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: | $2, 2, 3, 9$ |
| 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.
14.42-5.0.2-2-3-21.3.1
| (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) | |
| (1,26) (2,25) (3,24) (4,23) (5,22) (6,28) (7,27) (8,40) (9,39) (10,38) (11,37) (12,36) (13,42) (14,41) (15,33) (16,32) (17,31) (18,30) (19,29) (20,35) (21,34) | |
| (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) | |
| (1,18,14,3,20,9,5,15,11,7,17,13,2,19,8,4,21,10,6,16,12) (22,39,35,24,41,30,26,36,32,28,38,34,23,40,29,25,42,31,27,37,33) |
14.42-5.0.2-2-3-21.3.2
| (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) | |
| (1,40) (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) | |
| (1,15,8) (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) | |
| (1,18,14,3,20,9,5,15,11,7,17,13,2,19,8,4,21,10,6,16,12) (22,39,35,24,41,30,26,36,32,28,38,34,23,40,29,25,42,31,27,37,33) |