,23,42,33,24,36,34,25,37,35,26,38,29,27,39,30,28,40,31) |
14.42-5.0.2-2-3-21.4.2
| (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) | |
| (1,38) (2,37) (3,36) (4,42) (5,41) (6,40) (7,39) (8,31) (9,30) (10,29) (11,35) (12,34) (13,33) (14,32) (15,24) (16,23) (17,22) (18,28) (19,27) (20,26) (21,25) | |
| (1,15,8) (2,16,9) (3,17,10) (4,18,11) (5,19,12) (6,20,13) (7,21,14) (22,36,29) (23,37,30) (24,38,31) (25,39,32) (26,40,33) (27,41,34) (28,42,35) | |
| (1,20,11,2,21,12,3,15,13,4,16,14,5,17,8,6,18,9,7,19,10) (22,41,32,23,42,33,24,36,34,25,37,35,26,38,29,27,39,30,28,40,31) |