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: | $2, 2, 3, 8$ |
| 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.
14.42-5.0.2-2-3-21.2.1
| (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) | |
| (1,15,8) (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) | |
| (1,13,18,2,14,19,3,8,20,4,9,21,5,10,15,6,11,16,7,12,17) (22,34,39,23,35,40,24,29,41,25,30,42,26,31,36,27,32,37,28,33,38) |
14.42-5.0.2-2-3-21.2.2
| (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) | |
| (1,41) (2,40) (3,39) (4,38) (5,37) (6,36) (7,42) (8,34) (9,33) (10,32) (11,31) (12,30) (13,29) (14,35) (15,27) (16,26) (17,25) (18,24) (19,23) (20,22) (21,28) | |
| (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) | |
| (1,17,12,7,16,11,6,15,10,5,21,9,4,20,8,3,19,14,2,18,13) (22,38,33,28,37,32,27,36,31,26,42,30,25,41,29,24,40,35,23,39,34) |